From 1b4d19090699a1f11d65af7da11d1f24d0601398 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sat, 16 Nov 2024 18:20:32 -0500 Subject: [PATCH 01/51] Start actually writing a post --- .../1-introduction.mdx | 215 ++ .../2-transforms.mdx | 7 + .../3-log-density.mdx | 9 + blog/2024-11-15-playing-with-fire/4-color.mdx | 7 + .../banner-dark.png | Bin 0 -> 570793 bytes .../banner-light.png | Bin 0 -> 571025 bytes .../2024-11-15-playing-with-fire/params.flame | 120 + blog/2024-11-15-playing-with-fire/params.ts | 95 + blog/2024-11-15-playing-with-fire/types.ts | 24 + blog/2024-11-15-playing-with-fire/utility.ts | 29 + .../2024-11-15-playing-with-fire/variation.ts | 40 + package-lock.json | 2231 +++++++++++++++++ package.json | 2 + src/DualImage/index.tsx | 13 + src/css/custom.css | 5 + src/isDarkMode.ts | 6 + 16 files changed, 2803 insertions(+) create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction.mdx create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms.mdx create mode 100644 blog/2024-11-15-playing-with-fire/3-log-density.mdx create mode 100644 blog/2024-11-15-playing-with-fire/4-color.mdx create mode 100644 blog/2024-11-15-playing-with-fire/banner-dark.png create mode 100644 blog/2024-11-15-playing-with-fire/banner-light.png create mode 100644 blog/2024-11-15-playing-with-fire/params.flame create mode 100644 blog/2024-11-15-playing-with-fire/params.ts create mode 100644 blog/2024-11-15-playing-with-fire/types.ts create mode 100644 blog/2024-11-15-playing-with-fire/utility.ts create mode 100644 blog/2024-11-15-playing-with-fire/variation.ts create mode 100644 src/DualImage/index.tsx create mode 100644 src/isDarkMode.ts diff --git a/blog/2024-11-15-playing-with-fire/1-introduction.mdx b/blog/2024-11-15-playing-with-fire/1-introduction.mdx new file mode 100644 index 0000000..d1a756b --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction.mdx @@ -0,0 +1,215 @@ +--- +slug: 2024/11/playing-with-fire +title: "Playing with fire: Introduction" +date: 2024-11-15 12:00:00 +authors: [bspeice] +tags: [] +--- + +Wikipedia [describes](https://en.wikipedia.org/wiki/Fractal_flame) fractal flames as: + +> a member of the iterated function system class of fractals + +I think of them a different way: beauty in mathematics. + +import isDarkMode from "@site/src/isDarkMode"; +import bannerDark from "./banner-dark.png" +import bannerLight from "./banner-light.png" + +
+ + + +
+ + + +I don't remember exactly when or how I originally came across fractal flames, but I do remember becoming entranced by the images they created. +I also remember their unique appeal to my young engineering mind; this was an art form I could actively participate in. + +The [paper](https://flam3.com/flame_draves.pdf) describing their mathematical structure was too much +for me to handle at the time (I was ~12 years old), and I was content to play around and enjoy the pictures. +But the desire to understand it stuck with me, so I wanted to try again. With a graduate degree in Financial Engineering under my belt, +maybe it would be easier this time. + +--- + +## Iterated function systems + +Let's begin by defining an "[iterated function system](https://en.wikipedia.org/wiki/Iterated_function_system)" (IFS). +We'll start at the end and work backwards to build a practical understanding. In mathematical notation, an IFS is: + +$$ +S = \bigcup_{i=0}^{n-1} F_i(S) \\[0.6cm] +S \in \mathbb{R}^2 \\ +F_i(S) \in \mathbb{R}^2 \rightarrow \mathbb{R}^2 +$$ + +### Stationary point + +First, $S$. We're generating images, so everything is in two dimensions: $S \in \mathbb{R}^2$. The set $S$ is +all points that are "in the system." To generate our final image, we just plot every point in the system +like a coordinate chart. + +For example, if we say $S = \{(0,0), (1, 1), (2, 2)\}$, there are three points to plot: + +import Plot from "react-plotly.js" + +
+ +
+ +For fractal flames, we just need to figure out which points are in $S$ and plot them. While there are +technically an infinite number of points, if we find _enough_ points and plot them, we end up with a nice picture. + +### Transformation functions + +Second, $F_i(S)$. At their most basic, each $F_i$ is a function that takes in a 2-dimensional point and transforms +it into a new 2-dimensional point: $F_i \in \mathbb{R}^2 \rightarrow \mathbb{R}^2$. It's worth discussing +these functions, but not critical, so **this section is optional**. + +In mathematical terms, each $F_i$ is a special kind of function called an [affine transformation](https://en.wikipedia.org/wiki/Affine_transformation). +We can think of them like mapping from one coordinate system to another. For example, we can define a coordinate system +where everything is shifted over: + +$$ +F_{shift}(x, y) = (x + 1, y) +$$ + +That is, for an input point $(x, y)$, the output point will be $(x + 1, y)$: + +
+ +
+ +This is a simple example designed to illustrate the principle. In general, $F_i$ functions have the form: + +$$ +F_i(x,y) = (a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) +$$ + +The parameters ($a_i$, $b_i$, etc.) are values we get to choose. In the example above, we can represent our shift +function using these parameters: + +$$ +a_i = 1 \hspace{0.5cm} b_i = 0 \hspace{0.5cm} c_i = 1 \\ +d_i = 0 \hspace{0.5cm} e_i = 1 \hspace{0.5cm} f_i = 0 \\ +$$ + +$$ +\begin{align*} +F_{shift}(x,y) &= (1 \cdot x + 0 \cdot y + 1, 0 \cdot x + 1 \cdot y + 0) \\ +F_{shift}(x,y) &= (x + 1, y) +\end{align*} +$$ + +Fractal flames use more complex functions to produce a wide variety of images, but all follow this same format. + +## Sierpinski's gasket + +Using these definitions, we can build the first image. The paper defines a function system we can use as-is: + +$$ +F_0(x, y) = \left({x \over 2}, {y \over 2} \right) +\hspace{0.8cm} +F_1(x, y) = \left({{x + 1} \over 2}, {y \over 2} \right) +\hspace{0.8cm} +F_2(x, y) = \left({x \over 2}, {{y + 1} \over 2} \right) +$$ + +### The chaos game + +Next, how do we find out all the points in $S$? The paper lays out an algorithm called the "chaos game": + +$$ +\begin{align*} +&(x, y) = \text{a random point in the bi-unit square} \\ +&\text{iterate } \{ \\ +&\hspace{1cm} i = \text{a random integer from 0 to } n - 1 \text{ inclusive} \\ +&\hspace{1cm} (x,y) = F_i(x,y) \\ +&\hspace{1cm} \text{plot}(x,y) \text{ except during the first 20 iterations} \\ +\} +\end{align*} +$$ \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms.mdx b/blog/2024-11-15-playing-with-fire/2-transforms.mdx new file mode 100644 index 0000000..ed2fdfa --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms.mdx @@ -0,0 +1,7 @@ +--- +slug: 2024/11/playing-with-fire-transforms +title: "Playing with fire: Transforms and variations" +date: 2024-11-15 13:00:00 +authors: [bspeice] +tags: [] +--- \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density.mdx b/blog/2024-11-15-playing-with-fire/3-log-density.mdx new file mode 100644 index 0000000..fe7ddfe --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/3-log-density.mdx @@ -0,0 +1,9 @@ +--- +slug: 2024/11/playing-with-fire-log-density +title: "Playing with fire: Log-density display" +date: 2024-11-15 14:00:00 +authors: [bspeice] +tags: [] +--- + +Testing \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/4-color.mdx b/blog/2024-11-15-playing-with-fire/4-color.mdx new file mode 100644 index 0000000..e9a54aa --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/4-color.mdx @@ -0,0 +1,7 @@ +--- +slug: 2024/11/playing-with-fire-color +title: "Playing with fire: Color" +date: 2024-11-15 15:00:00 +authors: [bspeice] +tags: [] +--- \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/banner-dark.png b/blog/2024-11-15-playing-with-fire/banner-dark.png new file mode 100644 index 0000000000000000000000000000000000000000..7ebc14cb890f1f246c426f1a3b462e53613c7710 GIT binary patch literal 570793 zcmeFZbx>SQw>~;pAh-qz1a}$S-5r8EK?WGy-CcqvxVw9B5AN;+cXyY|`+jo1Q}r~y}e`lsBbBt9!cl?wK$}c?l$VJa_;AfFva;sssQ)vA!RV!hLvuw}xfo zdH?8jSJ7}(GH@ZXwYM<=TY`uj-E2WbAXl&n0N}c0rKpVzMGW`6hsg&CNAjiLi}e7> z{W+&*aLE~60vcap-LoU(d|#4`s3}QJ)lo7&B?UGZ!-_E*@yj=%sN=Yhmr$8O3F(J+`4e){|K8*UMzq(mGMo*HmhYk$48aoI6S9 z5mpW_4ij6Vt8RUL+;Fz5S5qBUT?q9V!p_-N$uSnaLk6DSkhifVYAILI` z7zI^gf?F)AGhnP9G(p=u8RD%KfX;Hm^;Pz_gXf>_{<{{O@ym)QhifXX9}xV0t_cUh zVy!~FZQz5nyD-u+D(arS9-|MsG54`YHN!S(2*^)vCOwjcyJ4g~!r75K>?UF&uiuB^_vpvWn}$;Ewtc1*@y^COKeKAdHcMl8-(`H zBu&Ql@tp(JzVIrNQH0MZ-gk2&3i6Fo8=MmthRcMcf@aueGnP+J3-zBV1=n#Kr?g(B z36dVj+UBNmBm~dcZSDR{ZS$?$!{T^Ok&D>p0pxu6QCc%6IY54X+F2H(C)!u|g(!k4 z?(wY<$jE+^kf2JB)|T2fo3}aEr#mS4bbBwIw~_Jp%yR|5XPAbZEVq%36@!7XjUkA^ z)ynog^#A}~0asfCBMXotks-(wY|Te<*3v;j1UBX)QD>85l(Q89nSmwU?Lo@!@+wB| z7DimgBm(^Kysq5u09GJJ10q)|OKS&iS3Z)zak<}*{}Ka9i2hb_wBRGrkW(ZQv9Sjc zu`;kSFw%>;f}NR3_~D6o?Tt;il|;q=3Gsf$M`GsaXv+-*y12M7xUewT*qZ{GxVX50 zjLbl0X8LyxdIvXaM*~-SYX{Q5ApU_N3UV;A2irP=ZLEp@!Za|nadPA%A$cz+`d9m` zY~|$s4R7u6PZr+!0J<930+|>XfmT+)|Fm#$6mxzD`DcUvj}{Ip?;RDW1ah!(vNr;W zIfJYnN&geV*y!K(wodkzf4gIB1O!=vtlm`}-fLz0Z&gZ2$tnKZ;x7tJ!B)0^TfLM0 z-!vV;CjUj&e{0)cC4al~pAC68|2OV`)Bcz5e=EOh$;okx+88xqUSJTGBDs^H85ajG5!xIDQgEu18XDD zUr_Jh4B&Shu6J`rHe(KY11c4p9jKq%OQ-?P%d z@;_Vk7nJck6cfnEfZ2$RiJpyxi-Vq(gO#1$klE0Ho*Bey!p;d|W@9%n{2R*Hh+Evo z-pb%ToM0;hQxMSB+Vt;&zX<0RQk3E&VP;_bFNvb1fuqU00UwDh*xJeUzY0{qRv=|Z zgTL5h;$UIo;Nsw9WMN`wX6EAfFC{gQy~BGZ{)NfJ$iTw+cgbI2;eL1Komhjv^7I|x zZ~40~+#>cM14kQs6&o8%K9awhMD&;Czl-JGyOXhjqk*V_Bj_EJk(rg7iHVzuU4@B* zn~k0Ooqk3(ZpQ!6w=o8rxcz@=|J8Yjc>fV{NwC9v{ceAY{?Vh9L3aN*`^Tvz`0uVn zMD%y3;5IP&hYJn{&Y*w9`yJ~aMMh=@)~2BM(c_=#`Y$>7|Bwny90r_B#vEMqhFlyb z@9{Hcqvtf_Vxb4IvcKmBGbbmf@jv4CZ*&J66Gs;VdytUnJCE;Ny{G5jToFbt|C?115&dr^|090?m#+V%>wm<+|48|Nv+IB9`X4dyKT`hR z?E3$WF8KdiPJyi7XF)FSizRnv*4y`m)(1lw2~oh?U(c+z!XNLFkG7JU4gdfG#$PW8 zKuQ|UyAakBAC4lxRI(=6;6t}B1dA^p^yjK-^3MSnV+nM$TIDO{@`o!8 zHfx?XJI^oQk`j|`=2|Vhj#BsZPwK{2RmV%(j(9yXg~!vW|9t(N3rk>Y{Ch%Lsp-2_ z;yUK{lAAgw;_*7#ty~OG8D&y=g^}Tn;L!eW;-2>#5{gplY-3evO-hSfwbh=sFriA# zG)d6t?j9ZpsSR|d62XOVxg|9m$F1B?P2-+SH4j7Ot86^Zjgb9uQHwlOVbw7qn#Go6(d%5yE_wq_vyAQoLS zFk;wCJ1S43?4WEYZ-6Zb6uSzR5Qq5=jh^_d7~imR0T4QHJ3RI{vxONn&N298$_xVd z+Beq5D;1h}-5^Qz*ObId&t7(TI`+_hA60wXp=>F>5)siOp)Mjrz9ja`&2Ya&aqXUy zxmGNaM?g>=p$XR`3Lx&@HD<_DzVkYdFy2gA9rEMzumt%25pe%y{YHqq1CeqJ1$(>D zalh5VkEi)@c~00N*)5skkE4tNiV0ZD=Xw(R9$Q(lwGM9cPv(8m`J6?iQd694YW
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b/blog/2024-11-15-playing-with-fire/params.ts @@ -0,0 +1,95 @@ +/** + * Parameters taken from the reference .flame file, + * translated into something that's easier to work with. + */ + +import {Coefs, Transform} from "./types"; +import { julia, linear, pdj, popcorn } from "./variation"; + +export const identityCoefs: Coefs = { + a: 1, b: 0, c: 0, + d: 0, e: 1, f: 0, +} + +export const xform1Weight = 0.56453495; +export const xform1: Transform = { + coefs: { + a: -1.381068, b: -1.381068, c: 0, + d: 1.381068, e: -1.381068, f: 0, + }, + coefsPost: identityCoefs, + variations: [[1, julia]], + color: 0 +} + +const xform2Weight = 0.013135; +export const xform2: Transform = { + coefs: { + a: 0.031393, b: 0.031367, c: 0, + d: -0.031367, e: 0.031393, f: 0, + }, + coefsPost: { + a: 1, b: 0, c: 0.241352, + d: 0, e: 1, f: 0.271521, + }, + variations: [ + [1, linear], + [1, popcorn] + ], + color: 0.844 +} + +export const xform3Weight = 0.42233; +export const xform3: Transform = { + coefs: { + a: 1.51523, b: -3.048677, c: 0.724135, + d: 0.740356, e: -1.455964, f: -0.362059, + }, + coefsPost: identityCoefs, + variations: [[1, pdj(1.09358, 2.13048, 2.54127, 2.37267)]], + color: 0.349 +} + +export const xformFinal: Transform = { + coefs: { + a: 2, b: 0, c: 0, + d: 0, e: 2, f: 0 + }, + coefsPost: identityCoefs, + variations: [[1, julia]], + color: 0 +} + +export const palette = + "7E3037762C45722B496E2A4E6A2950672853652754632656" + + "5C265C5724595322574D2155482153462050451F4E441E4D" + + "431E4C3F1E473F1E453F1E433F1E3F3F1E3B3E1E393E1E37" + + "421D36431C38451C3A471B3B491B3C4A1A3C4B1A3D4D1A3E" + + "4F19405318435517445817465A16475D15495E154960154A" + + "65134E6812506B12526E1153711055720F55740F55770E57" + + "7A0E59810C58840B58880A588B09588F0858910756930755" + + "9A05539D0451A1034FA5024BA90147AA0046AC0045B00242" + + "B4043DBB0634BE082EC20A29C30B27C50C26C90F1DCC1116" + + "D32110D6280EDA300CDC380ADF4109E04508E24A08E45106" + + "E75704EA6402EC6B01EE7300EE7600EF7A00F07E00F18300" + + "F29000F29300F39600F39900F39C00F3A000F3A100F3A201" + + "F2A502F1A805F0A906EFAA08EEA909EEA80AEDA60CEBA50F" + + "E5A313E1A113DD9F13DB9E13D99D14D49C15D09815CC9518" + + "C79318BE8B1ABB891BB9871DB4811FB07D1FAB7621A67123" + + "9C6227975C289256299053298E502A89482C853F2D803A2E" + + "7E3037762C45742B47722B496E2A4E6A2951672853632656" + + "5C265C5724595322575022564E2255482153452050451F4E" + + "431E4C3F1E473E1D463D1D453F1E43411E413F1E3B3E1E37" + + "421D36421D38431D3B451C3A471B3A491B3C4B1A3D4D1A3E" + + "4F19405318435418445518455817465A16475D154960154A" + + "65134E66124F6812506B12526E1153711055740F55770E57" + + "7A0E597E0D57810C58840B58880A588B09588F0858930755" + + "9A05539C04529E0452A1034FA5024BA90147AC0045B00242" + + "B4043DB7053ABB0634BE0831C20A29C50C26C90F1DCC1116" + + "D01711D32110D72A0EDA300CDD390ADF4109E24A08E45106" + + "E75704E95F03EA6402EC6C01EE7300EF7A00F07E00F18300" + + "F28900F29000F39300F39600F39C00F3A000F3A100F3A201" + + "F2A502F2A503F1A805F0A807EFAA08EEA80AEDA60CEBA50F" + + "E9A411E5A313E1A113DD9F13D99D14D49C15D09815CC9518" + + "C79318C38F1ABE8B1AB9871DB4811FB07D1FAB7621A67123" + + "A16A249C6227975E289256298E502A89482C853F2D803A2E" diff --git a/blog/2024-11-15-playing-with-fire/types.ts b/blog/2024-11-15-playing-with-fire/types.ts new file mode 100644 index 0000000..7d43ec5 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/types.ts @@ -0,0 +1,24 @@ +/** + * Affine transformation coefficients + */ +export type Coefs = { + a: number; + b: number; + c: number; + d: number; + e: number; + f: number; +}; + +export type Variation = ( + x: number, + y: number, + coefs: Coefs +) => [number, number]; + +export type Transform = { + coefs: Coefs, + coefsPost: Coefs, + variations: [number, Variation][], + color: number +} diff --git a/blog/2024-11-15-playing-with-fire/utility.ts b/blog/2024-11-15-playing-with-fire/utility.ts new file mode 100644 index 0000000..13c0039 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/utility.ts @@ -0,0 +1,29 @@ +/** + * Generate a uniform random number in the range (-1, 1) + * + * @returns + */ +export function randomBiUnit() { + return Math.random() * 2 - 1; +} + +/** + * Generate a uniform random integer in the range [min, max) + * + * @param min + * @param max + * @returns + */ +export function randomInteger(min: number, max: number) { + return Math.floor(Math.random() * (max - min)) + min; +} + +// https://stackoverflow.com/a/34356351 +export function hexToBytes(hex: string) { + var bytes = []; + for (var i = 0; i < hex.length; i += 2) { + bytes.push(parseInt(hex.substring(i, i + 2), 16)); + } + + return bytes; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/variation.ts b/blog/2024-11-15-playing-with-fire/variation.ts new file mode 100644 index 0000000..ddf9ce6 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/variation.ts @@ -0,0 +1,40 @@ +import { Variation } from "./types"; + +export const linear: Variation = (x, y) => [x, y]; + +function r(x: number, y: number) { + return Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2)); +} + +function theta(x: number, y: number) { + return Math.atan2(x, y); +} + +function omega(): number { + return Math.random() > 0.5 ? Math.PI : 0; +} + +export const julia: Variation = (x, y) => { + const sqrtR = Math.sqrt(r(x, y)); + const thetaVal = theta(x, y) / 2 + omega(); + return [sqrtR * Math.cos(thetaVal), sqrtR * Math.sin(thetaVal)]; +}; + +export const popcorn: Variation = (x, y, transformCoefs) => { + return [ + x + transformCoefs.c * Math.sin(Math.tan(3 * y)), + y + transformCoefs.f * Math.sin(Math.tan(3 * x)), + ]; +}; + +export const pdj: ( + pdjA: number, + pdjB: number, + pdjC: number, + pdjD: number +) => Variation = (pdjA, pdjB, pdjC, pdjD) => { + return (x, y) => [ + Math.sin(pdjA * y) - Math.cos(pdjB * x), + Math.sin(pdjC * x) - Math.cos(pdjD * y), + ]; +}; diff --git a/package-lock.json b/package-lock.json index d5e957b..b581d29 100644 --- a/package-lock.json +++ b/package-lock.json @@ -14,9 +14,11 @@ "@mdx-js/react": "^3.0.0", "clsx": "^2.0.0", "docusaurus-lunr-search": "^3.5.0", + "plotly.js": "^2.35.2", "prism-react-renderer": "^2.3.0", "react": "^18.0.0", "react-dom": "^18.0.0", + "react-plotly.js": "^2.6.0", "rehype-katex": "^7.0.1", "remark-math": "^6.0.0" }, @@ -1988,6 +1990,22 @@ "node": ">=6.9.0" } }, + "node_modules/@choojs/findup": { + "version": "0.2.1", + "resolved": "https://registry.npmjs.org/@choojs/findup/-/findup-0.2.1.tgz", + "integrity": "sha512-YstAqNb0MCN8PjdLCDfRsBcGVRN41f3vgLvaI0IrIcBp4AqILRSS0DeWNGkicC+f/zRIPJLc+9RURVSepwvfBw==", + "dependencies": { + "commander": "^2.15.1" + }, + "bin": { + "findup": "bin/findup.js" + } + }, + "node_modules/@choojs/findup/node_modules/commander": { + "version": "2.20.3", + "resolved": "https://registry.npmjs.org/commander/-/commander-2.20.3.tgz", + "integrity": "sha512-GpVkmM8vF2vQUkj2LvZmD35JxeJOLCwJ9cUkugyk2nuhbv3+mJvpLYYt+0+USMxE+oj+ey/lJEnhZw75x/OMcQ==" + }, "node_modules/@colors/colors": { "version": "1.5.0", "resolved": "https://registry.npmjs.org/@colors/colors/-/colors-1.5.0.tgz", @@ -2868,6 +2886,99 @@ "resolved": "https://registry.npmjs.org/@leichtgewicht/ip-codec/-/ip-codec-2.0.5.tgz", 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"version": "1.0.3", + "resolved": "https://registry.npmjs.org/world-calendars/-/world-calendars-1.0.3.tgz", + "integrity": "sha512-sAjLZkBnsbHkHWVhrsCU5Sa/EVuf9QqgvrN8zyJ2L/F9FR9Oc6CvVK0674+PGAtmmmYQMH98tCUSO4QLQv3/TQ==", + "dependencies": { + "object-assign": "^4.1.0" + } + }, "node_modules/wrap-ansi": { "version": "8.1.0", "resolved": "https://registry.npmjs.org/wrap-ansi/-/wrap-ansi-8.1.0.tgz", diff --git a/package.json b/package.json index a833e14..b99f70e 100644 --- a/package.json +++ b/package.json @@ -21,9 +21,11 @@ "@mdx-js/react": "^3.0.0", "clsx": "^2.0.0", "docusaurus-lunr-search": "^3.5.0", + "plotly.js": "^2.35.2", "prism-react-renderer": "^2.3.0", "react": "^18.0.0", "react-dom": "^18.0.0", + "react-plotly.js": "^2.6.0", "rehype-katex": "^7.0.1", "remark-math": "^6.0.0" }, diff --git a/src/DualImage/index.tsx b/src/DualImage/index.tsx new file mode 100644 index 0000000..2e94211 --- /dev/null +++ b/src/DualImage/index.tsx @@ -0,0 +1,13 @@ +import {useColorMode} from "@docusaurus/theme-common"; +import React from "react"; + +interface Props { + srcLight: string; + srcDark: string; + alt: string; +} +const DualImage = ({srcLight, srcDark, alt}: Props) => { + const {colorMode} = useColorMode(); + return {alt} +} +export default DualImage; \ No newline at end of file diff --git a/src/css/custom.css b/src/css/custom.css index bd7bd02..56086c9 100644 --- a/src/css/custom.css +++ b/src/css/custom.css @@ -21,4 +21,9 @@ [data-theme='dark'] .header-github-link::before { background: url("data:image/svg+xml,%3Csvg viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'%3E%3Cpath fill='white' d='M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12'/%3E%3C/svg%3E") no-repeat; +} + +/* Dark mode for Plotly, copied from https://github.com/plotly/plotly.js/issues/2006#issuecomment-2081535168 */ +[data-theme='dark'] .plot-container { + filter: invert(75%) hue-rotate(180deg); } \ No newline at end of file diff --git a/src/isDarkMode.ts b/src/isDarkMode.ts new file mode 100644 index 0000000..d1df51a --- /dev/null +++ b/src/isDarkMode.ts @@ -0,0 +1,6 @@ +import {useColorMode} from "@docusaurus/theme-common"; + +export default function isDarkMode() { + const {colorMode} = useColorMode(); + return colorMode === "dark"; +} \ No newline at end of file From 3a41d5c81ad4c9e22a4675f7250db935d5525835 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 17 Nov 2024 17:30:07 -0500 Subject: [PATCH 02/51] Render the gasket Need to get rid of Plotly, unfortuantely - causes issues with hydration. Seems like Victory is better able to handle what I need. --- .../{ => 1-introduction}/1-introduction.mdx | 41 +- .../1-introduction/Gasket.jsx | 43 + .../1-introduction/biunit.ts | 3 + .../1-introduction/plot.ts | 32 + .../1-introduction/randint.ts | 3 + .../1-introduction/scope.ts | 14 + blog/2024-11-15-playing-with-fire/utility.ts | 29 - docusaurus.config.ts | 3 +- package-lock.json | 2008 +++++++++++++---- package.json | 11 +- 10 files changed, 1737 insertions(+), 450 deletions(-) rename blog/2024-11-15-playing-with-fire/{ => 1-introduction}/1-introduction.mdx (83%) create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/plot.ts create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/randint.ts create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/scope.ts delete mode 100644 blog/2024-11-15-playing-with-fire/utility.ts diff --git a/blog/2024-11-15-playing-with-fire/1-introduction.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/1-introduction.mdx similarity index 83% rename from blog/2024-11-15-playing-with-fire/1-introduction.mdx rename to blog/2024-11-15-playing-with-fire/1-introduction/1-introduction.mdx index d1a756b..8331205 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/1-introduction.mdx @@ -1,6 +1,6 @@ --- slug: 2024/11/playing-with-fire -title: "Playing with fire: Introduction" +title: "Playing with fire: The fractal flame algorithm" date: 2024-11-15 12:00:00 authors: [bspeice] tags: [] @@ -12,9 +12,9 @@ Wikipedia [describes](https://en.wikipedia.org/wiki/Fractal_flame) fractal flame I think of them a different way: beauty in mathematics. -import isDarkMode from "@site/src/isDarkMode"; -import bannerDark from "./banner-dark.png" -import bannerLight from "./banner-light.png" +import isDarkMode from '@site/src/isDarkMode' +import bannerDark from '../banner-dark.png' +import bannerLight from '../banner-light.png'

    @@ -201,6 +201,8 @@ $$ ### The chaos game +import CodeBlock from '@theme/CodeBlock' + Next, how do we find out all the points in $S$? The paper lays out an algorithm called the "chaos game": $$ @@ -212,4 +214,33 @@ $$ &\hspace{1cm} \text{plot}(x,y) \text{ except during the first 20 iterations} \\ \} \end{align*} -$$ \ No newline at end of file +$$ + +Let's turn this into code, one piece at a time. + +First, the "bi-unit square" is the range $[-1, 1]$. We can pick a random point like this: + +import biunitSource from '!!raw-loader!./biunit' + +{biunitSource} + +Next, we need to choose a random integer from $0$ to $n - 1$: + +import randintSource from '!!raw-loader!./randint' + +{randintSource} + +Finally, implementing the `plot` function. Web browsers have a [Canvas API](https://developer.mozilla.org/en-US/docs/Web/API/Canvas_API) +we can use for 2D graphics. In our case, the plot function will take an $(x,y)$ coordinate and plot it by +coloring the corresponding pixel in an [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData): + +import plotSource from '!!raw-loader!./plot' + +{plotSource} + +import Playground from '@theme/Playground' +import Scope from './scope' + +import Gasket from '!!raw-loader!./Gasket' + +{Gasket} diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx new file mode 100644 index 0000000..59f25f0 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx @@ -0,0 +1,43 @@ +function Gasket(props) { + const iterations = 1000; + const functions = [ + (x, y) => [x / 2, y / 2], + (x, y) => [(x + 1) / 2, y / 2], + (x, y) => [x / 2, (y + 1) / 2] + ] + + function chaosGame(image) { + var [x, y] = [randomBiUnit(), randomBiUnit()]; + + for (var i = 0; i < iterations; i++) { + const f = functions[randomInteger(0, functions.length)]; + [x, y] = f(x, y); + + if (i > 20) { + plot(x, y, image); + } + } + } + + function onClickRender() { + /** @type{HTMLCanvasElement} */ + const canvas = document.getElementById('canvas-gasket'); + const context = canvas.getContext('2d'); + const image = context.createImageData(canvas.width, canvas.height); + chaosGame(image); + context.putImageData(image, 0, 0); + } + + return
    +
    + +
    +
    +
    + +
    +
    +} diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts b/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts new file mode 100644 index 0000000..c8e17c6 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts @@ -0,0 +1,3 @@ +export default function randomBiUnit(): number { + return Math.random() * 2 - 1; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts new file mode 100644 index 0000000..3bf9f03 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts @@ -0,0 +1,32 @@ +export default function plot(x: number, y: number, image: ImageData) { + // Translate (x,y) coordinates to pixel coordinates. + // The display range we care about is x=[0, 1], y=[0, 1], + // so our pixelX and pixelY coordinates are easy to calculate: + const pixelX = Math.floor(x * image.width); + const pixelY = Math.floor(y * image.height); + + // If we have an (x,y) coordinate outside the display range, + // skip it + if ( + pixelX < 0 || + pixelX > image.width || + pixelY < 0 || + pixelY > image.height + ) { + return; + } + + // ImageData is an array that contains four bytes per pixel + // (one for each of the red, green, blue, and alpha values). + // The (pixelX, pixelY) coordinates are used to find where + // in the image we need to write. + const index = pixelY * (image.width * 4) + pixelX * 4; + + // Set the pixel to black by writing a 0 to the first three + // bytes (red, green, blue), and 256 to the last byte (alpha), + // starting at our index: + image.data[index] = 0; + image.data[index + 1] = 0; + image.data[index + 2] = 0; + image.data[index + 3] = 0xff; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts b/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts new file mode 100644 index 0000000..0e922ba --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts @@ -0,0 +1,3 @@ +export default function randomInteger(min: number, max: number): number { + return Math.floor(Math.random() * (max - min)) + min; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts b/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts new file mode 100644 index 0000000..2d4c411 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts @@ -0,0 +1,14 @@ +import React from 'react'; + +import randomBiUnit from './biunit'; +import plot from './plot'; +import randomInteger from './randint'; + + +const Scope = { + React, + plot, + randomBiUnit, + randomInteger +} +export default Scope; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/utility.ts b/blog/2024-11-15-playing-with-fire/utility.ts deleted file mode 100644 index 13c0039..0000000 --- a/blog/2024-11-15-playing-with-fire/utility.ts +++ /dev/null @@ -1,29 +0,0 @@ -/** - * Generate a uniform random number in the range (-1, 1) - * - * @returns - */ -export function randomBiUnit() { - return Math.random() * 2 - 1; -} - -/** - * Generate a uniform random integer in the range [min, max) - * - * @param min - * @param max - * @returns - */ -export function randomInteger(min: number, max: number) { - return Math.floor(Math.random() * (max - min)) + min; -} - -// https://stackoverflow.com/a/34356351 -export function hexToBytes(hex: string) { - var bytes = []; - for (var i = 0; i < hex.length; i += 2) { - bytes.push(parseInt(hex.substring(i, i + 2), 16)); - } - - return bytes; -} \ No newline at end of file diff --git a/docusaurus.config.ts b/docusaurus.config.ts index 9667860..e2ee794 100644 --- a/docusaurus.config.ts +++ b/docusaurus.config.ts @@ -28,13 +28,14 @@ const config: Config = { locales: ['en'], }, + themes: ['@docusaurus/theme-live-codeblock'], presets: [ [ 'classic', { docs: false, blog: { - routeBasePath: "/", + routeBasePath: '/', blogSidebarTitle: 'All posts', blogSidebarCount: 'ALL', showReadingTime: true, diff --git a/package-lock.json b/package-lock.json index b581d29..4878ca7 100644 --- a/package-lock.json +++ b/package-lock.json @@ -8,19 +8,22 @@ "name": "speice-io", "version": "0.0.0", "dependencies": { - "@docusaurus/core": "^3.6.0", - "@docusaurus/faster": "^3.5.2", - "@docusaurus/preset-classic": "^3.6.0", + "@docusaurus/core": "^3.6.1", + "@docusaurus/faster": "^3.6.1", + "@docusaurus/preset-classic": "^3.6.1", + "@docusaurus/theme-live-codeblock": "^3.6.1", "@mdx-js/react": "^3.0.0", "clsx": "^2.0.0", "docusaurus-lunr-search": "^3.5.0", "plotly.js": "^2.35.2", "prism-react-renderer": "^2.3.0", + "raw-loader": "^4.0.2", "react": "^18.0.0", "react-dom": "^18.0.0", "react-plotly.js": "^2.6.0", "rehype-katex": "^7.0.1", - "remark-math": "^6.0.0" + "remark-math": "^6.0.0", + "victory": "^37.3.2" }, "devDependencies": { "@docusaurus/module-type-aliases": "^3.6.0", @@ -33,31 +36,31 @@ } }, "node_modules/@algolia/autocomplete-core": { - "version": "1.17.6", - "resolved": "https://registry.npmjs.org/@algolia/autocomplete-core/-/autocomplete-core-1.17.6.tgz", - "integrity": "sha512-lkDoW4I7h2kKlIgf3pUt1LqvxyYKkVyiypoGLlUnhPSnCpmeOwudM6rNq6YYsCmdQtnDQoW5lUNNuj6ASg3qeg==", + "version": "1.17.7", + "resolved": "https://registry.npmjs.org/@algolia/autocomplete-core/-/autocomplete-core-1.17.7.tgz", + "integrity": "sha512-BjiPOW6ks90UKl7TwMv7oNQMnzU+t/wk9mgIDi6b1tXpUek7MW0lbNOUHpvam9pe3lVCf4xPFT+lK7s+e+fs7Q==", "dependencies": { - "@algolia/autocomplete-plugin-algolia-insights": "1.17.6", - "@algolia/autocomplete-shared": "1.17.6" + "@algolia/autocomplete-plugin-algolia-insights": "1.17.7", + "@algolia/autocomplete-shared": "1.17.7" } }, "node_modules/@algolia/autocomplete-plugin-algolia-insights": { - "version": "1.17.6", - "resolved": "https://registry.npmjs.org/@algolia/autocomplete-plugin-algolia-insights/-/autocomplete-plugin-algolia-insights-1.17.6.tgz", - "integrity": "sha512-17NnaacuFzSWVuZu4NKzVeaFIe9Abpw8w+/gjc7xhZFtqj+GadufzodIdchwiB2eM2cDdiR3icW7gbNTB3K2YA==", + "version": "1.17.7", + "resolved": "https://registry.npmjs.org/@algolia/autocomplete-plugin-algolia-insights/-/autocomplete-plugin-algolia-insights-1.17.7.tgz", + "integrity": "sha512-Jca5Ude6yUOuyzjnz57og7Et3aXjbwCSDf/8onLHSQgw1qW3ALl9mrMWaXb5FmPVkV3EtkD2F/+NkT6VHyPu9A==", "dependencies": { - "@algolia/autocomplete-shared": "1.17.6" + "@algolia/autocomplete-shared": "1.17.7" }, "peerDependencies": { "search-insights": ">= 1 < 3" } }, "node_modules/@algolia/autocomplete-preset-algolia": { - "version": "1.17.6", - "resolved": "https://registry.npmjs.org/@algolia/autocomplete-preset-algolia/-/autocomplete-preset-algolia-1.17.6.tgz", - "integrity": "sha512-Cvg5JENdSCMuClwhJ1ON1/jSuojaYMiUW2KePm18IkdCzPJj/NXojaOxw58RFtQFpJgfVW8h2E8mEoDtLlMdeA==", + "version": "1.17.7", + "resolved": "https://registry.npmjs.org/@algolia/autocomplete-preset-algolia/-/autocomplete-preset-algolia-1.17.7.tgz", + "integrity": "sha512-ggOQ950+nwbWROq2MOCIL71RE0DdQZsceqrg32UqnhDz8FlO9rL8ONHNsI2R1MH0tkgVIDKI/D0sMiUchsFdWA==", "dependencies": { - "@algolia/autocomplete-shared": "1.17.6" + "@algolia/autocomplete-shared": "1.17.7" }, "peerDependencies": { "@algolia/client-search": ">= 4.9.1 < 6", @@ -65,9 +68,9 @@ } }, "node_modules/@algolia/autocomplete-shared": { - "version": "1.17.6", - "resolved": "https://registry.npmjs.org/@algolia/autocomplete-shared/-/autocomplete-shared-1.17.6.tgz", - "integrity": "sha512-aq/3V9E00Tw2GC/PqgyPGXtqJUlVc17v4cn1EUhSc+O/4zd04Uwb3UmPm8KDaYQQOrkt1lwvCj2vG2wRE5IKhw==", + "version": "1.17.7", + "resolved": "https://registry.npmjs.org/@algolia/autocomplete-shared/-/autocomplete-shared-1.17.7.tgz", + "integrity": "sha512-o/1Vurr42U/qskRSuhBH+VKxMvkkUVTLU6WZQr+L5lGZZLYWyhdzWjW0iGXY7EkwRTjBqvN2EsR81yCTGV/kmg==", "peerDependencies": { "@algolia/client-search": ">= 4.9.1 < 6", "algoliasearch": ">= 4.9.1 < 6" @@ -95,14 +98,14 @@ } }, "node_modules/@algolia/client-abtesting": { - "version": "5.13.0", - "resolved": "https://registry.npmjs.org/@algolia/client-abtesting/-/client-abtesting-5.13.0.tgz", - "integrity": "sha512-6CoQjlMi1pmQYMQO8tXfuGxSPf6iKX5FP9MuMe6IWmvC81wwTvOehnwchyBl2wuPVhcw2Ar53K53mQ60DAC64g==", + "version": "5.14.2", + "resolved": "https://registry.npmjs.org/@algolia/client-abtesting/-/client-abtesting-5.14.2.tgz", + "integrity": "sha512-7fq1tWIy1aNJEaNHxWy3EwDkuo4k22+NBnxq9QlYVSLLXtr6HqmAm6bQgNNzGT3vm21iKqWO9efk+HIhEM1SzQ==", "dependencies": { - "@algolia/client-common": "5.13.0", - "@algolia/requester-browser-xhr": "5.13.0", - "@algolia/requester-fetch": "5.13.0", - "@algolia/requester-node-http": "5.13.0" + "@algolia/client-common": "5.14.2", + "@algolia/requester-browser-xhr": "5.14.2", + "@algolia/requester-fetch": "5.14.2", + "@algolia/requester-node-http": "5.14.2" }, "engines": { "node": ">= 14.0.0" @@ -168,22 +171,22 @@ } }, "node_modules/@algolia/client-common": { - "version": "5.13.0", - "resolved": "https://registry.npmjs.org/@algolia/client-common/-/client-common-5.13.0.tgz", - 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"https://registry.npmjs.org/ansi-regex/-/ansi-regex-6.1.0.tgz", diff --git a/package.json b/package.json index b99f70e..34cb296 100644 --- a/package.json +++ b/package.json @@ -15,19 +15,22 @@ "typecheck": "tsc" }, "dependencies": { - "@docusaurus/core": "^3.6.0", - "@docusaurus/faster": "^3.5.2", - "@docusaurus/preset-classic": "^3.6.0", + "@docusaurus/core": "^3.6.1", + "@docusaurus/faster": "^3.6.1", + "@docusaurus/preset-classic": "^3.6.1", + "@docusaurus/theme-live-codeblock": "^3.6.1", "@mdx-js/react": "^3.0.0", "clsx": "^2.0.0", "docusaurus-lunr-search": "^3.5.0", "plotly.js": "^2.35.2", "prism-react-renderer": "^2.3.0", + "raw-loader": "^4.0.2", "react": "^18.0.0", "react-dom": "^18.0.0", "react-plotly.js": "^2.6.0", "rehype-katex": "^7.0.1", - "remark-math": "^6.0.0" + "remark-math": "^6.0.0", + "victory": "^37.3.2" }, "devDependencies": { "@docusaurus/module-type-aliases": "^3.6.0", From f26afcccf976ac4cc0444cdc8a2026651b58b9ce Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 17 Nov 2024 20:42:42 -0500 Subject: [PATCH 03/51] Updated gasket, fixed charts --- .../1-introduction/Canvas.tsx | 34 +++++ .../1-introduction/Gasket.jsx | 55 +++------ .../{1-introduction.mdx => index.mdx} | 116 +++++------------- .../1-introduction/scope.ts | 5 +- src/css/custom.css | 7 +- 5 files changed, 89 insertions(+), 128 deletions(-) create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/Canvas.tsx rename blog/2024-11-15-playing-with-fire/1-introduction/{1-introduction.mdx => index.mdx} (70%) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/Canvas.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/Canvas.tsx new file mode 100644 index 0000000..262c50d --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/Canvas.tsx @@ -0,0 +1,34 @@ +import {useEffect, useRef} from "react"; + +interface Props { + renderFn: (ImageData) => void +} + +export const Canvas: React.FC = ({renderFn}: Props) => { + const canvasRef = useRef(null); + + useEffect(() => { + const ctx = canvasRef.current?.getContext("2d"); + if (!ctx) { + console.log("Canvas not ready"); + } + + const image = ctx.createImageData(canvasRef.current.width, canvasRef.current.height); + renderFn(image); + ctx.putImageData(image, 0, 0); + }, []); + + return ( + + ); +}; + +export default Canvas; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx index 59f25f0..70b21aa 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx @@ -1,43 +1,24 @@ -function Gasket(props) { - const iterations = 1000; - const functions = [ - (x, y) => [x / 2, y / 2], - (x, y) => [(x + 1) / 2, y / 2], - (x, y) => [x / 2, (y + 1) / 2] - ] +// Hint: try increasing the iteration count +const iterations = 10000; - function chaosGame(image) { - var [x, y] = [randomBiUnit(), randomBiUnit()]; +// Hint: negating `x` and `y` also creates some interesting images +const functions = [ + (x, y) => [x / 2, y / 2], + (x, y) => [(x + 1) / 2, y / 2], + (x, y) => [x / 2, (y + 1) / 2] +] - for (var i = 0; i < iterations; i++) { - const f = functions[randomInteger(0, functions.length)]; - [x, y] = f(x, y); +function chaosGame(image) { + var [x, y] = [randomBiUnit(), randomBiUnit()]; - if (i > 20) { - plot(x, y, image); - } + for (var count = 0; count < iterations; count++) { + const i = randomInteger(0, functions.length); + [x, y] = functions[i](x, y); + + if (count > 20) { + plot(x, y, image); } } - - function onClickRender() { - /** @type{HTMLCanvasElement} */ - const canvas = document.getElementById('canvas-gasket'); - const context = canvas.getContext('2d'); - const image = context.createImageData(canvas.width, canvas.height); - chaosGame(image); - context.putImageData(image, 0, 0); - } - - return
    -
    - -
    -
    -
    - -
    -
    } + +render() diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/1-introduction.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx similarity index 70% rename from blog/2024-11-15-playing-with-fire/1-introduction/1-introduction.mdx rename to blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index 8331205..efd01b5 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/1-introduction.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -53,28 +53,16 @@ like a coordinate chart. For example, if we say $S = \{(0,0), (1, 1), (2, 2)\}$, there are three points to plot: -import Plot from "react-plotly.js" +import {VictoryChart, VictoryTheme, VictoryScatter, VictoryLegend} from "victory"; +export const simpleData = [ + {x: 0, y: 0}, + {x: 1, y: 1}, + {x: 2, y: 2} +] -
    - -
    + + + For fractal flames, we just need to figure out which points are in $S$ and plot them. While there are technically an infinite number of points, if we find _enough_ points and plot them, we end up with a nice picture. @@ -95,74 +83,21 @@ $$ That is, for an input point $(x, y)$, the output point will be $(x + 1, y)$: -
    - { return {x: x + 1, y} }) + + + + + -
    + This is a simple example designed to illustrate the principle. In general, $F_i$ functions have the form: @@ -243,4 +178,11 @@ import Scope from './scope' import Gasket from '!!raw-loader!./Gasket' -{Gasket} +{Gasket} + +
    + + +Note: The image our chaos game generates is different than the fractal flame paper, but I think the version displayed +here is correct. As confirmation, the next post will re-create the same image using a different method. + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts b/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts index 2d4c411..f020b05 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts @@ -3,12 +3,13 @@ import React from 'react'; import randomBiUnit from './biunit'; import plot from './plot'; import randomInteger from './randint'; - +import Canvas from './Canvas'; const Scope = { React, plot, randomBiUnit, - randomInteger + randomInteger, + Canvas } export default Scope; \ No newline at end of file diff --git a/src/css/custom.css b/src/css/custom.css index 56086c9..7d691f0 100644 --- a/src/css/custom.css +++ b/src/css/custom.css @@ -23,7 +23,10 @@ no-repeat; } -/* Dark mode for Plotly, copied from https://github.com/plotly/plotly.js/issues/2006#issuecomment-2081535168 */ -[data-theme='dark'] .plot-container { +/* +Inspired by https://github.com/plotly/plotly.js/issues/2006#issuecomment-2081535168, +adapted for Victory charts + */ +[data-theme='dark'] .VictoryContainer { filter: invert(75%) hue-rotate(180deg); } \ No newline at end of file From b46993bd51f92a5a1d699ea747caddc2eb99734a Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 17 Nov 2024 21:34:32 -0500 Subject: [PATCH 04/51] Fix for facebook/docusaurus#6032 --- .../1-introduction/Gasket.jsx | 2 +- src/theme/Playground/index.tsx | 135 ++++++++++++++++++ src/theme/Playground/styles.module.css | 43 ++++++ 3 files changed, 179 insertions(+), 1 deletion(-) create mode 100644 src/theme/Playground/index.tsx create mode 100644 src/theme/Playground/styles.module.css diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx index 70b21aa..5dcc0e5 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx @@ -1,7 +1,7 @@ // Hint: try increasing the iteration count const iterations = 10000; -// Hint: negating `x` and `y` also creates some interesting images +// Hint: negating `x` and `y` creates some interesting images const functions = [ (x, y) => [x / 2, y / 2], (x, y) => [(x + 1) / 2, y / 2], diff --git a/src/theme/Playground/index.tsx b/src/theme/Playground/index.tsx new file mode 100644 index 0000000..bf2aa21 --- /dev/null +++ b/src/theme/Playground/index.tsx @@ -0,0 +1,135 @@ +import React from 'react'; +import clsx from 'clsx'; +import useIsBrowser from '@docusaurus/useIsBrowser'; +import {LiveProvider, LiveEditor, LiveError, LivePreview} from 'react-live'; +import Translate from '@docusaurus/Translate'; +import useDocusaurusContext from '@docusaurus/useDocusaurusContext'; +import BrowserOnly from '@docusaurus/BrowserOnly'; +import { + ErrorBoundaryErrorMessageFallback, + usePrismTheme, +} from '@docusaurus/theme-common'; +import ErrorBoundary from '@docusaurus/ErrorBoundary'; + +import type {Props} from '@theme/Playground'; +import type {ThemeConfig} from '@docusaurus/theme-live-codeblock'; + +import styles from './styles.module.css'; + +function Header({children}: {children: React.ReactNode}) { + return
    {children}
    ; +} + +function LivePreviewLoader() { + // Is it worth improving/translating? + // eslint-disable-next-line @docusaurus/no-untranslated-text + return
    Loading...
    ; +} + +function Preview() { + // No SSR for the live preview + // See https://github.com/facebook/docusaurus/issues/5747 + return ( + }> + {() => ( + <> + ( + + )}> + + + + + )} + + ); +} + +function ResultWithHeader() { + return ( + <> +
    + + Result + +
    + {/* https://github.com/facebook/docusaurus/issues/5747 */} +
    + +
    + + ); +} + +function ThemedLiveEditor() { + const isBrowser = useIsBrowser(); + return ( + + ); +} + +function EditorWithHeader() { + return ( + <> +
    + + Live Editor + +
    + + + ); +} + +// this should rather be a stable function +// see https://github.com/facebook/docusaurus/issues/9630#issuecomment-1855682643 +const DEFAULT_TRANSFORM_CODE = (code: string) => `${code};`; + +export default function Playground({ + children, + transformCode, + ...props +}: Props): JSX.Element { + const { + siteConfig: {themeConfig}, + } = useDocusaurusContext(); + const { + liveCodeBlock: {playgroundPosition}, + } = themeConfig as ThemeConfig; + const prismTheme = usePrismTheme(); + + const noInline = props.metastring?.includes('noInline') ?? false; + + return ( +
    + + {playgroundPosition === 'top' ? ( + <> + + + + ) : ( + <> + + + + )} + +
    + ); +} diff --git a/src/theme/Playground/styles.module.css b/src/theme/Playground/styles.module.css new file mode 100644 index 0000000..b9d8031 --- /dev/null +++ b/src/theme/Playground/styles.module.css @@ -0,0 +1,43 @@ +.playgroundContainer { + margin-bottom: var(--ifm-leading); + border-radius: var(--ifm-global-radius); + box-shadow: var(--ifm-global-shadow-lw); + overflow: hidden; +} + +.playgroundHeader { + letter-spacing: 0.08rem; + padding: 0.75rem; + text-transform: uppercase; + font-weight: bold; + background: var(--ifm-color-emphasis-200); + color: var(--ifm-color-content); + font-size: var(--ifm-code-font-size); +} + +.playgroundHeader:first-of-type { + background: var(--ifm-color-emphasis-600); + color: var(--ifm-color-content-inverse); +} + +.playgroundEditor { + font: var(--ifm-code-font-size) / var(--ifm-pre-line-height) + var(--ifm-font-family-monospace) !important; + /* rtl:ignore */ + direction: ltr; +} + +.playgroundPreview { + padding: 1rem; + background-color: var(--ifm-pre-background); +} + +/* +Docusaurus global CSS applies a `border-radius` to `pre` that leads to a minor graphical issue +where the "LIVE EDITOR" title bar and code block meet - https://github.com/facebook/docusaurus/issues/6032#issuecomment-2481803877 + +This change disables the border radius so the edges properly join together + */ +.playgroundEditor > pre { + border-radius: 0; +} \ No newline at end of file From e1735404ae4a32f8fe15c91d4dd40f47403e7ecf Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Mon, 18 Nov 2024 22:01:31 -0500 Subject: [PATCH 05/51] Start on the transforms post --- .../1-introduction/biunit.ts | 2 +- .../1-introduction/index.mdx | 2 + .../1-introduction/randint.ts | 2 +- .../2-transforms.mdx | 7 - .../2-transforms/coefs.ts | 4 + .../2-transforms/index.mdx | 150 ++++++++++++++++++ 6 files changed, 158 insertions(+), 9 deletions(-) delete mode 100644 blog/2024-11-15-playing-with-fire/2-transforms.mdx create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/coefs.ts create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/index.mdx diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts b/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts index c8e17c6..21bf035 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts @@ -1,3 +1,3 @@ -export default function randomBiUnit(): number { +export default function randomBiUnit() { return Math.random() * 2 - 1; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index efd01b5..8887b59 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -51,6 +51,8 @@ First, $S$. We're generating images, so everything is in two dimensions: $S \in all points that are "in the system." To generate our final image, we just plot every point in the system like a coordinate chart. +TODO: What is a stationary point? How does it relate to the chaos game? + For example, if we say $S = \{(0,0), (1, 1), (2, 2)\}$, there are three points to plot: import {VictoryChart, VictoryTheme, VictoryScatter, VictoryLegend} from "victory"; diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts b/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts index 0e922ba..07d79a3 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts @@ -1,3 +1,3 @@ -export default function randomInteger(min: number, max: number): number { +export default function randomInteger(min: number, max: number) { return Math.floor(Math.random() * (max - min)) + min; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms.mdx b/blog/2024-11-15-playing-with-fire/2-transforms.mdx deleted file mode 100644 index ed2fdfa..0000000 --- a/blog/2024-11-15-playing-with-fire/2-transforms.mdx +++ /dev/null @@ -1,7 +0,0 @@ ---- -slug: 2024/11/playing-with-fire-transforms -title: "Playing with fire: Transforms and variations" -date: 2024-11-15 13:00:00 -authors: [bspeice] -tags: [] ---- \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/coefs.ts b/blog/2024-11-15-playing-with-fire/2-transforms/coefs.ts new file mode 100644 index 0000000..da5b1aa --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/coefs.ts @@ -0,0 +1,4 @@ +export interface Coefs { + a: number, b: number, c: number, + d: number, e: number, f: number +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx new file mode 100644 index 0000000..120fbc7 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -0,0 +1,150 @@ +--- +slug: 2024/11/playing-with-fire-transforms +title: "Playing with fire: Transforms and variations" +date: 2024-11-15 13:00:00 +authors: [bspeice] +tags: [] +--- + +Now that we have a basic chaos game in place, it's time to spice things up. Transforms and variations create the +interesting patterns that fractal flames are known for. + + + +This blog post uses a set of reference parameters ([available here](../params.flame)) to demonstrate a practical +implementation of the fractal flame algorithm. If you're interested in tweaking the parameters, or generating +your own art, [Apophysis](https://sourceforge.net/projects/apophysis/) is a good introductory tool. + +## Transforms and variations + +import CodeBlock from '@theme/CodeBlock' + +We previously introduced "transforms" as the "functions" of an "iterated function system." Their general format is: + +$$ +F_i(x,y) = (a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) +$$ + +Let's also start defining some types we can use in our code. The transform coefficients are a good place to start: + +```typescript +interface Coefs { + a: number, b: number, c: number, + d: number, e: number, f: number +} +``` + +We also introduced the Sierpinski Gasket functions ($F_0$, $F_1$, and $F_2$), demonstrating how they are related to +the general format. For example: + +$$ +\begin{align*} +F_0(x,y) &= \left({x \over 2}, {y \over 2}\right) \\ +&= (a_0 \cdot x + b_0 \cdot y + c_o, d_0 \cdot x + e_0 \cdot y + f_0) \\ +& a_0 = 0.5 \hspace{0.2cm} b_0 = 0 \hspace{0.2cm} c_0 = 0 \\ +& d_0 = 0 \hspace{0.2cm} e_0 = 0.5 \hspace{0.2cm} f_0 = 0 +\end{align*} +$$ + +However, these transforms are pretty boring. We can build more exciting images by using some additional functions +within the transform. These "sub-functions" are called "variations": + +$$ +F_i(x, y) = V_j(a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) +$$ + +The fractal flame paper lists 49 variation functions ($V_j$ above), but the sky's the limit here. +For example, the official `flam3` implementation supports +[98 variations](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/variations.c). + +In code, variations are pretty easy: + +```typescript +type Variation = (x: number, y: number) => [number, number]; +```` + +Our reference image will focus on just four variations: + +### Linear (variation 0) + +This variation returns the $x$ and $y$ coordinates as-is. In a way, the Sierpinski Gasket is +a fractal flame using only the linear variation. + +$$ +V_0(x,y) = (x,y) +$$ + +```typescript +function linear(x: number, y: number) { + return [x, y]; +} +``` + +### Julia (variation 13) + +This variation still uses just the $x$ and $y$ coordinates, but does some crazy things with them: + +TODO: Is this related to the Julia set? + +$$ +\begin{align*} +r &= \sqrt{x^2 + y^2} \\ +\theta &= \text{arctan}(x / y) \\ +\Omega &= \left\{ + \begin{array}{lr} + 0 \hspace{0.4cm} \text{w.p. } 0.5 \\ + \pi \hspace{0.4cm} \text{w.p. } 0.5 \\ + \end{array} +\right\} \\ + +V_{13}(x, y) &= \sqrt{r} \cdot (\text{cos} ( \theta / 2 + \Omega ), \text{sin} ( \theta / 2 + \Omega )) +\end{align*} +$$ + +```typescript +function julia(x: number, y: number) { + const r = Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2)); + const theta = Math.atan2(x, y); + const omega = Math.random() > 0.5 ? 0 : Math.PI; + + return [ + r * Math.cos(theta / 2 + omega), + r * Math.sin(theta / 2 + omega) + ] +} +``` + +### Popcorn (variation 17) + +This is known as a "dependent variation" because it depends on knowing the transform coefficients: + +$$ +V_{17}(x,y) = (x + c \cdot \text{sin}(\text{tan }3y), y + f \cdot \text{sin}(\text{tan }3x)) +$$ + +```typescript +function popcorn({c, f}: Coefs) { + return (x: number, y: number) => [ + x + c * Math.sin(Math.tan(3 * y)), + y + f * Math.sin(Math.tan(3 * x)) + ] +} +``` + +### PDJ (variation 24) + +This is known as a "parametric" variation because it has additional parameters given to it: + +$$ +p_1 = \text{pdj.a} \hspace{0.2cm} p_2 = \text{pdj.b} \hspace{0.2cm} p_3 = \text{pdj.c} \hspace{0.2cm} p_4 = \text{pdj.d} \\ +V_{24} = (\text{sin}(p_1 \cdot y) - \text{cos}(p_2 \cdot x), \text{sin}(p_3 \cdot x) - \text{cos}(p_4 \cdot y)) +$$ + +```typescript +function pdj(a: number, b: number, c: number, d: number) { + return (x: number, y: number) => [ + Math.sin(a * y) - Math.cos(b * x), + Math.sin(c * x) - Math.cos(d * y) + ] +} +``` \ No newline at end of file From 431ba2d0f486338964ea78f3366f2bcb039a00e2 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Mon, 18 Nov 2024 22:08:23 -0500 Subject: [PATCH 06/51] Tweaks --- .../2-transforms/index.mdx | 30 +++++-------------- 1 file changed, 8 insertions(+), 22 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 120fbc7..b67bbdd 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -25,15 +25,6 @@ $$ F_i(x,y) = (a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) $$ -Let's also start defining some types we can use in our code. The transform coefficients are a good place to start: - -```typescript -interface Coefs { - a: number, b: number, c: number, - d: number, e: number, f: number -} -``` - We also introduced the Sierpinski Gasket functions ($F_0$, $F_1$, and $F_2$), demonstrating how they are related to the general format. For example: @@ -57,18 +48,12 @@ The fractal flame paper lists 49 variation functions ($V_j$ above), but the sky' For example, the official `flam3` implementation supports [98 variations](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/variations.c). -In code, variations are pretty easy: - -```typescript -type Variation = (x: number, y: number) => [number, number]; -```` - Our reference image will focus on just four variations: ### Linear (variation 0) -This variation returns the $x$ and $y$ coordinates as-is. In a way, the Sierpinski Gasket is -a fractal flame using only the linear variation. +This variation returns the $x$ and $y$ coordinates as-is. As mentioned, the Sierpinski Gasket is +a fractal flame using only the linear variation: $$ V_0(x,y) = (x,y) @@ -82,7 +67,7 @@ function linear(x: number, y: number) { ### Julia (variation 13) -This variation still uses just the $x$ and $y$ coordinates, but does some crazy things with them: +This variation still uses just the $x$ and $y$ coordinates, but does crazy things with them: TODO: Is this related to the Julia set? @@ -116,17 +101,18 @@ function julia(x: number, y: number) { ### Popcorn (variation 17) -This is known as a "dependent variation" because it depends on knowing the transform coefficients: +This is known as a "dependent variation" because it depends on knowing the transform coefficients +(specifically, $c$ and $f$): $$ V_{17}(x,y) = (x + c \cdot \text{sin}(\text{tan }3y), y + f \cdot \text{sin}(\text{tan }3x)) $$ ```typescript -function popcorn({c, f}: Coefs) { +function popcorn(coefs: {c: number, f: number}) { return (x: number, y: number) => [ - x + c * Math.sin(Math.tan(3 * y)), - y + f * Math.sin(Math.tan(3 * x)) + x + coefs.c * Math.sin(Math.tan(3 * y)), + y + coefs.f * Math.sin(Math.tan(3 * x)) ] } ``` From aba3c9f9880193b7cb0256feecd3630e691bf33e Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Tue, 19 Nov 2024 21:42:03 -0500 Subject: [PATCH 07/51] Reorganize a bit, write some more --- .../1-introduction/index.mdx | 6 +- .../2-transforms/BaselineRender.ts | 5 ++ .../2-transforms/baseline.ts | 22 +++++ .../2-transforms/index.mdx | 76 +++++++++-------- .../{2-transforms => src}/coefs.ts | 0 .../2024-11-15-playing-with-fire/src/julia.ts | 13 +++ .../src/linear.ts | 4 + .../{ => src}/params.ts | 84 ++++++++++--------- blog/2024-11-15-playing-with-fire/src/pdj.ts | 9 ++ .../src/popcorn.ts | 10 +++ .../src/transform.ts | 9 ++ .../src/variations.ts | 1 + blog/2024-11-15-playing-with-fire/types.ts | 24 ------ .../2024-11-15-playing-with-fire/variation.ts | 40 --------- docusaurus.config.ts | 14 +++- src/DualImage/index.tsx | 13 --- src/css/custom.css | 7 ++ 17 files changed, 181 insertions(+), 156 deletions(-) create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/BaselineRender.ts create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/baseline.ts rename blog/2024-11-15-playing-with-fire/{2-transforms => src}/coefs.ts (100%) create mode 100644 blog/2024-11-15-playing-with-fire/src/julia.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/linear.ts rename blog/2024-11-15-playing-with-fire/{ => src}/params.ts (62%) create mode 100644 blog/2024-11-15-playing-with-fire/src/pdj.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/popcorn.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/transform.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/variations.ts delete mode 100644 blog/2024-11-15-playing-with-fire/types.ts delete mode 100644 blog/2024-11-15-playing-with-fire/variation.ts delete mode 100644 src/DualImage/index.tsx diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index 8887b59..9e6758c 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -51,7 +51,7 @@ First, $S$. We're generating images, so everything is in two dimensions: $S \in all points that are "in the system." To generate our final image, we just plot every point in the system like a coordinate chart. -TODO: What is a stationary point? How does it relate to the chaos game? +TODO: What is a stationary point? How does it relate to the chaos game? Why does the chaos game work? For example, if we say $S = \{(0,0), (1, 1), (2, 2)\}$, there are three points to plot: @@ -187,4 +187,6 @@ import Gasket from '!!raw-loader!./Gasket' Note: The image our chaos game generates is different than the fractal flame paper, but I think the version displayed here is correct. As confirmation, the next post will re-create the same image using a different method. - \ No newline at end of file + + +TODO: Explanation of function weights $w_i$ \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/BaselineRender.ts b/blog/2024-11-15-playing-with-fire/2-transforms/BaselineRender.ts new file mode 100644 index 0000000..315aacb --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/BaselineRender.ts @@ -0,0 +1,5 @@ +import {useColorMode, useThemeConfig} from "@docusaurus/theme-common"; + +export default function BaselineRender({children}) { + const {colorMode, setColorMode} = useColorMode(); +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/baseline.ts b/blog/2024-11-15-playing-with-fire/2-transforms/baseline.ts new file mode 100644 index 0000000..1708e81 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/baseline.ts @@ -0,0 +1,22 @@ +// hidden-start +import { Coefs } from './coefs' +import { Variation } from './variations' +// hidden-end +export function applyTransform( + x: number, + y: number, + coefs: Coefs, + variations: [number, Variation][]) +{ + const transformX = coefs.a * x + coefs.b * y + coefs.c; + const transformY = coefs.d * x + coefs.e * y + coefs.f; + + var finalX = 0; + var finalY = 0; + for (const [blend, variation] of variations) { + const [variationX, variationY] = variation(transformX, transformY); + finalX += blend * variationX; + finalY += blend * variationY; + } + return [finalX, finalY]; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index b67bbdd..ddccc50 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -25,6 +25,10 @@ $$ F_i(x,y) = (a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) $$ +import coefsSrc from '!!raw-loader!../src/coefs' + +{coefsSrc} + We also introduced the Sierpinski Gasket functions ($F_0$, $F_1$, and $F_2$), demonstrating how they are related to the general format. For example: @@ -37,7 +41,7 @@ F_0(x,y) &= \left({x \over 2}, {y \over 2}\right) \\ \end{align*} $$ -However, these transforms are pretty boring. We can build more exciting images by using some additional functions +However, these transforms are pretty boring. We can build more exciting images by using additional functions within the transform. These "sub-functions" are called "variations": $$ @@ -52,18 +56,18 @@ Our reference image will focus on just four variations: ### Linear (variation 0) -This variation returns the $x$ and $y$ coordinates as-is. As mentioned, the Sierpinski Gasket is -a fractal flame using only the linear variation: +This variation returns the $x$ and $y$ coordinates as-is: $$ V_0(x,y) = (x,y) $$ -```typescript -function linear(x: number, y: number) { - return [x, y]; -} -``` +import linearSrc from '!!raw-loader!../src/linear' + +{linearSrc} + +Before we move on, it's worth mentioning the relationship between this variation and the Sierpinski Gasket. +Specifically, we can think of the Gasket as a fractal flame that uses only the linear variation. ### Julia (variation 13) @@ -86,18 +90,9 @@ V_{13}(x, y) &= \sqrt{r} \cdot (\text{cos} ( \theta / 2 + \Omega ), \text{sin} ( \end{align*} $$ -```typescript -function julia(x: number, y: number) { - const r = Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2)); - const theta = Math.atan2(x, y); - const omega = Math.random() > 0.5 ? 0 : Math.PI; +import juliaSrc from '!!raw-loader!../src/julia' - return [ - r * Math.cos(theta / 2 + omega), - r * Math.sin(theta / 2 + omega) - ] -} -``` +{juliaSrc} ### Popcorn (variation 17) @@ -108,14 +103,9 @@ $$ V_{17}(x,y) = (x + c \cdot \text{sin}(\text{tan }3y), y + f \cdot \text{sin}(\text{tan }3x)) $$ -```typescript -function popcorn(coefs: {c: number, f: number}) { - return (x: number, y: number) => [ - x + coefs.c * Math.sin(Math.tan(3 * y)), - y + coefs.f * Math.sin(Math.tan(3 * x)) - ] -} -``` +import popcornSrc from '!!raw-loader!../src/popcorn' + +{popcornSrc} ### PDJ (variation 24) @@ -126,11 +116,27 @@ p_1 = \text{pdj.a} \hspace{0.2cm} p_2 = \text{pdj.b} \hspace{0.2cm} p_3 = \text{ V_{24} = (\text{sin}(p_1 \cdot y) - \text{cos}(p_2 \cdot x), \text{sin}(p_3 \cdot x) - \text{cos}(p_4 \cdot y)) $$ -```typescript -function pdj(a: number, b: number, c: number, d: number) { - return (x: number, y: number) => [ - Math.sin(a * y) - Math.cos(b * x), - Math.sin(c * x) - Math.cos(d * y) - ] -} -``` \ No newline at end of file +import pdjSrc from '!!raw-loader!../src/pdj' + +{pdjSrc} + +### Blending + +Now, one variation is fun, but we can also combine variations in a single transform by "blending." +First, each variation is assigned a value that describes how much it affects the transform function ($v_j$). +Afterward, sum up the $x$ and $y$ values respectively: + +$$ +F_i(x,y) = \sum_{j} v_{ij} V_j(a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) +$$ + +The formula looks intimidating, but it's not hard to implement: + +import baselineSrc from '!!raw-loader!./baseline' + +{baselineSrc} + +TODO: Mention that the Sierpinski Gasket is just a blend with linear weight 1, all others 0. Maybe replace comment above about Sierpinski Gasket and linear transform? + +And with that in place, we have enough to render a first full fractal flame: + diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/coefs.ts b/blog/2024-11-15-playing-with-fire/src/coefs.ts similarity index 100% rename from blog/2024-11-15-playing-with-fire/2-transforms/coefs.ts rename to blog/2024-11-15-playing-with-fire/src/coefs.ts diff --git a/blog/2024-11-15-playing-with-fire/src/julia.ts b/blog/2024-11-15-playing-with-fire/src/julia.ts new file mode 100644 index 0000000..5d21045 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/julia.ts @@ -0,0 +1,13 @@ +// hidden-start +import { Variation } from './variations' +// hidden-end +export const julia: Variation = (x, y) => { + const r = Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2)); + const theta = Math.atan2(x, y); + const omega = Math.random() > 0.5 ? 0 : Math.PI; + + return [ + r * Math.cos(theta / 2 + omega), + r * Math.sin(theta / 2 + omega) + ] +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/linear.ts b/blog/2024-11-15-playing-with-fire/src/linear.ts new file mode 100644 index 0000000..cbea1e7 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/linear.ts @@ -0,0 +1,4 @@ +// hidden-start +import {Variation} from "./variations" +//hidden-end +export const linear: Variation = (x, y) => [x, y]; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/params.ts b/blog/2024-11-15-playing-with-fire/src/params.ts similarity index 62% rename from blog/2024-11-15-playing-with-fire/params.ts rename to blog/2024-11-15-playing-with-fire/src/params.ts index b18c647..485347d 100644 --- a/blog/2024-11-15-playing-with-fire/params.ts +++ b/blog/2024-11-15-playing-with-fire/src/params.ts @@ -3,8 +3,12 @@ * translated into something that's easier to work with. */ -import {Coefs, Transform} from "./types"; -import { julia, linear, pdj, popcorn } from "./variation"; +import { Coefs } from './coefs'; +import { Transform } from './transform'; +import { linear } from './linear' +import { julia } from './julia' +import { popcorn } from './popcorn' +import { pdj } from './pdj' export const identityCoefs: Coefs = { a: 1, b: 0, c: 0, @@ -12,53 +16,51 @@ export const identityCoefs: Coefs = { } export const xform1Weight = 0.56453495; -export const xform1: Transform = { - coefs: { - a: -1.381068, b: -1.381068, c: 0, - d: 1.381068, e: -1.381068, f: 0, - }, - coefsPost: identityCoefs, - variations: [[1, julia]], - color: 0 +export const xform1Coefs = { + a: -1.381068, b: -1.381068, c: 0, + d: 1.381068, e: -1.381068, f: 0, } +export const xform1CoefsPost = identityCoefs; +export const xform1Variations = [ + [1, julia] +] +export const xform1Color = 0; -const xform2Weight = 0.013135; -export const xform2: Transform = { - coefs: { - a: 0.031393, b: 0.031367, c: 0, - d: -0.031367, e: 0.031393, f: 0, - }, - coefsPost: { - a: 1, b: 0, c: 0.241352, - d: 0, e: 1, f: 0.271521, - }, - variations: [ - [1, linear], - [1, popcorn] - ], - color: 0.844 +export const xform2Weight = 0.013135; +export const xform2Coefs = { + a: 0.031393, b: 0.031367, c: 0, + d: -0.031367, e: 0.031393, f: 0, } +export const xform2CoefsPost = { + a: 1, b: 0, c: 0.241352, + d: 0, e: 1, f: 0.271521, +} +export const xform2Variations = [ + [1, linear], + [1, popcorn(xform2Coefs)] +] +export const xform2Color = 0.844; export const xform3Weight = 0.42233; -export const xform3: Transform = { - coefs: { - a: 1.51523, b: -3.048677, c: 0.724135, - d: 0.740356, e: -1.455964, f: -0.362059, - }, - coefsPost: identityCoefs, - variations: [[1, pdj(1.09358, 2.13048, 2.54127, 2.37267)]], - color: 0.349 +export const xform3Coefs = { + a: 1.51523, b: -3.048677, c: 0.724135, + d: 0.740356, e: -1.455964, f: -0.362059, } +export const xform3CoefsPost = identityCoefs; +export const xform3Variations = [ + [1, pdj(1.09358, 2.13048, 2.54127, 2.37267)] +]; +export const xform3Color = 0.349; -export const xformFinal: Transform = { - coefs: { - a: 2, b: 0, c: 0, - d: 0, e: 2, f: 0 - }, - coefsPost: identityCoefs, - variations: [[1, julia]], - color: 0 +export const xformFinalCoefs = { + a: 2, b: 0, c: 0, + d: 0, e: 2, f: 0 } +export const xformFinalCoefsPost = identityCoefs; +export const xformFinalVariations = [ + [1, julia] +] +export const xformFinalColor = 0; export const palette = "7E3037762C45722B496E2A4E6A2950672853652754632656" + diff --git a/blog/2024-11-15-playing-with-fire/src/pdj.ts b/blog/2024-11-15-playing-with-fire/src/pdj.ts new file mode 100644 index 0000000..5360ced --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/pdj.ts @@ -0,0 +1,9 @@ +// hidden-start +import { Variation } from './variations' +//hidden-end +export function pdj(a: number, b: number, c: number, d: number): Variation { + return (x, y) => [ + Math.sin(a * y) - Math.cos(b * x), + Math.sin(c * x) - Math.cos(d * y) + ] +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/popcorn.ts b/blog/2024-11-15-playing-with-fire/src/popcorn.ts new file mode 100644 index 0000000..4652960 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/popcorn.ts @@ -0,0 +1,10 @@ +// hidden-start +import {Coefs} from './coefs' +import {Variation} from './variations' +// hidden-end +export function popcorn({c, f}: Coefs): Variation { + return (x, y) => [ + x + c * Math.sin(Math.tan(3 * y)), + y + f * Math.sin(Math.tan(3 * x)) + ]; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/transform.ts b/blog/2024-11-15-playing-with-fire/src/transform.ts new file mode 100644 index 0000000..e719c57 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/transform.ts @@ -0,0 +1,9 @@ +import { Coefs } from './coefs' +import { Variation } from './variations' + +export interface Transform { + coefs: Coefs, + variations: [number, Variation][], + coefsPost: Coefs, + color: number +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/variations.ts b/blog/2024-11-15-playing-with-fire/src/variations.ts new file mode 100644 index 0000000..3b90d18 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/variations.ts @@ -0,0 +1 @@ +export type Variation = (x: number, y: number) => [number, number]; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/types.ts b/blog/2024-11-15-playing-with-fire/types.ts deleted file mode 100644 index 7d43ec5..0000000 --- a/blog/2024-11-15-playing-with-fire/types.ts +++ /dev/null @@ -1,24 +0,0 @@ -/** - * Affine transformation coefficients - */ -export type Coefs = { - a: number; - b: number; - c: number; - d: number; - e: number; - f: number; -}; - -export type Variation = ( - x: number, - y: number, - coefs: Coefs -) => [number, number]; - -export type Transform = { - coefs: Coefs, - coefsPost: Coefs, - variations: [number, Variation][], - color: number -} diff --git a/blog/2024-11-15-playing-with-fire/variation.ts b/blog/2024-11-15-playing-with-fire/variation.ts deleted file mode 100644 index ddf9ce6..0000000 --- a/blog/2024-11-15-playing-with-fire/variation.ts +++ /dev/null @@ -1,40 +0,0 @@ -import { Variation } from "./types"; - -export const linear: Variation = (x, y) => [x, y]; - -function r(x: number, y: number) { - return Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2)); -} - -function theta(x: number, y: number) { - return Math.atan2(x, y); -} - -function omega(): number { - return Math.random() > 0.5 ? Math.PI : 0; -} - -export const julia: Variation = (x, y) => { - const sqrtR = Math.sqrt(r(x, y)); - const thetaVal = theta(x, y) / 2 + omega(); - return [sqrtR * Math.cos(thetaVal), sqrtR * Math.sin(thetaVal)]; -}; - -export const popcorn: Variation = (x, y, transformCoefs) => { - return [ - x + transformCoefs.c * Math.sin(Math.tan(3 * y)), - y + transformCoefs.f * Math.sin(Math.tan(3 * x)), - ]; -}; - -export const pdj: ( - pdjA: number, - pdjB: number, - pdjC: number, - pdjD: number -) => Variation = (pdjA, pdjB, pdjC, pdjD) => { - return (x, y) => [ - Math.sin(pdjA * y) - Math.cos(pdjB * x), - Math.sin(pdjC * x) - Math.cos(pdjD * y), - ]; -}; diff --git a/docusaurus.config.ts b/docusaurus.config.ts index e2ee794..72d1a9c 100644 --- a/docusaurus.config.ts +++ b/docusaurus.config.ts @@ -81,7 +81,19 @@ const config: Config = { prism: { theme: prismThemes.oneLight, darkTheme: prismThemes.oneDark, - additionalLanguages: ['bash', 'java', 'julia', 'nasm'] + additionalLanguages: ['bash', 'java', 'julia', 'nasm'], + magicComments: [ + // Remember to extend the default highlight class name as well! + { + className: 'theme-code-block-highlighted-line', + line: 'highlight-next-line', + block: {start: 'highlight-start', end: 'highlight-end'}, + }, + { + className: 'code-block-hidden', + block: {start: 'hidden-start', end: 'hidden-end'} + } + ] }, } satisfies Preset.ThemeConfig, plugins: [require.resolve('docusaurus-lunr-search')], diff --git a/src/DualImage/index.tsx b/src/DualImage/index.tsx deleted file mode 100644 index 2e94211..0000000 --- a/src/DualImage/index.tsx +++ /dev/null @@ -1,13 +0,0 @@ -import {useColorMode} from "@docusaurus/theme-common"; -import React from "react"; - -interface Props { - srcLight: string; - srcDark: string; - alt: string; -} -const DualImage = ({srcLight, srcDark, alt}: Props) => { - const {colorMode} = useColorMode(); - return {alt} -} -export default DualImage; \ No newline at end of file diff --git a/src/css/custom.css b/src/css/custom.css index 7d691f0..9a455f7 100644 --- a/src/css/custom.css +++ b/src/css/custom.css @@ -29,4 +29,11 @@ adapted for Victory charts */ [data-theme='dark'] .VictoryContainer { filter: invert(75%) hue-rotate(180deg); +} + +/* +Custom magic comment for Prism - hide parts of the code in display + */ +.code-block-hidden { + display: none; } \ No newline at end of file From e2a0ee1d72fa896b2dfc31703cbeb8d53e76b127 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sat, 23 Nov 2024 15:26:48 -0500 Subject: [PATCH 08/51] Attempt to generalize --- .../1-introduction/Gasket.jsx | 5 +- .../1-introduction/biunit.ts | 3 - .../1-introduction/index.mdx | 8 +- .../1-introduction/plot.ts | 62 +++++++----- .../1-introduction/randint.ts | 3 - .../1-introduction/scope.ts | 8 +- .../src/FlameCanvas.tsx | 99 +++++++++++++++++++ .../src/randomBiunit.ts | 3 + .../src/randomChoice.ts | 22 +++++ .../src/randomInteger.ts | 3 + .../src/transform.ts | 5 +- 11 files changed, 177 insertions(+), 44 deletions(-) delete mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts delete mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/randint.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/FlameCanvas.tsx create mode 100644 blog/2024-11-15-playing-with-fire/src/randomBiunit.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/randomChoice.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/randomInteger.ts diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx index 5dcc0e5..36b32ea 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx @@ -9,6 +9,7 @@ const functions = [ ] function chaosGame(image) { + var plotter = new Plotter(image.width, image.height); var [x, y] = [randomBiUnit(), randomBiUnit()]; for (var count = 0; count < iterations; count++) { @@ -16,9 +17,11 @@ function chaosGame(image) { [x, y] = functions[i](x, y); if (count > 20) { - plot(x, y, image); + plotter.plot(x, y); } } + + plotter.paint(image); } render() diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts b/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts deleted file mode 100644 index 21bf035..0000000 --- a/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts +++ /dev/null @@ -1,3 +0,0 @@ -export default function randomBiUnit() { - return Math.random() * 2 - 1; -} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index 9e6758c..74c34a3 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -157,15 +157,15 @@ Let's turn this into code, one piece at a time. First, the "bi-unit square" is the range $[-1, 1]$. We can pick a random point like this: -import biunitSource from '!!raw-loader!./biunit' +import randomBiunitSource from '!!raw-loader!../src/randomBiunit' -{biunitSource} +{randomBiunitSource} Next, we need to choose a random integer from $0$ to $n - 1$: -import randintSource from '!!raw-loader!./randint' +import randomIntegerSource from '!!raw-loader!../src/randomInteger' -{randintSource} +{randomIntegerSource} Finally, implementing the `plot` function. Web browsers have a [Canvas API](https://developer.mozilla.org/en-US/docs/Web/API/Canvas_API) we can use for 2D graphics. In our case, the plot function will take an $(x,y)$ coordinate and plot it by diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts index 3bf9f03..523635c 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts @@ -1,32 +1,40 @@ -export default function plot(x: number, y: number, image: ImageData) { - // Translate (x,y) coordinates to pixel coordinates. - // The display range we care about is x=[0, 1], y=[0, 1], - // so our pixelX and pixelY coordinates are easy to calculate: - const pixelX = Math.floor(x * image.width); - const pixelY = Math.floor(y * image.height); +export function imageIndex(x: number, y: number, width: number, stride: number): number { + return y * (width * stride) + x * 4; +} - // If we have an (x,y) coordinate outside the display range, - // skip it - if ( - pixelX < 0 || - pixelX > image.width || - pixelY < 0 || - pixelY > image.height - ) { - return; +export class Plotter { + private readonly pixels: Array; + + constructor(private readonly width: number, private readonly height: number) { + this.pixels = new Array(width * height).fill(false); } - // ImageData is an array that contains four bytes per pixel - // (one for each of the red, green, blue, and alpha values). - // The (pixelX, pixelY) coordinates are used to find where - // in the image we need to write. - const index = pixelY * (image.width * 4) + pixelX * 4; + public plot(x: number, y: number) { + // Translate (x,y) coordinates to pixel coordinates. + // The display range we care about is x=[0, 1], y=[0, 1], + // so our pixelX and pixelY coordinates are easy to calculate: + const pixelX = Math.floor(x * this.width); + const pixelY = Math.floor(y * this.height); - // Set the pixel to black by writing a 0 to the first three - // bytes (red, green, blue), and 256 to the last byte (alpha), - // starting at our index: - image.data[index] = 0; - image.data[index + 1] = 0; - image.data[index + 2] = 0; - image.data[index + 3] = 0xff; + // Translate the pixel coordinates into an index + const pixelIndex = imageIndex(pixelX, pixelY, this.width, 1); + + // If the index is valid, enable that pixel + if (0 <= pixelIndex && pixelIndex < this.pixels.length) { + this.pixels[pixelIndex] = true; + } + } + + public paint(image: ImageData) { + // "Paint" all our pixels by setting their value to black + for (var pixelIndex = 0; pixelIndex < this.pixels.length; pixelIndex++) { + if (this.pixels[pixelIndex]) { + const imageIndex = pixelIndex * 4; + image.data[imageIndex] = 0; // red + image.data[imageIndex + 1] = 0; // green + image.data[imageIndex + 2] = 0; // blue + image.data[imageIndex + 3] = 0xff; // alpha + } + } + } } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts b/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts deleted file mode 100644 index 07d79a3..0000000 --- a/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts +++ /dev/null @@ -1,3 +0,0 @@ -export default function randomInteger(min: number, max: number) { - return Math.floor(Math.random() * (max - min)) + min; -} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts b/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts index f020b05..ff3fcbf 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts @@ -1,13 +1,13 @@ import React from 'react'; -import randomBiUnit from './biunit'; -import plot from './plot'; -import randomInteger from './randint'; +import { randomBiUnit } from '../src/randomBiunit'; +import { Plotter } from './plot'; +import { randomInteger } from '../src/randomInteger'; import Canvas from './Canvas'; const Scope = { React, - plot, + Plotter, randomBiUnit, randomInteger, Canvas diff --git a/blog/2024-11-15-playing-with-fire/src/FlameCanvas.tsx b/blog/2024-11-15-playing-with-fire/src/FlameCanvas.tsx new file mode 100644 index 0000000..4b9563c --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/FlameCanvas.tsx @@ -0,0 +1,99 @@ +import {createContext, useEffect, useRef, useState} from "react"; +import {Transform} from "./transform"; +import {randomBiUnit} from "./randomBiunit"; +import {useColorMode} from "@docusaurus/theme-common"; +import {randomChoice} from "./randomChoice"; + +export interface Flame { + transforms: [number, Transform][]; + final: Transform; + palette: Uint8Array; +} + +interface IFlameContext { + setQuality?: (quality: number) => void; + setFlame?: (flame: Flame) => void; +} + +export const FlameContext = createContext({}); + +abstract class Renderer { + protected readonly _size: number; + protected _x: number = randomBiUnit(); + protected _y: number = randomBiUnit(); + protected _iterations: number = 0; + + protected _flame?: Flame; + + protected constructor(size: number) { + this._size = size; + } + + abstract plot(x: number, y: number, c: number): void; + abstract run(iterations: number): void; + abstract paint(image: ImageData): void; + + public get size(): number { + return this._size; + } + + public get iterations(): number { + return this._iterations; + } + + public set flame(value: Flame) { + [this._x, this._y] = [randomBiUnit(), randomBiUnit()]; + this._iterations = 0; + } +} + +export interface Props { + renderer: Renderer; + children?: React.ReactNode; +} + +export const FlameCanvas: React.FC = ({renderer, children}) => { + const ITER_STEP = 10000; + const canvasRef = useRef(null); + + const colorMode = useColorMode(); + const [quality, setQuality] = useState(); + const [flame, setFlame] = useState(null); + + var image: ImageData = null; + + function animate() { + renderer.run(ITER_STEP); + paint(); + + if (renderer.iterations < quality * renderer.size * renderer.size) { + requestAnimationFrame(this); + } + } + + function paint() { + + } + + useEffect(() => { + renderer.flame = flame; + requestAnimationFrame(animate); + }, [quality, flame]); + + useEffect(() => { paint(); }, [colorMode]); + + return ( + + + {children} + + ) +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/randomBiunit.ts b/blog/2024-11-15-playing-with-fire/src/randomBiunit.ts new file mode 100644 index 0000000..7e5f389 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/randomBiunit.ts @@ -0,0 +1,3 @@ +export function randomBiUnit() { + return Math.random() * 2 - 1; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/randomChoice.ts b/blog/2024-11-15-playing-with-fire/src/randomChoice.ts new file mode 100644 index 0000000..4920f87 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/randomChoice.ts @@ -0,0 +1,22 @@ +/** + * @param choices array of [weight, value] pairs + * @returns pair of [index, value] + */ +export function randomChoice(choices: [number, T][]): [number, T] { + const weightSum = choices.reduce( + (current, [weight, _]) => current + weight, + 0 + ); + var choice = Math.random() * weightSum; + + for (var i = 0; i < choices.length; i++) { + const [weight, t] = choices[i]; + if (choice < weight) { + return [i, t]; + } + + choice -= weight; + } + + throw "unreachable"; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/randomInteger.ts b/blog/2024-11-15-playing-with-fire/src/randomInteger.ts new file mode 100644 index 0000000..c3a6719 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/randomInteger.ts @@ -0,0 +1,3 @@ +export function randomInteger(min: number, max: number) { + return Math.floor(Math.random() * (max - min)) + min; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/transform.ts b/blog/2024-11-15-playing-with-fire/src/transform.ts index e719c57..3caf1fa 100644 --- a/blog/2024-11-15-playing-with-fire/src/transform.ts +++ b/blog/2024-11-15-playing-with-fire/src/transform.ts @@ -4,6 +4,7 @@ import { Variation } from './variations' export interface Transform { coefs: Coefs, variations: [number, Variation][], - coefsPost: Coefs, - color: number + enabled: boolean, + coefsPost?: Coefs, + color?: number } \ No newline at end of file From 0a45267ea187a5558d5ce02db7a03435a04033e9 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sat, 23 Nov 2024 15:27:02 -0500 Subject: [PATCH 09/51] Revert "Attempt to generalize" This reverts commit e2a0ee1d72fa896b2dfc31703cbeb8d53e76b127. --- .../1-introduction/Gasket.jsx | 5 +- .../1-introduction/biunit.ts | 3 + .../1-introduction/index.mdx | 8 +- .../1-introduction/plot.ts | 62 +++++------- .../1-introduction/randint.ts | 3 + .../1-introduction/scope.ts | 8 +- .../src/FlameCanvas.tsx | 99 ------------------- .../src/randomBiunit.ts | 3 - .../src/randomChoice.ts | 22 ----- .../src/randomInteger.ts | 3 - .../src/transform.ts | 5 +- 11 files changed, 44 insertions(+), 177 deletions(-) create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/randint.ts delete mode 100644 blog/2024-11-15-playing-with-fire/src/FlameCanvas.tsx delete mode 100644 blog/2024-11-15-playing-with-fire/src/randomBiunit.ts delete mode 100644 blog/2024-11-15-playing-with-fire/src/randomChoice.ts delete mode 100644 blog/2024-11-15-playing-with-fire/src/randomInteger.ts diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx index 36b32ea..5dcc0e5 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx @@ -9,7 +9,6 @@ const functions = [ ] function chaosGame(image) { - var plotter = new Plotter(image.width, image.height); var [x, y] = [randomBiUnit(), randomBiUnit()]; for (var count = 0; count < iterations; count++) { @@ -17,11 +16,9 @@ function chaosGame(image) { [x, y] = functions[i](x, y); if (count > 20) { - plotter.plot(x, y); + plot(x, y, image); } } - - plotter.paint(image); } render() diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts b/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts new file mode 100644 index 0000000..21bf035 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts @@ -0,0 +1,3 @@ +export default function randomBiUnit() { + return Math.random() * 2 - 1; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index 74c34a3..9e6758c 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -157,15 +157,15 @@ Let's turn this into code, one piece at a time. First, the "bi-unit square" is the range $[-1, 1]$. We can pick a random point like this: -import randomBiunitSource from '!!raw-loader!../src/randomBiunit' +import biunitSource from '!!raw-loader!./biunit' -{randomBiunitSource} +{biunitSource} Next, we need to choose a random integer from $0$ to $n - 1$: -import randomIntegerSource from '!!raw-loader!../src/randomInteger' +import randintSource from '!!raw-loader!./randint' -{randomIntegerSource} +{randintSource} Finally, implementing the `plot` function. Web browsers have a [Canvas API](https://developer.mozilla.org/en-US/docs/Web/API/Canvas_API) we can use for 2D graphics. In our case, the plot function will take an $(x,y)$ coordinate and plot it by diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts index 523635c..3bf9f03 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts @@ -1,40 +1,32 @@ -export function imageIndex(x: number, y: number, width: number, stride: number): number { - return y * (width * stride) + x * 4; -} +export default function plot(x: number, y: number, image: ImageData) { + // Translate (x,y) coordinates to pixel coordinates. + // The display range we care about is x=[0, 1], y=[0, 1], + // so our pixelX and pixelY coordinates are easy to calculate: + const pixelX = Math.floor(x * image.width); + const pixelY = Math.floor(y * image.height); -export class Plotter { - private readonly pixels: Array; - - constructor(private readonly width: number, private readonly height: number) { - this.pixels = new Array(width * height).fill(false); + // If we have an (x,y) coordinate outside the display range, + // skip it + if ( + pixelX < 0 || + pixelX > image.width || + pixelY < 0 || + pixelY > image.height + ) { + return; } - public plot(x: number, y: number) { - // Translate (x,y) coordinates to pixel coordinates. - // The display range we care about is x=[0, 1], y=[0, 1], - // so our pixelX and pixelY coordinates are easy to calculate: - const pixelX = Math.floor(x * this.width); - const pixelY = Math.floor(y * this.height); + // ImageData is an array that contains four bytes per pixel + // (one for each of the red, green, blue, and alpha values). + // The (pixelX, pixelY) coordinates are used to find where + // in the image we need to write. + const index = pixelY * (image.width * 4) + pixelX * 4; - // Translate the pixel coordinates into an index - const pixelIndex = imageIndex(pixelX, pixelY, this.width, 1); - - // If the index is valid, enable that pixel - if (0 <= pixelIndex && pixelIndex < this.pixels.length) { - this.pixels[pixelIndex] = true; - } - } - - public paint(image: ImageData) { - // "Paint" all our pixels by setting their value to black - for (var pixelIndex = 0; pixelIndex < this.pixels.length; pixelIndex++) { - if (this.pixels[pixelIndex]) { - const imageIndex = pixelIndex * 4; - image.data[imageIndex] = 0; // red - image.data[imageIndex + 1] = 0; // green - image.data[imageIndex + 2] = 0; // blue - image.data[imageIndex + 3] = 0xff; // alpha - } - } - } + // Set the pixel to black by writing a 0 to the first three + // bytes (red, green, blue), and 256 to the last byte (alpha), + // starting at our index: + image.data[index] = 0; + image.data[index + 1] = 0; + image.data[index + 2] = 0; + image.data[index + 3] = 0xff; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts b/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts new file mode 100644 index 0000000..07d79a3 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts @@ -0,0 +1,3 @@ +export default function randomInteger(min: number, max: number) { + return Math.floor(Math.random() * (max - min)) + min; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts b/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts index ff3fcbf..f020b05 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts @@ -1,13 +1,13 @@ import React from 'react'; -import { randomBiUnit } from '../src/randomBiunit'; -import { Plotter } from './plot'; -import { randomInteger } from '../src/randomInteger'; +import randomBiUnit from './biunit'; +import plot from './plot'; +import randomInteger from './randint'; import Canvas from './Canvas'; const Scope = { React, - Plotter, + plot, randomBiUnit, randomInteger, Canvas diff --git a/blog/2024-11-15-playing-with-fire/src/FlameCanvas.tsx b/blog/2024-11-15-playing-with-fire/src/FlameCanvas.tsx deleted file mode 100644 index 4b9563c..0000000 --- a/blog/2024-11-15-playing-with-fire/src/FlameCanvas.tsx +++ /dev/null @@ -1,99 +0,0 @@ -import {createContext, useEffect, useRef, useState} from "react"; -import {Transform} from "./transform"; -import {randomBiUnit} from "./randomBiunit"; -import {useColorMode} from "@docusaurus/theme-common"; -import {randomChoice} from "./randomChoice"; - -export interface Flame { - transforms: [number, Transform][]; - final: Transform; - palette: Uint8Array; -} - -interface IFlameContext { - setQuality?: (quality: number) => void; - setFlame?: (flame: Flame) => void; -} - -export const FlameContext = createContext({}); - -abstract class Renderer { - protected readonly _size: number; - protected _x: number = randomBiUnit(); - protected _y: number = randomBiUnit(); - protected _iterations: number = 0; - - protected _flame?: Flame; - - protected constructor(size: number) { - this._size = size; - } - - abstract plot(x: number, y: number, c: number): void; - abstract run(iterations: number): void; - abstract paint(image: ImageData): void; - - public get size(): number { - return this._size; - } - - public get iterations(): number { - return this._iterations; - } - - public set flame(value: Flame) { - [this._x, this._y] = [randomBiUnit(), randomBiUnit()]; - this._iterations = 0; - } -} - -export interface Props { - renderer: Renderer; - children?: React.ReactNode; -} - -export const FlameCanvas: React.FC = ({renderer, children}) => { - const ITER_STEP = 10000; - const canvasRef = useRef(null); - - const colorMode = useColorMode(); - const [quality, setQuality] = useState(); - const [flame, setFlame] = useState(null); - - var image: ImageData = null; - - function animate() { - renderer.run(ITER_STEP); - paint(); - - if (renderer.iterations < quality * renderer.size * renderer.size) { - requestAnimationFrame(this); - } - } - - function paint() { - - } - - useEffect(() => { - renderer.flame = flame; - requestAnimationFrame(animate); - }, [quality, flame]); - - useEffect(() => { paint(); }, [colorMode]); - - return ( - - - {children} - - ) -} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/randomBiunit.ts b/blog/2024-11-15-playing-with-fire/src/randomBiunit.ts deleted file mode 100644 index 7e5f389..0000000 --- a/blog/2024-11-15-playing-with-fire/src/randomBiunit.ts +++ /dev/null @@ -1,3 +0,0 @@ -export function randomBiUnit() { - return Math.random() * 2 - 1; -} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/randomChoice.ts b/blog/2024-11-15-playing-with-fire/src/randomChoice.ts deleted file mode 100644 index 4920f87..0000000 --- a/blog/2024-11-15-playing-with-fire/src/randomChoice.ts +++ /dev/null @@ -1,22 +0,0 @@ -/** - * @param choices array of [weight, value] pairs - * @returns pair of [index, value] - */ -export function randomChoice(choices: [number, T][]): [number, T] { - const weightSum = choices.reduce( - (current, [weight, _]) => current + weight, - 0 - ); - var choice = Math.random() * weightSum; - - for (var i = 0; i < choices.length; i++) { - const [weight, t] = choices[i]; - if (choice < weight) { - return [i, t]; - } - - choice -= weight; - } - - throw "unreachable"; -} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/randomInteger.ts b/blog/2024-11-15-playing-with-fire/src/randomInteger.ts deleted file mode 100644 index c3a6719..0000000 --- a/blog/2024-11-15-playing-with-fire/src/randomInteger.ts +++ /dev/null @@ -1,3 +0,0 @@ -export function randomInteger(min: number, max: number) { - return Math.floor(Math.random() * (max - min)) + min; -} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/transform.ts b/blog/2024-11-15-playing-with-fire/src/transform.ts index 3caf1fa..e719c57 100644 --- a/blog/2024-11-15-playing-with-fire/src/transform.ts +++ b/blog/2024-11-15-playing-with-fire/src/transform.ts @@ -4,7 +4,6 @@ import { Variation } from './variations' export interface Transform { coefs: Coefs, variations: [number, Variation][], - enabled: boolean, - coefsPost?: Coefs, - color?: number + coefsPost: Coefs, + color: number } \ No newline at end of file From 22a4ffff7cb4f45ae37c04a9489494e13cb5a86f Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 24 Nov 2024 00:06:22 -0500 Subject: [PATCH 10/51] Move image painting to a context component --- .../1-introduction/Canvas.tsx | 34 ----------- .../{Gasket.jsx => chaosGame.js} | 2 +- .../1-introduction/index.mdx | 4 +- .../1-introduction/scope.ts | 15 ----- .../1-introduction/scope.tsx | 30 ++++++++++ .../src/Canvas.tsx | 59 +++++++++++++++++++ 6 files changed, 92 insertions(+), 52 deletions(-) delete mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/Canvas.tsx rename blog/2024-11-15-playing-with-fire/1-introduction/{Gasket.jsx => chaosGame.js} (93%) delete mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/scope.ts create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx create mode 100644 blog/2024-11-15-playing-with-fire/src/Canvas.tsx diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/Canvas.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/Canvas.tsx deleted file mode 100644 index 262c50d..0000000 --- a/blog/2024-11-15-playing-with-fire/1-introduction/Canvas.tsx +++ /dev/null @@ -1,34 +0,0 @@ -import {useEffect, useRef} from "react"; - -interface Props { - renderFn: (ImageData) => void -} - -export const Canvas: React.FC = ({renderFn}: Props) => { - const canvasRef = useRef(null); - - useEffect(() => { - const ctx = canvasRef.current?.getContext("2d"); - if (!ctx) { - console.log("Canvas not ready"); - } - - const image = ctx.createImageData(canvasRef.current.width, canvasRef.current.height); - renderFn(image); - ctx.putImageData(image, 0, 0); - }, []); - - return ( - - ); -}; - -export default Canvas; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js similarity index 93% rename from blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx rename to blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js index 5dcc0e5..49f004f 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.jsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js @@ -21,4 +21,4 @@ function chaosGame(image) { } } -render() +render() diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index 9e6758c..7cdeb02 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -178,9 +178,9 @@ import plotSource from '!!raw-loader!./plot' import Playground from '@theme/Playground' import Scope from './scope' -import Gasket from '!!raw-loader!./Gasket' +import chaosGameSource from '!!raw-loader!./chaosGame' -{Gasket} +{chaosGameSource}
    diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts b/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts deleted file mode 100644 index f020b05..0000000 --- a/blog/2024-11-15-playing-with-fire/1-introduction/scope.ts +++ /dev/null @@ -1,15 +0,0 @@ -import React from 'react'; - -import randomBiUnit from './biunit'; -import plot from './plot'; -import randomInteger from './randint'; -import Canvas from './Canvas'; - -const Scope = { - React, - plot, - randomBiUnit, - randomInteger, - Canvas -} -export default Scope; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx new file mode 100644 index 0000000..eeefb2c --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx @@ -0,0 +1,30 @@ +import React, {useContext, useEffect} from "react"; +import randomBiUnit from './biunit'; +import plot from './plot'; +import randomInteger from './randint'; +import Canvas, {ImageContext} from "../src/Canvas"; + +interface Props { + renderFn: (image: ImageData) => void; +} +function Render({renderFn}: Props) { + const {width, height, setImage} = useContext(ImageContext); + const image = new ImageData(width, height); + + useEffect(() => { + renderFn(image); + setImage(image); + }, []); + + return <>; +} + +const Scope = { + plot, + randomBiUnit, + randomInteger, + Canvas, + Gasket: ({renderFn}: Props) => + +} +export default Scope; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx new file mode 100644 index 0000000..2835555 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -0,0 +1,59 @@ +import React, {createContext, useCallback, useContext, useEffect, useRef, useState} from "react"; +import {useColorMode} from "@docusaurus/theme-common"; + +interface IImageContext { + width: number; + height: number; + setImage: (image: ImageData) => void; +} +export const ImageContext = createContext(null); + +interface Props { + width: number; + height: number; + children?: React.ReactNode; +} +export default function Canvas({width, height, children}) { + const [canvasCtx, setCanvasCtx] = useState(null); + const canvasRef = useCallback(node => { + if (node !== null) { + setCanvasCtx(node.getContext("2d")); + } + }, []); + + const {colorMode} = useColorMode(); + const [image, setImage] = useState(new ImageData(width, height)); + const paintImage = new ImageData(width, height); + + useEffect(() => { + if (!canvasCtx) { + return; + } + + for (const [index, value] of image.data.entries()) { + // If dark mode is active, invert the color scheme + const adjustValue = colorMode === 'light' ? value : 255 - value; + + // Alpha values never change + paintImage.data[index] = index % 4 === 3 ? value : adjustValue; + } + + console.log("Painting image"); + canvasCtx.putImageData(paintImage, 0, 0); + }, [canvasCtx, colorMode, image]); + + return ( + + + {children} + + ) +} \ No newline at end of file From 4c3f4246a4579e0b425c9deadc30aea8eb7bb790 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 24 Nov 2024 18:59:11 -0500 Subject: [PATCH 11/51] Incremental rendering --- .../1-introduction/chaosGame.js | 48 ++++++++++------ .../1-introduction/scope.tsx | 22 +------- .../src/Canvas.tsx | 55 ++++++++++--------- 3 files changed, 64 insertions(+), 61 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js index 49f004f..ca42723 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js @@ -1,24 +1,40 @@ -// Hint: try increasing the iteration count -const iterations = 10000; +function Gasket() { + // Hint: try increasing the iteration count + const iterations = 10000; -// Hint: negating `x` and `y` creates some interesting images -const functions = [ - (x, y) => [x / 2, y / 2], - (x, y) => [(x + 1) / 2, y / 2], - (x, y) => [x / 2, (y + 1) / 2] -] + // Hint: negating `x` and `y` creates some interesting images + const functions = [ + (x, y) => [x / 2, y / 2], + (x, y) => [(x + 1) / 2, y / 2], + (x, y) => [x / 2, (y + 1) / 2] + ] -function chaosGame(image) { - var [x, y] = [randomBiUnit(), randomBiUnit()]; + const image = new ImageData(600, 600); + function* chaosGame() { + var [x, y] = [randomBiUnit(), randomBiUnit()]; - for (var count = 0; count < iterations; count++) { - const i = randomInteger(0, functions.length); - [x, y] = functions[i](x, y); + for (var count = 0; count < iterations; count++) { + const i = randomInteger(0, functions.length); + [x, y] = functions[i](x, y); - if (count > 20) { - plot(x, y, image); + if (count > 20) { + plot(x, y, image); + } + + if (count % 1000 === 0) { + yield image; + } } + + yield image; } + + return ( + + ) } -render() +render() diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx index eeefb2c..d5d2d99 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx @@ -1,30 +1,12 @@ -import React, {useContext, useEffect} from "react"; import randomBiUnit from './biunit'; import plot from './plot'; import randomInteger from './randint'; -import Canvas, {ImageContext} from "../src/Canvas"; - -interface Props { - renderFn: (image: ImageData) => void; -} -function Render({renderFn}: Props) { - const {width, height, setImage} = useContext(ImageContext); - const image = new ImageData(width, height); - - useEffect(() => { - renderFn(image); - setImage(image); - }, []); - - return <>; -} +import Canvas from "../src/Canvas"; const Scope = { plot, randomBiUnit, randomInteger, - Canvas, - Gasket: ({renderFn}: Props) => - + Canvas } export default Scope; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 2835555..35f3c7a 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -1,49 +1,54 @@ -import React, {createContext, useCallback, useContext, useEffect, useRef, useState} from "react"; +import React, {useCallback, useEffect, useState} from "react"; import {useColorMode} from "@docusaurus/theme-common"; -interface IImageContext { - width: number; - height: number; - setImage: (image: ImageData) => void; -} -export const ImageContext = createContext(null); - interface Props { width: number; height: number; + painter: Iterator; children?: React.ReactNode; } -export default function Canvas({width, height, children}) { - const [canvasCtx, setCanvasCtx] = useState(null); +export default function Canvas({width, height, painter, children}: Props) { + const {colorMode} = useColorMode(); + const [image, setImage] = useState<[ImageData]>(null); + + const [canvasCtx, setCanvasCtx] = useState(null); const canvasRef = useCallback(node => { if (node !== null) { setCanvasCtx(node.getContext("2d")); } }, []); - const {colorMode} = useColorMode(); - const [image, setImage] = useState(new ImageData(width, height)); const paintImage = new ImageData(width, height); - - useEffect(() => { - if (!canvasCtx) { + const paint = () => { + if (!canvasCtx || !image) { return; } - for (const [index, value] of image.data.entries()) { - // If dark mode is active, invert the color scheme - const adjustValue = colorMode === 'light' ? value : 255 - value; - - // Alpha values never change - paintImage.data[index] = index % 4 === 3 ? value : adjustValue; + for (const [index, value] of image[0].data.entries()) { + if (index % 4 === 3) { + // Alpha values are copied as-is + paintImage.data[index] = value; + } else { + // If dark mode is active, invert the color + paintImage.data[index] = colorMode === 'light' ? value : 255 - value; + } } - console.log("Painting image"); canvasCtx.putImageData(paintImage, 0, 0); - }, [canvasCtx, colorMode, image]); + } + useEffect(paint, [colorMode, image]); + + const animate = () => { + const nextImage = painter.next().value; + if (nextImage) { + setImage([nextImage]) + requestAnimationFrame(animate); + } + } + useEffect(animate, [canvasCtx]); return ( - + <> {children} - + ) } \ No newline at end of file From 7759b58dbe3ef13aa960ca0baa20ada19054feed Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 24 Nov 2024 22:37:53 -0500 Subject: [PATCH 12/51] Basic function weights --- .../1-introduction/GasketWeighted.tsx | 61 +++++++++++++++++++ .../1-introduction/biunit.ts | 3 - .../1-introduction/chaosGame.js | 10 ++- .../1-introduction/chaosGameWeighted.ts | 32 ++++++++++ .../1-introduction/index.mdx | 26 ++++++-- .../1-introduction/plot.ts | 2 +- .../1-introduction/randint.ts | 3 - .../1-introduction/scope.tsx | 6 +- .../2-transforms/BaselineRender.ts | 5 -- .../2-transforms/baseline.ts | 22 ------- .../2-transforms/index.mdx | 10 +-- .../src/Canvas.tsx | 7 ++- .../2024-11-15-playing-with-fire/src/julia.ts | 2 +- .../src/linear.ts | 2 +- .../src/params.ts | 1 - blog/2024-11-15-playing-with-fire/src/pdj.ts | 2 +- .../src/popcorn.ts | 2 +- .../src/randomBiUnit.ts | 3 + .../src/randomChoice.ts | 15 +++++ .../src/randomInteger.ts | 3 + .../src/transform.ts | 2 +- .../src/{variations.ts => variation.ts} | 0 package-lock.json | 14 +++++ package.json | 1 + 24 files changed, 172 insertions(+), 62 deletions(-) create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx delete mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts delete mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/randint.ts delete mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/BaselineRender.ts delete mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/baseline.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/randomBiUnit.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/randomChoice.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/randomInteger.ts rename blog/2024-11-15-playing-with-fire/src/{variations.ts => variation.ts} (100%) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx new file mode 100644 index 0000000..d909aeb --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx @@ -0,0 +1,61 @@ +import {useEffect, useState} from "react"; +import Canvas from "../src/Canvas"; +import { Params, chaosGameWeighted } from "./chaosGameWeighted"; +import TeX from '@matejmazur/react-katex'; + +type Transform = (x: number, y: number) => [number, number]; + +function WeightInput({value, setValue, children}) { + return ( +
    + {children} + setValue(Number(e.currentTarget.value))}/> +
    + ) +} + +export default function GasketWeighted() { + const image = new ImageData(600, 600); + const iterations = 100_000; + const step = 1000; + + const [f0Weight, setF0Weight] = useState(1); + const [f1Weight, setF1Weight] = useState(1); + const [f2Weight, setF2Weight] = useState(1); + + const f0: Transform = (x, y) => [x / 2, y / 2]; + const f1: Transform = (x, y) => [(x + 1) / 2, y / 2]; + const f2: Transform = (x, y) => [x / 2, (y + 1) / 2]; + + const [game, setGame] = useState>(null); + useEffect(() => { + const params: Params = { + transforms: [ + [f0Weight, f0], + [f1Weight, f1], + [f2Weight, f2] + ], + image, + iterations, + step + } + setGame(chaosGameWeighted(params)) + }, [f0Weight, f1Weight, f2Weight]); + + return ( + <> + +
    + +

    F_0 weight:{f0Weight}

    +
    + +

    F_1 weight:{f1Weight}

    +
    + +

    F_2 weight:{f2Weight}

    +
    +
    + + ) +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts b/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts deleted file mode 100644 index 21bf035..0000000 --- a/blog/2024-11-15-playing-with-fire/1-introduction/biunit.ts +++ /dev/null @@ -1,3 +0,0 @@ -export default function randomBiUnit() { - return Math.random() * 2 - 1; -} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js index ca42723..8d02cc4 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js @@ -2,20 +2,24 @@ function Gasket() { // Hint: try increasing the iteration count const iterations = 10000; + // Display the progress every `step` iterations + const step = 1000; + // Hint: negating `x` and `y` creates some interesting images - const functions = [ + const transforms = [ (x, y) => [x / 2, y / 2], (x, y) => [(x + 1) / 2, y / 2], (x, y) => [x / 2, (y + 1) / 2] ] const image = new ImageData(600, 600); + function* chaosGame() { var [x, y] = [randomBiUnit(), randomBiUnit()]; for (var count = 0; count < iterations; count++) { - const i = randomInteger(0, functions.length); - [x, y] = functions[i](x, y); + const i = randomInteger(0, transforms.length); + [x, y] = transforms[i](x, y); if (count > 20) { plot(x, y, image); diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts new file mode 100644 index 0000000..4f39635 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts @@ -0,0 +1,32 @@ +// hidden-start +import { randomBiUnit } from "../src/randomBiUnit"; +import { randomChoice } from "../src/randomChoice"; +import { plot } from "./plot" +export type Transform = (x: number, y: number) => [number, number]; +export type Params = { + transforms: [number, Transform][], + image: ImageData, + iterations: number, + step: number +} +// hidden-end +export function* chaosGameWeighted({transforms, image, iterations, step}: Params) { + var [x, y] = [randomBiUnit(), randomBiUnit()]; + + for (let i = 0; i < iterations; i++) { + // highlight-start + const [_, transform] = randomChoice(transforms); + // highlight-end + [x, y] = transform(x, y); + + if (i > 20) { + plot(x, y, image); + } + + if (i % step === 0) { + yield image; + } + } + + yield image; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index 7cdeb02..a8c1347 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -126,7 +126,7 @@ Fractal flames use more complex functions to produce a wide variety of images, b ## Sierpinski's gasket -Using these definitions, we can build the first image. The paper defines a function system we can use as-is: +Using these definitions, we can build the first image. The paper defines a function system for us: $$ F_0(x, y) = \left({x \over 2}, {y \over 2} \right) @@ -157,13 +157,13 @@ Let's turn this into code, one piece at a time. First, the "bi-unit square" is the range $[-1, 1]$. We can pick a random point like this: -import biunitSource from '!!raw-loader!./biunit' +import biunitSource from '!!raw-loader!../src/randomBiUnit' {biunitSource} Next, we need to choose a random integer from $0$ to $n - 1$: -import randintSource from '!!raw-loader!./randint' +import randintSource from '!!raw-loader!../src/randomInteger' {randintSource} @@ -185,8 +185,22 @@ import chaosGameSource from '!!raw-loader!./chaosGame'
    -Note: The image our chaos game generates is different than the fractal flame paper, but I think the version displayed -here is correct. As confirmation, the next post will re-create the same image using a different method. +Note: The image here is different than the fractal flame paper, but I think the paper has an error. -TODO: Explanation of function weights $w_i$ \ No newline at end of file +## Weights + +Finally, we'll introduce a "weight" parameter ($w_i$) assigned to each function, which controls +how often that function is used: + +import randomChoiceSource from '!!raw-loader!../src/randomChoice' + +{randomChoiceSource} + +import chaosGameWeightedSource from "!!raw-loader!./chaosGameWeighted"; + +{chaosGameWeightedSource} + +import GasketWeighted from "./GasketWeighted" + + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts index 3bf9f03..e18a5b0 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts @@ -1,4 +1,4 @@ -export default function plot(x: number, y: number, image: ImageData) { +export function plot(x: number, y: number, image: ImageData) { // Translate (x,y) coordinates to pixel coordinates. // The display range we care about is x=[0, 1], y=[0, 1], // so our pixelX and pixelY coordinates are easy to calculate: diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts b/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts deleted file mode 100644 index 07d79a3..0000000 --- a/blog/2024-11-15-playing-with-fire/1-introduction/randint.ts +++ /dev/null @@ -1,3 +0,0 @@ -export default function randomInteger(min: number, max: number) { - return Math.floor(Math.random() * (max - min)) + min; -} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx index d5d2d99..5b2dd7b 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx @@ -1,6 +1,6 @@ -import randomBiUnit from './biunit'; -import plot from './plot'; -import randomInteger from './randint'; +import { plot } from './plot'; +import { randomBiUnit } from '../src/randomBiUnit'; +import { randomInteger } from '../src/randomInteger'; import Canvas from "../src/Canvas"; const Scope = { diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/BaselineRender.ts b/blog/2024-11-15-playing-with-fire/2-transforms/BaselineRender.ts deleted file mode 100644 index 315aacb..0000000 --- a/blog/2024-11-15-playing-with-fire/2-transforms/BaselineRender.ts +++ /dev/null @@ -1,5 +0,0 @@ -import {useColorMode, useThemeConfig} from "@docusaurus/theme-common"; - -export default function BaselineRender({children}) { - const {colorMode, setColorMode} = useColorMode(); -} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/baseline.ts b/blog/2024-11-15-playing-with-fire/2-transforms/baseline.ts deleted file mode 100644 index 1708e81..0000000 --- a/blog/2024-11-15-playing-with-fire/2-transforms/baseline.ts +++ /dev/null @@ -1,22 +0,0 @@ -// hidden-start -import { Coefs } from './coefs' -import { Variation } from './variations' -// hidden-end -export function applyTransform( - x: number, - y: number, - coefs: Coefs, - variations: [number, Variation][]) -{ - const transformX = coefs.a * x + coefs.b * y + coefs.c; - const transformY = coefs.d * x + coefs.e * y + coefs.f; - - var finalX = 0; - var finalY = 0; - for (const [blend, variation] of variations) { - const [variationX, variationY] = variation(transformX, transformY); - finalX += blend * variationX; - finalY += blend * variationY; - } - return [finalX, finalY]; -} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index ddccc50..87e4e53 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -66,9 +66,6 @@ import linearSrc from '!!raw-loader!../src/linear' {linearSrc} -Before we move on, it's worth mentioning the relationship between this variation and the Sierpinski Gasket. -Specifically, we can think of the Gasket as a fractal flame that uses only the linear variation. - ### Julia (variation 13) This variation still uses just the $x$ and $y$ coordinates, but does crazy things with them: @@ -132,11 +129,6 @@ $$ The formula looks intimidating, but it's not hard to implement: -import baselineSrc from '!!raw-loader!./baseline' - -{baselineSrc} - -TODO: Mention that the Sierpinski Gasket is just a blend with linear weight 1, all others 0. Maybe replace comment above about Sierpinski Gasket and linear transform? +TODO: Blending implementation? And with that in place, we have enough to render a first full fractal flame: - diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 35f3c7a..4b9b4d4 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -39,13 +39,18 @@ export default function Canvas({width, height, painter, children}: Props) { useEffect(paint, [colorMode, image]); const animate = () => { + if (!painter) { + return; + } + + console.log("Animating"); const nextImage = painter.next().value; if (nextImage) { setImage([nextImage]) requestAnimationFrame(animate); } } - useEffect(animate, [canvasCtx]); + useEffect(animate, [painter, canvasCtx]); return ( <> diff --git a/blog/2024-11-15-playing-with-fire/src/julia.ts b/blog/2024-11-15-playing-with-fire/src/julia.ts index 5d21045..19c5040 100644 --- a/blog/2024-11-15-playing-with-fire/src/julia.ts +++ b/blog/2024-11-15-playing-with-fire/src/julia.ts @@ -1,5 +1,5 @@ // hidden-start -import { Variation } from './variations' +import { Variation } from './variation' // hidden-end export const julia: Variation = (x, y) => { const r = Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2)); diff --git a/blog/2024-11-15-playing-with-fire/src/linear.ts b/blog/2024-11-15-playing-with-fire/src/linear.ts index cbea1e7..36b234a 100644 --- a/blog/2024-11-15-playing-with-fire/src/linear.ts +++ b/blog/2024-11-15-playing-with-fire/src/linear.ts @@ -1,4 +1,4 @@ // hidden-start -import {Variation} from "./variations" +import {Variation} from "./variation" //hidden-end export const linear: Variation = (x, y) => [x, y]; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/params.ts b/blog/2024-11-15-playing-with-fire/src/params.ts index 485347d..3ec90cd 100644 --- a/blog/2024-11-15-playing-with-fire/src/params.ts +++ b/blog/2024-11-15-playing-with-fire/src/params.ts @@ -4,7 +4,6 @@ */ import { Coefs } from './coefs'; -import { Transform } from './transform'; import { linear } from './linear' import { julia } from './julia' import { popcorn } from './popcorn' diff --git a/blog/2024-11-15-playing-with-fire/src/pdj.ts b/blog/2024-11-15-playing-with-fire/src/pdj.ts index 5360ced..8456692 100644 --- a/blog/2024-11-15-playing-with-fire/src/pdj.ts +++ b/blog/2024-11-15-playing-with-fire/src/pdj.ts @@ -1,5 +1,5 @@ // hidden-start -import { Variation } from './variations' +import { Variation } from './variation' //hidden-end export function pdj(a: number, b: number, c: number, d: number): Variation { return (x, y) => [ diff --git a/blog/2024-11-15-playing-with-fire/src/popcorn.ts b/blog/2024-11-15-playing-with-fire/src/popcorn.ts index 4652960..bcb2741 100644 --- a/blog/2024-11-15-playing-with-fire/src/popcorn.ts +++ b/blog/2024-11-15-playing-with-fire/src/popcorn.ts @@ -1,6 +1,6 @@ // hidden-start import {Coefs} from './coefs' -import {Variation} from './variations' +import {Variation} from './variation' // hidden-end export function popcorn({c, f}: Coefs): Variation { return (x, y) => [ diff --git a/blog/2024-11-15-playing-with-fire/src/randomBiUnit.ts b/blog/2024-11-15-playing-with-fire/src/randomBiUnit.ts new file mode 100644 index 0000000..7e5f389 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/randomBiUnit.ts @@ -0,0 +1,3 @@ +export function randomBiUnit() { + return Math.random() * 2 - 1; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/randomChoice.ts b/blog/2024-11-15-playing-with-fire/src/randomChoice.ts new file mode 100644 index 0000000..0494924 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/randomChoice.ts @@ -0,0 +1,15 @@ +export function randomChoice(choices: [number, T][]): [number, T] { + const weightSum = choices.reduce((sum, [weight, _]) => sum + weight, 0); + let choice = Math.random() * weightSum; + + for (const [index, element] of choices.entries()) { + const [weight, t] = element; + if (choice < weight) { + return [index, t]; + } + choice -= weight; + } + + const index = choices.length - 1; + return [index, choices[index][1]]; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/randomInteger.ts b/blog/2024-11-15-playing-with-fire/src/randomInteger.ts new file mode 100644 index 0000000..c3a6719 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/randomInteger.ts @@ -0,0 +1,3 @@ +export function randomInteger(min: number, max: number) { + return Math.floor(Math.random() * (max - min)) + min; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/transform.ts b/blog/2024-11-15-playing-with-fire/src/transform.ts index e719c57..4829133 100644 --- a/blog/2024-11-15-playing-with-fire/src/transform.ts +++ b/blog/2024-11-15-playing-with-fire/src/transform.ts @@ -1,5 +1,5 @@ import { Coefs } from './coefs' -import { Variation } from './variations' +import { Variation } from './variation' export interface Transform { coefs: Coefs, diff --git a/blog/2024-11-15-playing-with-fire/src/variations.ts b/blog/2024-11-15-playing-with-fire/src/variation.ts similarity index 100% rename from blog/2024-11-15-playing-with-fire/src/variations.ts rename to blog/2024-11-15-playing-with-fire/src/variation.ts diff --git a/package-lock.json b/package-lock.json index 4878ca7..7eb6dc8 100644 --- a/package-lock.json +++ b/package-lock.json @@ -12,6 +12,7 @@ "@docusaurus/faster": "^3.6.1", "@docusaurus/preset-classic": "^3.6.1", "@docusaurus/theme-live-codeblock": "^3.6.1", + "@matejmazur/react-katex": "^3.1.3", "@mdx-js/react": "^3.0.0", "clsx": "^2.0.0", "docusaurus-lunr-search": "^3.5.0", @@ -3031,6 +3032,19 @@ "resolved": "https://registry.npmjs.org/tinyqueue/-/tinyqueue-3.0.0.tgz", "integrity": "sha512-gRa9gwYU3ECmQYv3lslts5hxuIa90veaEcxDYuu3QGOIAEM2mOZkVHp48ANJuu1CURtRdHKUBY5Lm1tHV+sD4g==" }, + "node_modules/@matejmazur/react-katex": { + "version": "3.1.3", + "resolved": "https://registry.npmjs.org/@matejmazur/react-katex/-/react-katex-3.1.3.tgz", + "integrity": "sha512-rBp7mJ9An7ktNoU653BWOYdO4FoR4YNwofHZi+vaytX/nWbIlmHVIF+X8VFOn6c3WYmrLT5FFBjKqCZ1sjR5uQ==", + "engines": { + "node": ">=12", + "yarn": ">=1.1" + }, + "peerDependencies": { + "katex": ">=0.9", + "react": ">=16" + } + }, "node_modules/@mdx-js/mdx": { "version": "3.1.0", "resolved": "https://registry.npmjs.org/@mdx-js/mdx/-/mdx-3.1.0.tgz", diff --git a/package.json b/package.json index 34cb296..47f0fda 100644 --- a/package.json +++ b/package.json @@ -19,6 +19,7 @@ "@docusaurus/faster": "^3.6.1", "@docusaurus/preset-classic": "^3.6.1", "@docusaurus/theme-live-codeblock": "^3.6.1", + "@matejmazur/react-katex": "^3.1.3", "@mdx-js/react": "^3.0.0", "clsx": "^2.0.0", "docusaurus-lunr-search": "^3.5.0", From 137bd74d4d044b1f24dfbd362b1f84b7c8315639 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 24 Nov 2024 22:41:19 -0500 Subject: [PATCH 13/51] Get `npm run build` going again --- blog/2024-11-15-playing-with-fire/1-introduction/index.mdx | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index a8c1347..df6d974 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -201,6 +201,9 @@ import chaosGameWeightedSource from "!!raw-loader!./chaosGameWeighted"; {chaosGameWeightedSource} +import BrowserOnly from "@docusaurus/BrowserOnly"; import GasketWeighted from "./GasketWeighted" - \ No newline at end of file + + + \ No newline at end of file From ce5a28b7bda36e1d33a705723aaea7b53aa25e5f Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Fri, 29 Nov 2024 19:25:29 -0500 Subject: [PATCH 14/51] Flame blending example --- .../1-introduction/GasketWeighted.tsx | 33 ++-- .../1-introduction/chaosGame.js | 12 +- .../1-introduction/chaosGameWeighted.ts | 6 +- .../1-introduction/index.mdx | 11 +- .../2-transforms/FlameBlend.tsx | 142 ++++++++++++++++++ .../2-transforms/blend.ts | 14 ++ .../2-transforms/index.mdx | 11 +- .../banner-light.png | Bin 571025 -> 0 bytes .../{banner-dark.png => banner.png} | Bin .../src/camera.ts | 44 ++++++ .../2024-11-15-playing-with-fire/src/coefs.ts | 7 + .../src/css/styles.module.css | 4 + .../src/params.ts | 9 +- blog/2024-11-15-playing-with-fire/src/pdj.ts | 3 +- .../src/plotBinary.ts | 17 +++ .../src/transform.ts | 10 +- 16 files changed, 269 insertions(+), 54 deletions(-) create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/blend.ts delete mode 100644 blog/2024-11-15-playing-with-fire/banner-light.png rename blog/2024-11-15-playing-with-fire/{banner-dark.png => banner.png} (100%) create mode 100644 blog/2024-11-15-playing-with-fire/src/camera.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/css/styles.module.css create mode 100644 blog/2024-11-15-playing-with-fire/src/plotBinary.ts diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx index d909aeb..fc3f6bb 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx @@ -3,16 +3,9 @@ import Canvas from "../src/Canvas"; import { Params, chaosGameWeighted } from "./chaosGameWeighted"; import TeX from '@matejmazur/react-katex'; -type Transform = (x: number, y: number) => [number, number]; +import styles from "../src/css/styles.module.css" -function WeightInput({value, setValue, children}) { - return ( -
    - {children} - setValue(Number(e.currentTarget.value))}/> -
    - ) -} +type Transform = (x: number, y: number) => [number, number]; export default function GasketWeighted() { const image = new ImageData(600, 600); @@ -42,19 +35,23 @@ export default function GasketWeighted() { setGame(chaosGameWeighted(params)) }, [f0Weight, f1Weight, f2Weight]); + const weightInput = (title, weight, setWeight) => ( + <> +
    +

    {title} weight:{weight}

    + setWeight(Number(e.currentTarget.value))}/> +
    + + ) + return ( <>
    - -

    F_0 weight:{f0Weight}

    -
    - -

    F_1 weight:{f1Weight}

    -
    - -

    F_2 weight:{f2Weight}

    -
    + {weightInput("F_0", f0Weight, setF0Weight)} + {weightInput("F_1", f1Weight, setF1Weight)} + {weightInput("F_2", f2Weight, setF2Weight)}
    ) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js index 8d02cc4..e51648c 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js @@ -2,9 +2,6 @@ function Gasket() { // Hint: try increasing the iteration count const iterations = 10000; - // Display the progress every `step` iterations - const step = 1000; - // Hint: negating `x` and `y` creates some interesting images const transforms = [ (x, y) => [x / 2, y / 2], @@ -21,16 +18,12 @@ function Gasket() { const i = randomInteger(0, transforms.length); [x, y] = transforms[i](x, y); - if (count > 20) { + if (count > 20) plot(x, y, image); - } - if (count % 1000 === 0) { + if (count % 1000 === 0) yield image; - } } - - yield image; } return ( @@ -40,5 +33,4 @@ function Gasket() { painter={chaosGame()}/> ) } - render() diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts index 4f39635..5001ff3 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts @@ -19,13 +19,11 @@ export function* chaosGameWeighted({transforms, image, iterations, step}: Params // highlight-end [x, y] = transform(x, y); - if (i > 20) { + if (i > 20) plot(x, y, image); - } - if (i % step === 0) { + if (i % step === 0) yield image; - } } yield image; diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index df6d974..22b022b 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -13,13 +13,10 @@ Wikipedia [describes](https://en.wikipedia.org/wiki/Fractal_flame) fractal flame I think of them a different way: beauty in mathematics. import isDarkMode from '@site/src/isDarkMode' -import bannerDark from '../banner-dark.png' -import bannerLight from '../banner-light.png' +import banner from '../banner.png'
    - - - +
    @@ -204,6 +201,4 @@ import chaosGameWeightedSource from "!!raw-loader!./chaosGameWeighted"; import BrowserOnly from "@docusaurus/BrowserOnly"; import GasketWeighted from "./GasketWeighted" - - - \ No newline at end of file +{() => } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx new file mode 100644 index 0000000..cc49d53 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx @@ -0,0 +1,142 @@ +import {useState} from "react"; +import { blend } from "./blend"; +import { applyCoefs, Coefs } from "../src/coefs" +import {randomBiUnit} from "../src/randomBiUnit"; +import {linear} from "../src/linear"; +import {julia} from "../src/julia"; +import {popcorn} from "../src/popcorn"; +import {pdj} from "../src/pdj"; +import {Variation} from "../src/variation"; +import {Transform} from "../src/transform"; +import { + pdjParams, + xform1Coefs, + xform1Weight, + xform2Coefs, + xform2Weight, + xform3Coefs, + xform3Weight +} from "../src/params"; +import {randomChoice} from "../src/randomChoice"; +import {plotBinary} from "../src/plotBinary" +import Canvas from "../src/Canvas" + +import styles from "../src/css/styles.module.css" + +type VariationBlend = { + linear: number, + julia: number, + popcorn: number, + pdj: number +} + +export default function FlameBlend() { + const image = new ImageData(400, 400); + const quality = 2; + const step = 5000; + + const xform1Default: VariationBlend = { + linear: 0, + julia: 1, + popcorn: 0, + pdj: 0, + } + const [xform1Variations, setXform1Variations] = useState(xform1Default) + + const xform2Default: VariationBlend = { + linear: 1, + julia: 0, + popcorn: 1, + pdj: 0 + } + const [xform2Variations, setXform2Variations] = useState(xform2Default) + + const xform3Default: VariationBlend = { + linear: 0, + julia: 0, + popcorn: 0, + pdj: 1 + } + const [xform3Variations, setXform3Variations] = useState(xform3Default) + + function buildTransform(coefs: Coefs, variations: VariationBlend): Transform { + return (x: number, y: number) => { + const [varX, varY] = applyCoefs(x, y, coefs); + const varFunctions: [number, Variation][] = [ + [variations.linear, linear], + [variations.julia, julia], + [variations.popcorn, popcorn(coefs)], + [variations.pdj, pdj(pdjParams)] + ] + + return blend(varX, varY, varFunctions); + } + } + + function* chaosGame() { + let [x, y] = [randomBiUnit(), randomBiUnit()]; + const transforms: [number, Transform][] = [ + [xform1Weight, buildTransform(xform1Coefs, xform1Variations)], + [xform2Weight, buildTransform(xform2Coefs, xform2Variations)], + [xform3Weight, buildTransform(xform3Coefs, xform3Variations)] + ] + + const iterations = quality * image.width * image.height; + for (let i = 0; i < iterations; i++) { + let [_, transform] = randomChoice(transforms); + [x, y] = transform(x, y); + + if (i > 20) + plotBinary(x, y, image); + + if (i % step === 0) { + console.log(`Checking in; iterations=${i}`) + yield image; + } + } + + yield image; + } + + const variationEditor = (title, variations, setVariations) => { + return ( + <> +

    {title}:

    +
    +

    Linear: {variations.linear}

    + setVariations({...variations, linear: Number(e.currentTarget.value)})}/> +
    +
    +

    Julia: {variations.julia}

    + setVariations({...variations, julia: Number(e.currentTarget.value)})}/> +
    +
    +

    Popcorn: {variations.popcorn}

    + setVariations({...variations, popcorn: Number(e.currentTarget.value)})}/> +
    +
    +

    PDJ: {variations.pdj}

    + setVariations({...variations, pdj: Number(e.currentTarget.value)})}/> +
    + + ) + } + + return ( + <> + +
    + {variationEditor("Transform 1", xform1Variations, setXform1Variations)} + {variationEditor("Transform 2", xform2Variations, setXform2Variations)} + {variationEditor("Transform 3", xform3Variations, setXform3Variations)} +
    + + ) +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/blend.ts b/blog/2024-11-15-playing-with-fire/2-transforms/blend.ts new file mode 100644 index 0000000..0f8778e --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/blend.ts @@ -0,0 +1,14 @@ +// hidden-start +import { Variation } from "../src/variation" +// hidden-end +export function blend(x: number, y: number, variations: [number, Variation][]): [number, number] { + let [finalX, finalY] = [0, 0]; + + for (const [weight, variation] of variations) { + const [varX, varY] = variation(x, y); + finalX += weight * varX; + finalY += weight * varY; + } + + return [finalX, finalY]; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 87e4e53..5af277d 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -15,6 +15,8 @@ This blog post uses a set of reference parameters ([available here](../params.fl implementation of the fractal flame algorithm. If you're interested in tweaking the parameters, or generating your own art, [Apophysis](https://sourceforge.net/projects/apophysis/) is a good introductory tool. +TODO: Include the reference image here + ## Transforms and variations import CodeBlock from '@theme/CodeBlock' @@ -120,8 +122,9 @@ import pdjSrc from '!!raw-loader!../src/pdj' ### Blending Now, one variation is fun, but we can also combine variations in a single transform by "blending." -First, each variation is assigned a value that describes how much it affects the transform function ($v_j$). -Afterward, sum up the $x$ and $y$ values respectively: +Each variation receives the same $x$ and $y$ inputs, and we add together each variation's $x$ and $y$ outputs. +We'll also give each variation a weight ($v_j$) that scales the output, which allows us to control +how much each variation contributes to the transform: $$ F_i(x,y) = \sum_{j} v_{ij} V_j(a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) @@ -132,3 +135,7 @@ The formula looks intimidating, but it's not hard to implement: TODO: Blending implementation? And with that in place, we have enough to render a first full fractal flame: + +import FlameBlend from "./FlameBlend"; + + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/banner-light.png b/blog/2024-11-15-playing-with-fire/banner-light.png deleted file mode 100644 index 9ed271915dc59a443986f6de21079b9f28203838..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 571025 zcmeFYbx>SgvpzaN&;Y^Rf(3VXcXyY8!F6ya5D4xJ!7aGETL|v%7A&|0x6Au}a=ugd zS9R-D-QRy_re002;AWhB%902q$9<1qxdw{Hh{ zPX4!_pWYfeu4<+pWKLj53u`+NnX8u*hz#UuZ2=&n`?t9TfNcKYWo8`63rN$oyz!uAouI*JacMl!A3_!tO<0#txu;0q(N8;W&%3 zk^lfyh_$%5imbT!zx;XgBEv6UP^MP|FLdKYMv^|l9nE=AC6gg6g2x6sLgnKuQU%{P zg9ms;f&?sF>7Ito%?aRKPoJ(fytXLX6O^;NlbUNhMwdJiBT%5Z?dxsl?d~amw=pyO z9C8dysRe$Cgu$S>cE}`s>(p0&y3n!@+r0;gM~ z;3x7Hb8vF^U`-&BhD;3U(+B_C`B7!1X4x&C$qV2LDTRm?uGOsFfY68b>?v;0=g;~%wqqyyS42f0 zMAE#I+o4cVKTkn}s(jkp>N*@>=Q$p4VURMxeg?0j6K{#W{&nursj@7 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values in the flame coordinate system to pixel coordinates + * + * The way `flam3` actually calculates the "camera" for mapping a point + * to its pixel coordinate is fairly involved - it also needs to calculate + * zoom and rotation (see the bucket accumulator code in rect.c). + * We'll make some simplifying assumptions: + * - The final image is square + * - We want to plot the range [-2, 2] + * + * The reference parameters were designed in Apophysis, which uses the + * range [-2, 2] by default (the `scale` parameter in XML defines the + * "pixels per unit", and with the default zoom, is chosen to give a + * range of [-2, 2]). + * + * @param x point in the range [-2, 2] + * @param y point in the range [-2, 2] + * @param size image size + * @returns pair of pixel coordinates + */ +export function camera(x: number, y: number, size: number): [number, number] { + return [Math.floor(((x + 2) * size) / 4), Math.floor(((y + 2) * size) / 4)]; +} + +/** + * Translate values in pixel coordinates to a 1-dimensional array index + * + * Unlike the camera function, this mapping doesn't assume a square image, + * and only requires knowing the image width. + * + * The stride parameter is used to calculate indices that take into account + * how many "values" each pixel has. For example, in an ImageData, each pixel + * has a red, green, blue, and alpha component per pixel, so a stride of 4 + * is appropriate. For situations where there are separate red/green/blue/alpha + * arrays per pixel, a stride of 1 is appropriate + * + * @param x point in the range [0, size) + * @param y point in the range [0, size) + * @param width width of image in pixel units + * @param stride values per pixel coordinate + */ +export function histIndex(x: number, y: number, width: number, stride: number): number { + return y * (width * stride) + x * stride; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/coefs.ts b/blog/2024-11-15-playing-with-fire/src/coefs.ts index da5b1aa..121d451 100644 --- a/blog/2024-11-15-playing-with-fire/src/coefs.ts +++ b/blog/2024-11-15-playing-with-fire/src/coefs.ts @@ -1,4 +1,11 @@ export interface Coefs { a: number, b: number, c: number, d: number, e: number, f: number +} + +export function applyCoefs(x: number, y: number, coefs: Coefs) { + return [ + (x * coefs.a + y * coefs.b + coefs.c), + (x * coefs.d + y * coefs.e + coefs.f) + ] } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css new file mode 100644 index 0000000..c129a5c --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css @@ -0,0 +1,4 @@ +.inputDiv { + padding-left: .5em; + padding-right: 1em; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/params.ts b/blog/2024-11-15-playing-with-fire/src/params.ts index 3ec90cd..0dee991 100644 --- a/blog/2024-11-15-playing-with-fire/src/params.ts +++ b/blog/2024-11-15-playing-with-fire/src/params.ts @@ -7,13 +7,18 @@ import { Coefs } from './coefs'; import { linear } from './linear' import { julia } from './julia' import { popcorn } from './popcorn' -import { pdj } from './pdj' +import {pdj, PdjParams} from './pdj' +import {Variation} from "./variation" export const identityCoefs: Coefs = { a: 1, b: 0, c: 0, d: 0, e: 1, f: 0, } +export const pdjParams: PdjParams = { + a: 1.09358, b: 2.13048, c: 2.54127, d: 2.37267 +} + export const xform1Weight = 0.56453495; export const xform1Coefs = { a: -1.381068, b: -1.381068, c: 0, @@ -47,7 +52,7 @@ export const xform3Coefs = { } export const xform3CoefsPost = identityCoefs; export const xform3Variations = [ - [1, pdj(1.09358, 2.13048, 2.54127, 2.37267)] + [1, pdj(pdjParams)] ]; export const xform3Color = 0.349; diff --git a/blog/2024-11-15-playing-with-fire/src/pdj.ts b/blog/2024-11-15-playing-with-fire/src/pdj.ts index 8456692..5afd470 100644 --- a/blog/2024-11-15-playing-with-fire/src/pdj.ts +++ b/blog/2024-11-15-playing-with-fire/src/pdj.ts @@ -1,7 +1,8 @@ // hidden-start import { Variation } from './variation' //hidden-end -export function pdj(a: number, b: number, c: number, d: number): Variation { +export type PdjParams = {a: number, b: number, c: number, d: number}; +export function pdj({a, b, c, d}: PdjParams): Variation { return (x, y) => [ Math.sin(a * y) - Math.cos(b * x), Math.sin(c * x) - Math.cos(d * y) diff --git a/blog/2024-11-15-playing-with-fire/src/plotBinary.ts b/blog/2024-11-15-playing-with-fire/src/plotBinary.ts new file mode 100644 index 0000000..5b9fb64 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/plotBinary.ts @@ -0,0 +1,17 @@ +import { camera, histIndex } from "./camera" + +export function plotBinary(x: number, y: number, image: ImageData) { + const [pixelX, pixelY] = camera(x, y, image.width); + if ( + pixelX < 0 || pixelX >= image.width || pixelY < 0 || pixelY > image.height + ) { + return; + } + + const pixelIndex = histIndex(pixelX, pixelY, image.width, 4); + + image.data[pixelIndex] = 0; + image.data[pixelIndex + 1] = 0; + image.data[pixelIndex + 2] = 0; + image.data[pixelIndex + 3] = 0xff; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/transform.ts b/blog/2024-11-15-playing-with-fire/src/transform.ts index 4829133..ce099a0 100644 --- a/blog/2024-11-15-playing-with-fire/src/transform.ts +++ b/blog/2024-11-15-playing-with-fire/src/transform.ts @@ -1,9 +1 @@ -import { Coefs } from './coefs' -import { Variation } from './variation' - -export interface Transform { - coefs: Coefs, - variations: [number, Variation][], - coefsPost: Coefs, - color: number -} \ No newline at end of file +export type Transform = (x: number, y: number) => [number, number]; \ No newline at end of file From 112470ce5a564cf71828d52331a1d4a1ab4d33ec Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Fri, 29 Nov 2024 23:08:47 -0500 Subject: [PATCH 15/51] Rewrite canvas to use React state management properly --- .../1-introduction/GasketWeighted.tsx | 30 ++-- .../1-introduction/chaosGame.js | 54 +++--- .../1-introduction/chaosGameWeighted.ts | 13 +- .../1-introduction/index.mdx | 8 +- .../1-introduction/scope.tsx | 7 +- .../2-transforms/FlameBlend.tsx | 25 ++- .../2-transforms/index.mdx | 11 +- .../src/Canvas.tsx | 154 +++++++++++++----- .../src/camera.ts | 6 +- 9 files changed, 190 insertions(+), 118 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx index fc3f6bb..d2edb62 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx @@ -1,6 +1,6 @@ -import {useEffect, useState} from "react"; -import Canvas from "../src/Canvas"; -import { Params, chaosGameWeighted } from "./chaosGameWeighted"; +import {useEffect, useState, useContext} from "react"; +import {PainterContext} from "../src/Canvas"; +import {chaosGameWeighted } from "./chaosGameWeighted"; import TeX from '@matejmazur/react-katex'; import styles from "../src/css/styles.module.css" @@ -8,10 +8,6 @@ import styles from "../src/css/styles.module.css" type Transform = (x: number, y: number) => [number, number]; export default function GasketWeighted() { - const image = new ImageData(600, 600); - const iterations = 100_000; - const step = 1000; - const [f0Weight, setF0Weight] = useState(1); const [f1Weight, setF1Weight] = useState(1); const [f2Weight, setF2Weight] = useState(1); @@ -20,19 +16,14 @@ export default function GasketWeighted() { const f1: Transform = (x, y) => [(x + 1) / 2, y / 2]; const f2: Transform = (x, y) => [x / 2, (y + 1) / 2]; - const [game, setGame] = useState>(null); + const {setPainter} = useContext(PainterContext); + useEffect(() => { - const params: Params = { - transforms: [ - [f0Weight, f0], - [f1Weight, f1], - [f2Weight, f2] - ], - image, - iterations, - step - } - setGame(chaosGameWeighted(params)) + setPainter(chaosGameWeighted([ + [f0Weight, f0], + [f1Weight, f1], + [f2Weight, f2] + ])); }, [f0Weight, f1Weight, f2Weight]); const weightInput = (title, weight, setWeight) => ( @@ -47,7 +38,6 @@ export default function GasketWeighted() { return ( <> -

    {weightInput("F_0", f0Weight, setF0Weight)} {weightInput("F_1", f1Weight, setF1Weight)} diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js index e51648c..a3e6ce0 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js @@ -1,36 +1,36 @@ -function Gasket() { - // Hint: try increasing the iteration count - const iterations = 10000; +// Hint: try increasing the iteration count +const iterations = 10000; - // Hint: negating `x` and `y` creates some interesting images - const transforms = [ - (x, y) => [x / 2, y / 2], - (x, y) => [(x + 1) / 2, y / 2], - (x, y) => [x / 2, (y + 1) / 2] - ] +// Hint: negating `x` and `y` creates some interesting images +const transforms = [ + (x, y) => [x / 2, y / 2], + (x, y) => [(x + 1) / 2, y / 2], + (x, y) => [x / 2, (y + 1) / 2] +] - const image = new ImageData(600, 600); +function* chaosGame() { + let image = new ImageData(500, 500); + let [x, y] = [randomBiUnit(), randomBiUnit()]; - function* chaosGame() { - var [x, y] = [randomBiUnit(), randomBiUnit()]; + for (var count = 0; count < iterations; count++) { + const i = randomInteger(0, transforms.length); + [x, y] = transforms[i](x, y); - for (var count = 0; count < iterations; count++) { - const i = randomInteger(0, transforms.length); - [x, y] = transforms[i](x, y); + if (count > 20) + plot(x, y, image); - if (count > 20) - plot(x, y, image); - - if (count % 1000 === 0) - yield image; - } + if (count % 1000 === 0) + yield image; } - return ( - - ) + yield image; +} + +// Wiring so the code above displays properly +function Gasket() { + const {setPainter} = useContext(PainterContext); + setPainter(chaosGame()); + + return (<>) } render() diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts index 5001ff3..fac18d1 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts @@ -2,15 +2,12 @@ import { randomBiUnit } from "../src/randomBiUnit"; import { randomChoice } from "../src/randomChoice"; import { plot } from "./plot" -export type Transform = (x: number, y: number) => [number, number]; -export type Params = { - transforms: [number, Transform][], - image: ImageData, - iterations: number, - step: number -} +import {Transform} from "../src/transform"; +const iterations = 50_000; +const step = 1000; // hidden-end -export function* chaosGameWeighted({transforms, image, iterations, step}: Params) { +export function* chaosGameWeighted(transforms: [number, Transform][]) { + let image = new ImageData(500, 500); var [x, y] = [randomBiUnit(), randomBiUnit()]; for (let i = 0; i < iterations; i++) { diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index 22b022b..c4f1890 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -177,7 +177,9 @@ import Scope from './scope' import chaosGameSource from '!!raw-loader!./chaosGame' +
    @@ -198,7 +200,9 @@ import chaosGameWeightedSource from "!!raw-loader!./chaosGameWeighted"; {chaosGameWeightedSource} -import BrowserOnly from "@docusaurus/BrowserOnly"; import GasketWeighted from "./GasketWeighted" +import Canvas from "../src/Canvas" -{() => } \ No newline at end of file + + + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx index 5b2dd7b..4ffe6d4 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx @@ -1,12 +1,15 @@ +import {useContext} from "react"; import { plot } from './plot'; import { randomBiUnit } from '../src/randomBiUnit'; import { randomInteger } from '../src/randomInteger'; -import Canvas from "../src/Canvas"; +import Canvas, {PainterContext} from "../src/Canvas"; const Scope = { + Canvas, + PainterContext, plot, randomBiUnit, randomInteger, - Canvas + useContext, } export default Scope; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx index cc49d53..5ef84c7 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx @@ -1,4 +1,4 @@ -import {useState} from "react"; +import {useContext, useEffect, useState} from "react"; import { blend } from "./blend"; import { applyCoefs, Coefs } from "../src/coefs" import {randomBiUnit} from "../src/randomBiUnit"; @@ -19,7 +19,7 @@ import { } from "../src/params"; import {randomChoice} from "../src/randomChoice"; import {plotBinary} from "../src/plotBinary" -import Canvas from "../src/Canvas" +import {PainterContext} from "../src/Canvas" import styles from "../src/css/styles.module.css" @@ -31,10 +31,11 @@ type VariationBlend = { } export default function FlameBlend() { - const image = new ImageData(400, 400); const quality = 2; const step = 5000; + const {width, height, setPainter} = useContext(PainterContext); + const xform1Default: VariationBlend = { linear: 0, julia: 1, @@ -73,6 +74,7 @@ export default function FlameBlend() { } } + const image = new ImageData(width, height); function* chaosGame() { let [x, y] = [randomBiUnit(), randomBiUnit()]; const transforms: [number, Transform][] = [ @@ -97,6 +99,7 @@ export default function FlameBlend() { yield image; } + useEffect(() => setPainter(chaosGame()), [xform1Variations, xform2Variations, xform3Variations]); const variationEditor = (title, variations, setVariations) => { return ( @@ -127,16 +130,10 @@ export default function FlameBlend() { } return ( - <> - -
    - {variationEditor("Transform 1", xform1Variations, setXform1Variations)} - {variationEditor("Transform 2", xform2Variations, setXform2Variations)} - {variationEditor("Transform 3", xform3Variations, setXform3Variations)} -
    - +
    + {variationEditor("Transform 1", xform1Variations, setXform1Variations)} + {variationEditor("Transform 2", xform2Variations, setXform2Variations)} + {variationEditor("Transform 3", xform3Variations, setXform3Variations)} +
    ) } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 5af277d..fe8f569 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -119,7 +119,7 @@ import pdjSrc from '!!raw-loader!../src/pdj' {pdjSrc} -### Blending +## Blending Now, one variation is fun, but we can also combine variations in a single transform by "blending." Each variation receives the same $x$ and $y$ inputs, and we add together each variation's $x$ and $y$ outputs. @@ -132,10 +132,15 @@ $$ The formula looks intimidating, but it's not hard to implement: -TODO: Blending implementation? +import blendSource from "!!raw-loader!./blend"; + +{blendSource} And with that in place, we have enough to render a first full fractal flame: +import Canvas from "../src/Canvas"; import FlameBlend from "./FlameBlend"; - \ No newline at end of file + + + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 4b9b4d4..8d46cfd 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -1,16 +1,53 @@ -import React, {useCallback, useEffect, useState} from "react"; +import React, {useCallback, useEffect, useState, createContext} from "react"; import {useColorMode} from "@docusaurus/theme-common"; -interface Props { +export interface PainterProps { + readonly width: number; + readonly height: number; + readonly setPainter: (painter: Iterator) => void; +} + +/** + * Context provider for child elements to submit image iterator functions + * (painters) for rendering + */ +export const PainterContext = createContext(null); + +interface CanvasProps { width: number; height: number; - painter: Iterator; children?: React.ReactNode; } -export default function Canvas({width, height, painter, children}: Props) { - const {colorMode} = useColorMode(); - const [image, setImage] = useState<[ImageData]>(null); +/** + * Draw fractal flames to a canvas. + * + * This component is a bit involved because it attempts to solve + * a couple problems at the same time: + * - Incrementally drawing an image to the canvas + * - Interrupting drawing with new parameters on demand + * - Dark mode + * + * Image iterators provide a means to draw incremental images; + * iterators can easily checkpoint state, and this component will + * request the next image on the next animation frame. As a result, + * the browser should be responsive even though we run CPU-heavy + * code on the main thread. + * + * Swapping a new iterator allows interrupting a render in progress, + * as the canvas completely repaints on each provided image. + * + * Finally, check whether dark mode is active, and invert the most + * recent image prior to painting if so. + * + * PainterContext is used to allow child elements to swap in + * new iterators. + * + * @param width Canvas draw width + * @param height Canvas draw height + * @param children Child elements + */ +export default function Canvas({width, height, children}: CanvasProps) { const [canvasCtx, setCanvasCtx] = useState(null); const canvasRef = useCallback(node => { if (node !== null) { @@ -18,52 +55,93 @@ export default function Canvas({width, height, painter, children}: Props) { } }, []); - const paintImage = new ImageData(width, height); - const paint = () => { - if (!canvasCtx || !image) { + const {colorMode} = useColorMode(); + + // Holder objects are used to force re-painting even if the iterator + // returns a modified image with the same reference + type ImageHolder = { image?: ImageData }; + const [imageHolder, setImageHolder] = useState({ image: null }); + useEffect(() => { + const image = imageHolder.image; + if (!image) { + // No image is available, leave the canvas as-is return; } - for (const [index, value] of image[0].data.entries()) { - if (index % 4 === 3) { - // Alpha values are copied as-is - paintImage.data[index] = value; - } else { - // If dark mode is active, invert the color - paintImage.data[index] = colorMode === 'light' ? value : 255 - value; - } + if (!canvasCtx) { + // Canvas is not ready for the image we have, + // re-submit the image and wait for the ref to populate + setImageHolder({ image }); + return; } - canvasCtx.putImageData(paintImage, 0, 0); - } - useEffect(paint, [colorMode, image]); + // If light mode is active, paint the image as-is + if (colorMode === 'light') { + canvasCtx.putImageData(image, 0, 0); + return; + } - const animate = () => { + // If dark mode is active, copy the image into a new buffer + // and invert colors prior to painting. + // Copy alpha values as-is. + const paintImage = new ImageData(image.width, image.height); + image.data.forEach((value, index) => { + const isAlpha = index % 4 === 3; + paintImage.data[index] = isAlpha ? value : 255 - value; + }) + canvasCtx.putImageData(paintImage, 0, 0); + }, [colorMode, imageHolder]); + + // Image iterators (painters) are also in a holder; this allows + // re-submitting the existing iterator to draw the next frame, + // and also allows child components to over-write the iterator + // if a new set of parameters becomes available + // TODO(bspeice): Potential race condition? + // Not sure if it's possible for painters submitted by children + // to be over-ridden as a result re-submitting the + // existing iterator + type PainterHolder = { painter?: Iterator }; + const [animHolder, setAnimHolder] = useState({ painter: null }); + useEffect(() => { + const painter = animHolder.painter; if (!painter) { return; } - console.log("Animating"); - const nextImage = painter.next().value; - if (nextImage) { - setImage([nextImage]) - requestAnimationFrame(animate); + if (!canvasCtx) { + setAnimHolder({ painter }); + return; } - } - useEffect(animate, [painter, canvasCtx]); + + const image = painter.next().value; + if (image) { + setImageHolder({ image }); + setAnimHolder({ painter }); + } else { + setAnimHolder({ painter: null }); + } + }, [animHolder, canvasCtx]); + + // Finally, child elements submit painters through a context provider + const [painter, setPainter] = useState>(null); + useEffect(() => setAnimHolder({ painter }), [painter]); return ( <> - - {children} +
    + +
    + + {children} + ) } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/camera.ts b/blog/2024-11-15-playing-with-fire/src/camera.ts index 28dd927..afef3af 100644 --- a/blog/2024-11-15-playing-with-fire/src/camera.ts +++ b/blog/2024-11-15-playing-with-fire/src/camera.ts @@ -4,9 +4,7 @@ * The way `flam3` actually calculates the "camera" for mapping a point * to its pixel coordinate is fairly involved - it also needs to calculate * zoom and rotation (see the bucket accumulator code in rect.c). - * We'll make some simplifying assumptions: - * - The final image is square - * - We want to plot the range [-2, 2] + * We simplify things here by assuming a square image * * The reference parameters were designed in Apophysis, which uses the * range [-2, 2] by default (the `scale` parameter in XML defines the @@ -15,7 +13,7 @@ * * @param x point in the range [-2, 2] * @param y point in the range [-2, 2] - * @param size image size + * @param size image width/height in pixels * @returns pair of pixel coordinates */ export function camera(x: number, y: number, size: number): [number, number] { From f327b5386301d4269ab0ba2f9ce5ee3de714f612 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Fri, 29 Nov 2024 23:19:19 -0500 Subject: [PATCH 16/51] Fix initial posts to use the new painter API --- .../1-introduction/Gasket.tsx | 16 ++++++++++++++++ .../1-introduction/chaosGame.js | 8 +------- .../1-introduction/index.mdx | 2 -- .../1-introduction/scope.tsx | 7 ++----- 4 files changed, 19 insertions(+), 14 deletions(-) create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx new file mode 100644 index 0000000..1b96395 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx @@ -0,0 +1,16 @@ +import Canvas, {PainterContext} from "../src/Canvas"; +import {useContext} from "react"; + +export function Render({f}) { + const {setPainter} = useContext(PainterContext); + setPainter(f); + return <>; +} + +export default function Gasket({f}) { + return ( + + + + ) +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js index a3e6ce0..2644edf 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js @@ -27,10 +27,4 @@ function* chaosGame() { } // Wiring so the code above displays properly -function Gasket() { - const {setPainter} = useContext(PainterContext); - setPainter(chaosGame()); - - return (<>) -} -render() +render() diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index c4f1890..eb904cf 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -177,9 +177,7 @@ import Scope from './scope' import chaosGameSource from '!!raw-loader!./chaosGame' -
    diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx index 4ffe6d4..dc05043 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx @@ -1,15 +1,12 @@ -import {useContext} from "react"; +import Gasket from "./Gasket"; import { plot } from './plot'; import { randomBiUnit } from '../src/randomBiUnit'; import { randomInteger } from '../src/randomInteger'; -import Canvas, {PainterContext} from "../src/Canvas"; const Scope = { - Canvas, - PainterContext, + Gasket, plot, randomBiUnit, randomInteger, - useContext, } export default Scope; \ No newline at end of file From 12c88ef8e365fe1a06c195f0884b57d9694e0b58 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Fri, 29 Nov 2024 23:22:31 -0500 Subject: [PATCH 17/51] Build works again --- blog/2024-11-15-playing-with-fire/1-introduction/index.mdx | 7 ++++--- blog/2024-11-15-playing-with-fire/2-transforms/index.mdx | 3 ++- 2 files changed, 6 insertions(+), 4 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index eb904cf..67181ea 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -198,9 +198,10 @@ import chaosGameWeightedSource from "!!raw-loader!./chaosGameWeighted"; {chaosGameWeightedSource} -import GasketWeighted from "./GasketWeighted" -import Canvas from "../src/Canvas" +import BrowserOnly from "@docusaurus/BrowserOnly"; +import GasketWeighted from "./GasketWeighted"; +import Canvas from "../src/Canvas"; - + {() => } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index fe8f569..2826880 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -138,9 +138,10 @@ import blendSource from "!!raw-loader!./blend"; And with that in place, we have enough to render a first full fractal flame: +import BrowserOnly from "@docusaurus/BrowserOnly"; import Canvas from "../src/Canvas"; import FlameBlend from "./FlameBlend"; - + {() => } \ No newline at end of file From 1aa45e3f59bc90b206d6cfc6d75a62b9536252cb Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sat, 30 Nov 2024 12:39:54 -0500 Subject: [PATCH 18/51] Split paint/render image to handle callback depth Iterator state still uses the same pattern, not sure how problematic that is. --- .../src/Canvas.tsx | 33 +++++++++---------- 1 file changed, 16 insertions(+), 17 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 8d46cfd..85e152f 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -55,29 +55,28 @@ export default function Canvas({width, height, children}: CanvasProps) { } }, []); - const {colorMode} = useColorMode(); - // Holder objects are used to force re-painting even if the iterator // returns a modified image with the same reference type ImageHolder = { image?: ImageData }; - const [imageHolder, setImageHolder] = useState({ image: null }); - useEffect(() => { - const image = imageHolder.image; - if (!image) { - // No image is available, leave the canvas as-is - return; - } - if (!canvasCtx) { - // Canvas is not ready for the image we have, - // re-submit the image and wait for the ref to populate - setImageHolder({ image }); + const [paintImage, setPaintImage] = useState({ image: null }); + useEffect(() => { + if (paintImage.image && canvasCtx) { + canvasCtx.putImageData(paintImage.image, 0, 0); + } + }, [paintImage, canvasCtx]); + + const {colorMode} = useColorMode(); + const [renderImage, setRenderImage] = useState({ image: null }); + useEffect(() => { + const image = renderImage.image; + if (!image) { return; } // If light mode is active, paint the image as-is if (colorMode === 'light') { - canvasCtx.putImageData(image, 0, 0); + setPaintImage({ image }); return; } @@ -89,8 +88,8 @@ export default function Canvas({width, height, children}: CanvasProps) { const isAlpha = index % 4 === 3; paintImage.data[index] = isAlpha ? value : 255 - value; }) - canvasCtx.putImageData(paintImage, 0, 0); - }, [colorMode, imageHolder]); + setPaintImage({ image: paintImage }); + }, [colorMode, renderImage]); // Image iterators (painters) are also in a holder; this allows // re-submitting the existing iterator to draw the next frame, @@ -115,7 +114,7 @@ export default function Canvas({width, height, children}: CanvasProps) { const image = painter.next().value; if (image) { - setImageHolder({ image }); + setRenderImage({ image }); setAnimHolder({ painter }); } else { setAnimHolder({ painter: null }); From 6c4d73f0817876f86c13719d8b522377603cc6cd Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sat, 30 Nov 2024 17:35:42 -0500 Subject: [PATCH 19/51] Post/final transform implementation --- .../1-introduction/GasketWeighted.tsx | 6 +- .../2-transforms/CoefEditor.tsx | 48 +++++++ .../2-transforms/FlameBlend.tsx | 118 +++--------------- .../2-transforms/FlameFinal.tsx | 64 ++++++++++ .../2-transforms/FlamePost.tsx | 46 +++++++ .../2-transforms/VariationEditor.tsx | 42 +++++++ .../2-transforms/blend.ts | 7 +- .../2-transforms/buildTransform.ts | 26 ++++ .../2-transforms/chaosGameFinal.ts | 29 +++++ .../2-transforms/index.mdx | 45 +++++-- .../2-transforms/post.ts | 7 ++ .../2024-11-15-playing-with-fire/src/blend.ts | 0 .../2024-11-15-playing-with-fire/src/coefs.ts | 2 +- .../src/css/styles.module.css | 21 +++- .../2024-11-15-playing-with-fire/src/julia.ts | 7 +- .../src/params.ts | 10 +- .../src/variationBlend.ts | 2 + 17 files changed, 360 insertions(+), 120 deletions(-) create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/buildTransform.ts create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts create mode 100644 blog/2024-11-15-playing-with-fire/2-transforms/post.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/blend.ts create mode 100644 blog/2024-11-15-playing-with-fire/src/variationBlend.ts diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx index d2edb62..c3f91f1 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx @@ -28,8 +28,8 @@ export default function GasketWeighted() { const weightInput = (title, weight, setWeight) => ( <> -
    -

    {title} weight:{weight}

    +
    +

    {title} weight: {weight}

    setWeight(Number(e.currentTarget.value))}/>
    @@ -38,7 +38,7 @@ export default function GasketWeighted() { return ( <> -
    +
    {weightInput("F_0", f0Weight, setF0Weight)} {weightInput("F_1", f1Weight, setF1Weight)} {weightInput("F_2", f2Weight, setF2Weight)} diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx new file mode 100644 index 0000000..8536381 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx @@ -0,0 +1,48 @@ +import TeX from "@matejmazur/react-katex"; +import {Coefs} from "../src/coefs"; + +import styles from "../src/css/styles.module.css"; + +export interface Props { + title: String; + isPost: boolean; + coefs: Coefs; + setCoefs: (coefs: Coefs) => void; +} +export const CoefEditor = ({title, isPost, coefs, setCoefs}: Props) => { + return ( +
    +

    {title}

    +
    +

    {isPost ? \alpha : 'a'}: {coefs.a}

    + setCoefs({...coefs, a: Number(e.currentTarget.value)})}/> +
    +
    +

    {isPost ? \beta : 'b'}: {coefs.b}

    + setCoefs({...coefs, b: Number(e.currentTarget.value)})}/> +
    +
    +

    {isPost ? \gamma : 'c'}: {coefs.c}

    + setCoefs({...coefs, c: Number(e.currentTarget.value)})}/> +
    +
    +

    {isPost ? \delta : 'd'}: {coefs.d}

    + setCoefs({...coefs, d: Number(e.currentTarget.value)})}/> +
    +
    +

    {isPost ? \epsilon : 'e'}: {coefs.e}

    + setCoefs({...coefs, e: Number(e.currentTarget.value)})}/> +
    +
    +

    {isPost ? \zeta : 'f'}: {coefs.f}

    + setCoefs({...coefs, f: Number(e.currentTarget.value)})}/> +
    +
    + ) +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx index 5ef84c7..b54db96 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx @@ -1,15 +1,7 @@ import {useContext, useEffect, useState} from "react"; -import { blend } from "./blend"; -import { applyCoefs, Coefs } from "../src/coefs" -import {randomBiUnit} from "../src/randomBiUnit"; -import {linear} from "../src/linear"; -import {julia} from "../src/julia"; -import {popcorn} from "../src/popcorn"; -import {pdj} from "../src/pdj"; -import {Variation} from "../src/variation"; import {Transform} from "../src/transform"; import { - pdjParams, + identityCoefs, xform1Coefs, xform1Weight, xform2Coefs, @@ -17,26 +9,15 @@ import { xform3Coefs, xform3Weight } from "../src/params"; -import {randomChoice} from "../src/randomChoice"; -import {plotBinary} from "../src/plotBinary" import {PainterContext} from "../src/Canvas" - -import styles from "../src/css/styles.module.css" - -type VariationBlend = { - linear: number, - julia: number, - popcorn: number, - pdj: number -} +import {buildBlend, buildTransform} from "./buildTransform" +import {chaosGameFinal} from "./chaosGameFinal" +import {VariationEditor, VariationProps} from "./VariationEditor" export default function FlameBlend() { - const quality = 2; - const step = 5000; - const {width, height, setPainter} = useContext(PainterContext); - const xform1Default: VariationBlend = { + const xform1Default: VariationProps = { linear: 0, julia: 1, popcorn: 0, @@ -44,7 +25,7 @@ export default function FlameBlend() { } const [xform1Variations, setXform1Variations] = useState(xform1Default) - const xform2Default: VariationBlend = { + const xform2Default: VariationProps = { linear: 1, julia: 0, popcorn: 1, @@ -52,7 +33,7 @@ export default function FlameBlend() { } const [xform2Variations, setXform2Variations] = useState(xform2Default) - const xform3Default: VariationBlend = { + const xform3Default: VariationProps = { linear: 0, julia: 0, popcorn: 0, @@ -60,80 +41,21 @@ export default function FlameBlend() { } const [xform3Variations, setXform3Variations] = useState(xform3Default) - function buildTransform(coefs: Coefs, variations: VariationBlend): Transform { - return (x: number, y: number) => { - const [varX, varY] = applyCoefs(x, y, coefs); - const varFunctions: [number, Variation][] = [ - [variations.linear, linear], - [variations.julia, julia], - [variations.popcorn, popcorn(coefs)], - [variations.pdj, pdj(pdjParams)] - ] + // Cheating a bit here; for purposes of code re-use, use the post- and final-transform-enabled chaos game, + // and swap in identity components for each + const identityXform: Transform = (x, y) => [x, y]; - return blend(varX, varY, varFunctions); - } - } - - const image = new ImageData(width, height); - function* chaosGame() { - let [x, y] = [randomBiUnit(), randomBiUnit()]; - const transforms: [number, Transform][] = [ - [xform1Weight, buildTransform(xform1Coefs, xform1Variations)], - [xform2Weight, buildTransform(xform2Coefs, xform2Variations)], - [xform3Weight, buildTransform(xform3Coefs, xform3Variations)] - ] - - const iterations = quality * image.width * image.height; - for (let i = 0; i < iterations; i++) { - let [_, transform] = randomChoice(transforms); - [x, y] = transform(x, y); - - if (i > 20) - plotBinary(x, y, image); - - if (i % step === 0) { - console.log(`Checking in; iterations=${i}`) - yield image; - } - } - - yield image; - } - useEffect(() => setPainter(chaosGame()), [xform1Variations, xform2Variations, xform3Variations]); - - const variationEditor = (title, variations, setVariations) => { - return ( - <> -

    {title}:

    -
    -

    Linear: {variations.linear}

    - setVariations({...variations, linear: Number(e.currentTarget.value)})}/> -
    -
    -

    Julia: {variations.julia}

    - setVariations({...variations, julia: Number(e.currentTarget.value)})}/> -
    -
    -

    Popcorn: {variations.popcorn}

    - setVariations({...variations, popcorn: Number(e.currentTarget.value)})}/> -
    -
    -

    PDJ: {variations.pdj}

    - setVariations({...variations, pdj: Number(e.currentTarget.value)})}/> -
    - - ) - } + useEffect(() => setPainter(chaosGameFinal(width, height, [ + [xform1Weight, buildTransform(xform1Coefs, buildBlend(xform1Coefs, xform1Variations))], + [xform2Weight, buildTransform(xform2Coefs, buildBlend(xform2Coefs, xform2Variations))], + [xform3Weight, buildTransform(xform3Coefs, buildBlend(xform3Coefs, xform3Variations))] + ], identityXform)), [xform1Variations, xform2Variations, xform3Variations]); return ( -
    - {variationEditor("Transform 1", xform1Variations, setXform1Variations)} - {variationEditor("Transform 2", xform2Variations, setXform2Variations)} - {variationEditor("Transform 3", xform3Variations, setXform3Variations)} -
    + <> + + + + ) } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx new file mode 100644 index 0000000..ade4637 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx @@ -0,0 +1,64 @@ +import {useContext, useEffect, useState} from "react"; +import {Coefs} from "../src/coefs" +import { + xform1Coefs, + xform1Weight, + xform1Variations, + xform1CoefsPost, + xform2Coefs, + xform2Weight, + xform2Variations, + xform2CoefsPost, + xform3Coefs, + xform3Weight, + xform3Variations, + xform3CoefsPost, + xformFinalCoefs as xformFinalCoefsDefault, + xformFinalCoefsPost as xformFinalCoefsPostDefault, +} from "../src/params"; +import {PainterContext} from "../src/Canvas" +import {buildBlend, buildTransform} from "./buildTransform"; +import {transformPost} from "./post"; +import {chaosGameFinal} from "./chaosGameFinal" +import {VariationEditor, VariationProps} from "./VariationEditor"; +import {CoefEditor} from "./CoefEditor"; +import {Transform} from "../src/transform"; + +export default function FlameFinal() { + const {width, height, setPainter} = useContext(PainterContext); + + const [xformFinalCoefs, setXformFinalCoefs] = useState(xformFinalCoefsDefault); + + const xformFinalVariationsDefault: VariationProps = { + linear: 0, + julia: 1, + popcorn: 0, + pdj: 0 + } + const [xformFinalVariations, setXformFinalVariations] = useState(xformFinalVariationsDefault); + + const [xformFinalCoefsPost, setXformFinalCoefsPost] = useState(xformFinalCoefsPostDefault); + + useEffect(() => { + const transforms: [number, Transform][] = [ + [xform1Weight, transformPost(buildTransform(xform1Coefs, xform1Variations), xform1CoefsPost)], + [xform2Weight, transformPost(buildTransform(xform2Coefs, xform2Variations), xform2CoefsPost)], + [xform3Weight, transformPost(buildTransform(xform3Coefs, xform3Variations), xform3CoefsPost)] + ]; + + const finalBlend = buildBlend(xformFinalCoefs, xformFinalVariations); + const finalTransform = buildTransform(xformFinalCoefs, finalBlend); + const finalPost = transformPost(finalTransform, xformFinalCoefsPost); + + setPainter(chaosGameFinal(width, height, transforms, finalPost)); + }, [xformFinalCoefs, xformFinalVariations, xformFinalCoefsPost]); + + return ( + <> + + + + + ) +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx new file mode 100644 index 0000000..9b5a6a4 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx @@ -0,0 +1,46 @@ +import {useContext, useEffect, useState} from "react"; +import {Coefs} from "../src/coefs" +import {Transform} from "../src/transform"; +import { + xform1Coefs, + xform1Weight, + xform1Variations, + xform1CoefsPost as xform1CoefsPostDefault, + xform2Coefs, + xform2Weight, + xform2Variations, + xform2CoefsPost as xform2CoefsPostDefault, + xform3Coefs, + xform3Weight, + xform3Variations, + xform3CoefsPost as xform3CoefsPostDefault +} from "../src/params"; +import {PainterContext} from "../src/Canvas" +import {chaosGameFinal} from "./chaosGameFinal" +import {CoefEditor} from "./CoefEditor" +import {transformPost} from "./post"; +import {buildTransform} from "./buildTransform"; + +export default function FlamePost() { + const {width, height, setPainter} = useContext(PainterContext); + + const [xform1CoefsPost, setXform1PostCoefs] = useState(xform1CoefsPostDefault); + const [xform2CoefsPost, setXform2PostCoefs] = useState(xform2CoefsPostDefault); + const [xform3CoefsPost, setXform3PostCoefs] = useState(xform3CoefsPostDefault); + + const identityXform: Transform = (x, y) => [x, y]; + + useEffect(() => setPainter(chaosGameFinal(width, height, [ + [xform1Weight, transformPost(buildTransform(xform1Coefs, xform1Variations), xform1CoefsPost)], + [xform2Weight, transformPost(buildTransform(xform2Coefs, xform2Variations), xform2CoefsPost)], + [xform3Weight, transformPost(buildTransform(xform3Coefs, xform3Variations), xform3CoefsPost)] + ], identityXform)), [xform1CoefsPost, xform2CoefsPost, xform3CoefsPost]); + + return ( + <> + + + + + ) +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx new file mode 100644 index 0000000..212ffcf --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx @@ -0,0 +1,42 @@ +import styles from "../src/css/styles.module.css" + +export interface VariationProps { + linear: number; + julia: number; + popcorn: number; + pdj: number; +} + +export interface Props { + title: String; + variations: VariationProps; + setVariations: (variations: VariationProps) => void; +} + +export const VariationEditor = ({title, variations, setVariations}: Props) => { + return ( +
    +

    {title}

    +
    + Linear: {variations.linear} + setVariations({...variations, linear: Number(e.currentTarget.value)})}/> +
    +
    + Julia: {variations.julia} + setVariations({...variations, julia: Number(e.currentTarget.value)})}/> +
    +
    + Popcorn: {variations.popcorn} + setVariations({...variations, popcorn: Number(e.currentTarget.value)})}/> +
    +
    + PDJ: {variations.pdj} + setVariations({...variations, pdj: Number(e.currentTarget.value)})}/> +
    +
    + ) +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/blend.ts b/blog/2024-11-15-playing-with-fire/2-transforms/blend.ts index 0f8778e..4f3b0da 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/blend.ts +++ b/blog/2024-11-15-playing-with-fire/2-transforms/blend.ts @@ -1,7 +1,10 @@ // hidden-start -import { Variation } from "../src/variation" +import {VariationBlend} from "../src/variationBlend"; // hidden-end -export function blend(x: number, y: number, variations: [number, Variation][]): [number, number] { +export function blend( + x: number, + y: number, + variations: VariationBlend): [number, number] { let [finalX, finalY] = [0, 0]; for (const [weight, variation] of variations) { diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/buildTransform.ts b/blog/2024-11-15-playing-with-fire/2-transforms/buildTransform.ts new file mode 100644 index 0000000..57c1e07 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/buildTransform.ts @@ -0,0 +1,26 @@ +import {applyCoefs, Coefs} from "../src/coefs"; +import {VariationProps} from "./VariationEditor"; +import {Transform} from "../src/transform"; +import {linear} from "../src/linear"; +import {julia} from "../src/julia"; +import {popcorn} from "../src/popcorn"; +import {pdj} from "../src/pdj"; +import {pdjParams} from "../src/params"; +import {blend} from "./blend"; +import {VariationBlend} from "../src/variationBlend"; + +export function buildBlend(coefs: Coefs, variations: VariationProps): VariationBlend { + return [ + [variations.linear, linear], + [variations.julia, julia], + [variations.popcorn, popcorn(coefs)], + [variations.pdj, pdj(pdjParams)] + ] +} + +export function buildTransform(coefs: Coefs, variations: VariationBlend): Transform { + return (x: number, y: number) => { + [x, y] = applyCoefs(x, y, coefs); + return blend(x, y, variations); + } +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts b/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts new file mode 100644 index 0000000..910eba6 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts @@ -0,0 +1,29 @@ +// hidden-start +import { randomBiUnit } from "../src/randomBiUnit"; +import { randomChoice } from "../src/randomChoice"; +import { plotBinary as plot } from "../src/plotBinary" +import {Transform} from "../src/transform"; +const iterations = 500_000; +const step = 1000; +// hidden-end +export function* chaosGameFinal(width: number, height: number, transforms: [number, Transform][], final: Transform) { + let image = new ImageData(width, height); + let [x, y] = [randomBiUnit(), randomBiUnit()]; + + for (let i = 0; i < iterations; i++) { + const [_, transform] = randomChoice(transforms); + [x, y] = transform(x, y); + + // highlight-start + [x, y] = final(x, y); + // highlight-end + + if (i > 20) + plot(x, y, image); + + if (i % step === 0) + yield image; + } + + yield image; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 2826880..5209003 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -37,12 +37,14 @@ the general format. For example: $$ \begin{align*} F_0(x,y) &= \left({x \over 2}, {y \over 2}\right) \\ -&= (a_0 \cdot x + b_0 \cdot y + c_o, d_0 \cdot x + e_0 \cdot y + f_0) \\ +&= (a_0 \cdot x + b_0 \cdot y + c_0, d_0 \cdot x + e_0 \cdot y + f_0) \\ & a_0 = 0.5 \hspace{0.2cm} b_0 = 0 \hspace{0.2cm} c_0 = 0 \\ & d_0 = 0 \hspace{0.2cm} e_0 = 0.5 \hspace{0.2cm} f_0 = 0 \end{align*} $$ +TODO: Explain the applyCoefs function + However, these transforms are pretty boring. We can build more exciting images by using additional functions within the transform. These "sub-functions" are called "variations": @@ -79,10 +81,10 @@ $$ r &= \sqrt{x^2 + y^2} \\ \theta &= \text{arctan}(x / y) \\ \Omega &= \left\{ - \begin{array}{lr} - 0 \hspace{0.4cm} \text{w.p. } 0.5 \\ - \pi \hspace{0.4cm} \text{w.p. } 0.5 \\ - \end{array} +\begin{array}{lr} +0 \hspace{0.4cm} \text{w.p. } 0.5 \\ +\pi \hspace{0.4cm} \text{w.p. } 0.5 \\ +\end{array} \right\} \\ V_{13}(x, y) &= \sqrt{r} \cdot (\text{cos} ( \theta / 2 + \Omega ), \text{sin} ( \theta / 2 + \Omega )) @@ -123,8 +125,7 @@ import pdjSrc from '!!raw-loader!../src/pdj' Now, one variation is fun, but we can also combine variations in a single transform by "blending." Each variation receives the same $x$ and $y$ inputs, and we add together each variation's $x$ and $y$ outputs. -We'll also give each variation a weight ($v_j$) that scales the output, which allows us to control -how much each variation contributes to the transform: +We'll also give each variation a weight ($v_{ij}$) to control how much it contributes to the transform: $$ F_i(x,y) = \sum_{j} v_{ij} V_j(a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) @@ -136,7 +137,10 @@ import blendSource from "!!raw-loader!./blend"; {blendSource} -And with that in place, we have enough to render a first full fractal flame: +And with that in place, we have enough to render a first full fractal flame. +The sliders below change the variation weights for each transform (the $v_{ij}$ parameters); +try changing them around to see which parts of the image are controlled by +each transform. import BrowserOnly from "@docusaurus/BrowserOnly"; import Canvas from "../src/Canvas"; @@ -144,4 +148,29 @@ import FlameBlend from "./FlameBlend"; {() => } + + +## Post transforms + +After variation blending, we apply a second set of transform coordinates. + +The fractal flame below starts with the same initial transforms/variations as the previous fractal flame, +but allows modifying the post-transform coefficients. + +$$ +P_i(x, y) = (\alpha_i x + \beta_i y + \gamma_i, \delta_i x + \epsilon_i y + \zeta_i) +$$ + +import FlamePost from "./FlamePost"; + + + {() => } + + +## Final transform + +import FlameFinal from "./FlameFinal"; + + + {() => } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/post.ts b/blog/2024-11-15-playing-with-fire/2-transforms/post.ts new file mode 100644 index 0000000..fc9a777 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/2-transforms/post.ts @@ -0,0 +1,7 @@ +// hidden-start +import {Coefs} from "../src/coefs"; +import {Transform} from "../src/transform"; +import {applyCoefs} from "../src/coefs"; +// hidden-end +export const transformPost = (transform: Transform, coefs: Coefs): Transform => + (x, y): [number, number] => applyCoefs(...transform(x, y), coefs) \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/blend.ts b/blog/2024-11-15-playing-with-fire/src/blend.ts new file mode 100644 index 0000000..e69de29 diff --git a/blog/2024-11-15-playing-with-fire/src/coefs.ts b/blog/2024-11-15-playing-with-fire/src/coefs.ts index 121d451..da7e129 100644 --- a/blog/2024-11-15-playing-with-fire/src/coefs.ts +++ b/blog/2024-11-15-playing-with-fire/src/coefs.ts @@ -3,7 +3,7 @@ export interface Coefs { d: number, e: number, f: number } -export function applyCoefs(x: number, y: number, coefs: Coefs) { +export function applyCoefs(x: number, y: number, coefs: Coefs): [number, number] { return [ (x * coefs.a + y * coefs.b + coefs.c), (x * coefs.d + y * coefs.e + coefs.f) diff --git a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css index c129a5c..f6fe4d3 100644 --- a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css +++ b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css @@ -1,4 +1,23 @@ -.inputDiv { +.inputGroup { + padding: .5em; + margin: .5em; + border: 1px solid; + border-radius: var(--ifm-global-radius); + border-color: var(--ifm-color-emphasis-500); +} + +.inputTitle { + border: 0 solid; + border-bottom: 1px solid; + border-color: var(--ifm-color-emphasis-500); + margin-bottom: .5em; +} + +.inputElement { padding-left: .5em; padding-right: 1em; +} + +.inputElement > p { + margin: 0 } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/julia.ts b/blog/2024-11-15-playing-with-fire/src/julia.ts index 19c5040..cd0ede6 100644 --- a/blog/2024-11-15-playing-with-fire/src/julia.ts +++ b/blog/2024-11-15-playing-with-fire/src/julia.ts @@ -3,11 +3,14 @@ import { Variation } from './variation' // hidden-end export const julia: Variation = (x, y) => { const r = Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2)); + const theta = Math.atan2(x, y); const omega = Math.random() > 0.5 ? 0 : Math.PI; + const sqrtR = Math.sqrt(r); + const thetaVal = theta / 2 + omega; return [ - r * Math.cos(theta / 2 + omega), - r * Math.sin(theta / 2 + omega) + sqrtR * Math.cos(thetaVal), + sqrtR * Math.sin(thetaVal) ] } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/params.ts b/blog/2024-11-15-playing-with-fire/src/params.ts index 0dee991..6b0acd4 100644 --- a/blog/2024-11-15-playing-with-fire/src/params.ts +++ b/blog/2024-11-15-playing-with-fire/src/params.ts @@ -4,11 +4,11 @@ */ import { Coefs } from './coefs'; +import {VariationBlend} from "./variationBlend"; import { linear } from './linear' import { julia } from './julia' import { popcorn } from './popcorn' import {pdj, PdjParams} from './pdj' -import {Variation} from "./variation" export const identityCoefs: Coefs = { a: 1, b: 0, c: 0, @@ -25,7 +25,7 @@ export const xform1Coefs = { d: 1.381068, e: -1.381068, f: 0, } export const xform1CoefsPost = identityCoefs; -export const xform1Variations = [ +export const xform1Variations: VariationBlend = [ [1, julia] ] export const xform1Color = 0; @@ -39,7 +39,7 @@ export const xform2CoefsPost = { a: 1, b: 0, c: 0.241352, d: 0, e: 1, f: 0.271521, } -export const xform2Variations = [ +export const xform2Variations: VariationBlend = [ [1, linear], [1, popcorn(xform2Coefs)] ] @@ -51,7 +51,7 @@ export const xform3Coefs = { d: 0.740356, e: -1.455964, f: -0.362059, } export const xform3CoefsPost = identityCoefs; -export const xform3Variations = [ +export const xform3Variations: VariationBlend = [ [1, pdj(pdjParams)] ]; export const xform3Color = 0.349; @@ -61,7 +61,7 @@ export const xformFinalCoefs = { d: 0, e: 2, f: 0 } export const xformFinalCoefsPost = identityCoefs; -export const xformFinalVariations = [ +export const xformFinalVariations: VariationBlend = [ [1, julia] ] export const xformFinalColor = 0; diff --git a/blog/2024-11-15-playing-with-fire/src/variationBlend.ts b/blog/2024-11-15-playing-with-fire/src/variationBlend.ts new file mode 100644 index 0000000..37a24f6 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/src/variationBlend.ts @@ -0,0 +1,2 @@ +import {Variation} from "./variation"; +export type VariationBlend = [number, Variation][]; \ No newline at end of file From b7eed2297ae36e97f553689ad3d9da2ca98abc5b Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sat, 30 Nov 2024 18:01:29 -0500 Subject: [PATCH 20/51] Add a reset button Probably overkill, but I kinda like it. --- .../1-introduction/index.mdx | 4 +-- .../2-transforms/CoefEditor.tsx | 7 ++++-- .../2-transforms/FlameBlend.tsx | 25 +++++++++++-------- .../2-transforms/FlameFinal.tsx | 11 +++++--- .../2-transforms/FlamePost.tsx | 20 ++++++++++----- .../2-transforms/VariationEditor.tsx | 7 ++++-- .../2-transforms/index.mdx | 12 +++------ .../2024-11-15-playing-with-fire/params.flame | 4 +-- .../src/Canvas.tsx | 6 +++-- .../src/css/styles.module.css | 5 ++++ .../src/params.ts | 4 +-- 11 files changed, 64 insertions(+), 41 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index 67181ea..ed60823 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -202,6 +202,4 @@ import BrowserOnly from "@docusaurus/BrowserOnly"; import GasketWeighted from "./GasketWeighted"; import Canvas from "../src/Canvas"; - - {() => } - \ No newline at end of file +{() => } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx index 8536381..1eeeb86 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx @@ -8,11 +8,14 @@ export interface Props { isPost: boolean; coefs: Coefs; setCoefs: (coefs: Coefs) => void; + resetCoefs: () => void; } -export const CoefEditor = ({title, isPost, coefs, setCoefs}: Props) => { +export const CoefEditor = ({title, isPost, coefs, setCoefs, resetCoefs}: Props) => { + const resetButton = + return (
    -

    {title}

    +

    {title} {resetButton}

    {isPost ? \alpha : 'a'}: {coefs.a}

    setXform1Variations(xform1VariationsDefault); - const xform2Default: VariationProps = { + const xform2VariationsDefault: VariationProps = { linear: 1, julia: 0, popcorn: 1, pdj: 0 } - const [xform2Variations, setXform2Variations] = useState(xform2Default) + const [xform2Variations, setXform2Variations] = useState(xform2VariationsDefault) + const resetXform2Variations = () => setXform2Variations(xform2VariationsDefault); - const xform3Default: VariationProps = { + const xform3VariationsDefault: VariationProps = { linear: 0, julia: 0, popcorn: 0, pdj: 1 } - const [xform3Variations, setXform3Variations] = useState(xform3Default) + const [xform3Variations, setXform3Variations] = useState(xform3VariationsDefault) + const resetXform3Variations = () => setXform3Variations(xform3VariationsDefault); // Cheating a bit here; for purposes of code re-use, use the post- and final-transform-enabled chaos game, // and swap in identity components for each @@ -53,9 +55,12 @@ export default function FlameBlend() { return ( <> - - - + + + ) } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx index ade4637..f9365b8 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx @@ -28,6 +28,7 @@ export default function FlameFinal() { const {width, height, setPainter} = useContext(PainterContext); const [xformFinalCoefs, setXformFinalCoefs] = useState(xformFinalCoefsDefault); + const resetXformFinalCoefs = () => setXformFinalCoefs(xformFinalCoefsDefault); const xformFinalVariationsDefault: VariationProps = { linear: 0, @@ -36,8 +37,10 @@ export default function FlameFinal() { pdj: 0 } const [xformFinalVariations, setXformFinalVariations] = useState(xformFinalVariationsDefault); + const resetXformFinalVariations = () => setXformFinalVariations(xformFinalVariationsDefault); const [xformFinalCoefsPost, setXformFinalCoefsPost] = useState(xformFinalCoefsPostDefault); + const resetXformFinalCoefsPost = () => setXformFinalCoefsPost(xformFinalCoefsPostDefault); useEffect(() => { const transforms: [number, Transform][] = [ @@ -55,10 +58,12 @@ export default function FlameFinal() { return ( <> - + - + setVariations={setXformFinalVariations} resetVariations={resetXformFinalVariations}/> + ) } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx index 9b5a6a4..8d1590c 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx @@ -24,9 +24,14 @@ import {buildTransform} from "./buildTransform"; export default function FlamePost() { const {width, height, setPainter} = useContext(PainterContext); - const [xform1CoefsPost, setXform1PostCoefs] = useState(xform1CoefsPostDefault); - const [xform2CoefsPost, setXform2PostCoefs] = useState(xform2CoefsPostDefault); - const [xform3CoefsPost, setXform3PostCoefs] = useState(xform3CoefsPostDefault); + const [xform1CoefsPost, setXform1CoefsPost] = useState(xform1CoefsPostDefault); + const resetXform1CoefsPost = () => setXform1CoefsPost(xform1CoefsPostDefault); + + const [xform2CoefsPost, setXform2CoefsPost] = useState(xform2CoefsPostDefault); + const resetXform2CoefsPost = () => setXform2CoefsPost(xform2CoefsPostDefault); + + const [xform3CoefsPost, setXform3CoefsPost] = useState(xform3CoefsPostDefault); + const resetXform3CoefsPost = () => setXform1CoefsPost(xform3CoefsPostDefault); const identityXform: Transform = (x, y) => [x, y]; @@ -38,9 +43,12 @@ export default function FlamePost() { return ( <> - - - + + + ) } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx index 212ffcf..1785ea7 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx @@ -11,12 +11,15 @@ export interface Props { title: String; variations: VariationProps; setVariations: (variations: VariationProps) => void; + resetVariations: () => void; } -export const VariationEditor = ({title, variations, setVariations}: Props) => { +export const VariationEditor = ({title, variations, setVariations, resetVariations}: Props) => { + const resetButton = + return (
    -

    {title}

    +

    {title} {resetButton}

    Linear: {variations.linear} - {() => } - +{() => } ## Post transforms @@ -163,14 +161,10 @@ $$ import FlamePost from "./FlamePost"; - - {() => } - +{() => } ## Final transform import FlameFinal from "./FlameFinal"; - - {() => } - \ No newline at end of file +{() => } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/params.flame b/blog/2024-11-15-playing-with-fire/params.flame index 2bc531b..b13e1c3 100644 --- a/blog/2024-11-15-playing-with-fire/params.flame +++ b/blog/2024-11-15-playing-with-fire/params.flame @@ -2,7 +2,7 @@ - + 3A78875998AA5E9DAC78B1C2599BAB36798A2252601B3438 1823270D1215080705010101000000000002080A090A0809 @@ -80,7 +80,7 @@ - + 7E3037762C45722B496E2A4E6A2950672853652754632656 diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 85e152f..16f694d 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -14,8 +14,8 @@ export interface PainterProps { export const PainterContext = createContext(null); interface CanvasProps { - width: number; - height: number; + width?: number; + height?: number; children?: React.ReactNode; } @@ -125,6 +125,8 @@ export default function Canvas({width, height, children}: CanvasProps) { const [painter, setPainter] = useState>(null); useEffect(() => setAnimHolder({ painter }), [painter]); + width = width ?? 500; + height = height ?? 500; return ( <>
    diff --git a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css index f6fe4d3..4ceecaf 100644 --- a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css +++ b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css @@ -20,4 +20,9 @@ .inputElement > p { margin: 0 +} + +.inputReset { + display: flex; + float: right; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/params.ts b/blog/2024-11-15-playing-with-fire/src/params.ts index 6b0acd4..1688eec 100644 --- a/blog/2024-11-15-playing-with-fire/src/params.ts +++ b/blog/2024-11-15-playing-with-fire/src/params.ts @@ -36,8 +36,8 @@ export const xform2Coefs = { d: -0.031367, e: 0.031393, f: 0, } export const xform2CoefsPost = { - a: 1, b: 0, c: 0.241352, - d: 0, e: 1, f: 0.271521, + a: 1, b: 0, c: 0.24, + d: 0, e: 1, f: 0.27, } export const xform2Variations: VariationBlend = [ [1, linear], From 06069fdceaf9dc543767a90b643c39ca505262d0 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 1 Dec 2024 15:16:30 -0500 Subject: [PATCH 21/51] Update documentation --- .../1-introduction/plot.ts | 4 +- .../3-log-density.mdx | 9 ----- .../3-log-density/FlameHistogram.tsx | 5 +++ .../3-log-density/PlotHistogram.ts | 35 +++++++++++++++++ .../3-log-density/index.mdx | 28 ++++++++++++++ .../src/Canvas.tsx | 38 ++++++++++++------- 6 files changed, 95 insertions(+), 24 deletions(-) delete mode 100644 blog/2024-11-15-playing-with-fire/3-log-density.mdx create mode 100644 blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx create mode 100644 blog/2024-11-15-playing-with-fire/3-log-density/PlotHistogram.ts create mode 100644 blog/2024-11-15-playing-with-fire/3-log-density/index.mdx diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts index e18a5b0..23f0b2f 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts @@ -1,5 +1,7 @@ export function plot(x: number, y: number, image: ImageData) { - // Translate (x,y) coordinates to pixel coordinates. + // Translate (x,y) coordinates to pixel coordinates; + // also known as a "camera" function. + // // The display range we care about is x=[0, 1], y=[0, 1], // so our pixelX and pixelY coordinates are easy to calculate: const pixelX = Math.floor(x * image.width); diff --git a/blog/2024-11-15-playing-with-fire/3-log-density.mdx b/blog/2024-11-15-playing-with-fire/3-log-density.mdx deleted file mode 100644 index fe7ddfe..0000000 --- a/blog/2024-11-15-playing-with-fire/3-log-density.mdx +++ /dev/null @@ -1,9 +0,0 @@ ---- -slug: 2024/11/playing-with-fire-log-density -title: "Playing with fire: Log-density display" -date: 2024-11-15 14:00:00 -authors: [bspeice] -tags: [] ---- - -Testing \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx new file mode 100644 index 0000000..3e134d7 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx @@ -0,0 +1,5 @@ +import {VictoryArea} from "victory"; + +function F() { + return (); + this.pixels.forEach(value => { + const bucket = 32 - Math.clz32(value); + + if (bucket in data) { + data[bucket] += 1; + } else { + data[bucket] = 1; + } + }) + + const output: {x: number, y: number}[] = []; + data.forEach((bucket, value) => + output.push({x: Math.pow(bucket, 2), y: value})); + return output; + } +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx new file mode 100644 index 0000000..37292ec --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -0,0 +1,28 @@ +--- +slug: 2024/11/playing-with-fire-log-density +title: "Playing with fire: Log-density display" +date: 2024-11-15 14:00:00 +authors: [bspeice] +tags: [] +--- + +So far, our `plot()` function has been fairly simple; map an input coordinate +to a specific pixel, and color in that pixel. +This works well for simple function systems (like Sierpinski's Gasket), +but more complex systems (like our reference parameters) produce grainy images. + +Every time we "turn on" pixels that have already been enabled, we're wasting work. +Can we do something more intelligent with that information? + + + +## Image histograms + +To start with, it's worth demonstrating how much work is actually "wasted." +We'll render the reference image again, but this time, counting the times +we tried to turn on a pixel. + +import CodeBlock from "@theme/CodeBlock"; +import plotHistogramSource from "!!raw-loader!./PlotHistogram"; + +{plotHistogramSource} diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 16f694d..5788598 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -16,6 +16,7 @@ export const PainterContext = createContext(null); interface CanvasProps { width?: number; height?: number; + hidden?: boolean; children?: React.ReactNode; } @@ -23,31 +24,39 @@ interface CanvasProps { * Draw fractal flames to a canvas. * * This component is a bit involved because it attempts to solve - * a couple problems at the same time: + * a couple problems at once: * - Incrementally drawing an image to the canvas - * - Interrupting drawing with new parameters on demand + * - Interrupting drawing with new parameters * - Dark mode * - * Image iterators provide a means to draw incremental images; - * iterators can easily checkpoint state, and this component will - * request the next image on the next animation frame. As a result, - * the browser should be responsive even though we run CPU-heavy - * code on the main thread. + * Running a full render is labor-intensive, so we model it + * as an iterator that yields an image of the current system. + * Internally, that iterator is re-queued on each new image; + * so long as that image is returned quickly, we keep + * the main loop running even with CPU-heavy code. * - * Swapping a new iterator allows interrupting a render in progress, - * as the canvas completely repaints on each provided image. + * To interrupt drawing, children set the active iterator + * through the context provider. This component doesn't care + * about which iterator is in progress, it exists only + * to fetch the next image and paint it to our canvas. * - * Finally, check whether dark mode is active, and invert the most - * recent image prior to painting if so. + * Finally, we make a distinction between "render" and "paint" buffers. + * The render image is provided by the iterator, and then: + * - If light mode is active, draw it to the canvas as-is + * - If dark mode is active, copy the "render" buffer to the "paint" buffer, + * invert colors, and then draw the image * - * PainterContext is used to allow child elements to swap in - * new iterators. + * TODO(bspeice): Can we make this "re-queueing iterator" pattern generic? + * It would be nice to have iterators returning arbitrary objects, + * but we rely on contexts to manage the iterator, and there's + * no good way to make those generic. * * @param width Canvas draw width * @param height Canvas draw height + * @param hidden Hide the canvas * @param children Child elements */ -export default function Canvas({width, height, children}: CanvasProps) { +export default function Canvas({width, height, hidden, children}: CanvasProps) { const [canvasCtx, setCanvasCtx] = useState(null); const canvasRef = useCallback(node => { if (node !== null) { @@ -134,6 +143,7 @@ export default function Canvas({width, height, children}: CanvasProps) { ref={canvasRef} width={width} height={height} + hidden={hidden ?? false} style={{ aspectRatio: width / height, width: '80%' From 79b66337e80919143310799bfbb48ae44e159000 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 1 Dec 2024 18:17:36 -0500 Subject: [PATCH 22/51] Checkpoint for histogram It takes a lot of render time to get a usable result, and it's not that interesting. Committing so I can save the work if I want to revisit it, but abandoning the idea for now. --- .../1-introduction/index.mdx | 3 +- .../2-transforms/FlameFinal.tsx | 12 +- .../2-transforms/index.mdx | 7 +- .../3-log-density/FlameHistogram.tsx | 31 ++- .../3-log-density/PlotHistogram.ts | 35 ---- .../3-log-density/chaosGameHistogram.ts | 34 ++++ .../3-log-density/index.mdx | 9 +- .../3-log-density/plotHistogram.ts | 23 +++ .../src/Canvas.tsx | 191 ++++++++---------- 9 files changed, 192 insertions(+), 153 deletions(-) delete mode 100644 blog/2024-11-15-playing-with-fire/3-log-density/PlotHistogram.ts create mode 100644 blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts create mode 100644 blog/2024-11-15-playing-with-fire/3-log-density/plotHistogram.ts diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index ed60823..e4f1988 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -198,8 +198,7 @@ import chaosGameWeightedSource from "!!raw-loader!./chaosGameWeighted"; {chaosGameWeightedSource} -import BrowserOnly from "@docusaurus/BrowserOnly"; import GasketWeighted from "./GasketWeighted"; import Canvas from "../src/Canvas"; -{() => } \ No newline at end of file + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx index f9365b8..b11d9d4 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx @@ -24,6 +24,12 @@ import {VariationEditor, VariationProps} from "./VariationEditor"; import {CoefEditor} from "./CoefEditor"; import {Transform} from "../src/transform"; +export const transforms: [number, Transform][] = [ + [xform1Weight, transformPost(buildTransform(xform1Coefs, xform1Variations), xform1CoefsPost)], + [xform2Weight, transformPost(buildTransform(xform2Coefs, xform2Variations), xform2CoefsPost)], + [xform3Weight, transformPost(buildTransform(xform3Coefs, xform3Variations), xform3CoefsPost)] +]; + export default function FlameFinal() { const {width, height, setPainter} = useContext(PainterContext); @@ -43,12 +49,6 @@ export default function FlameFinal() { const resetXformFinalCoefsPost = () => setXformFinalCoefsPost(xformFinalCoefsPostDefault); useEffect(() => { - const transforms: [number, Transform][] = [ - [xform1Weight, transformPost(buildTransform(xform1Coefs, xform1Variations), xform1CoefsPost)], - [xform2Weight, transformPost(buildTransform(xform2Coefs, xform2Variations), xform2CoefsPost)], - [xform3Weight, transformPost(buildTransform(xform3Coefs, xform3Variations), xform3CoefsPost)] - ]; - const finalBlend = buildBlend(xformFinalCoefs, xformFinalVariations); const finalTransform = buildTransform(xformFinalCoefs, finalBlend); const finalPost = transformPost(finalTransform, xformFinalCoefsPost); diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 59e24cd..481e4b6 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -142,11 +142,10 @@ The sliders below change the variation weights for each transform (the $v_{ij}$ try changing them around to see which parts of the image are controlled by each transform. -import BrowserOnly from "@docusaurus/BrowserOnly"; import Canvas from "../src/Canvas"; import FlameBlend from "./FlameBlend"; -{() => } + ## Post transforms @@ -161,10 +160,10 @@ $$ import FlamePost from "./FlamePost"; -{() => } + ## Final transform import FlameFinal from "./FlameFinal"; -{() => } \ No newline at end of file + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx index 3e134d7..976f6fb 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx @@ -1,5 +1,30 @@ -import {VictoryArea} from "victory"; +import {VictoryChart, VictoryLine, VictoryScatter, VictoryTheme} from "victory"; +import {useContext, useEffect, useState} from "react"; +import {PainterContext} from "../src/Canvas"; +import {chaosGameHistogram} from "./chaosGameHistogram"; +import {PlotData, plotHistogram} from "./plotHistogram"; -function F() { - return void, setCdf: (data: PlotData) => void) { + const emptyImage = new ImageData(width, height); + for (let histogram of chaosGameHistogram(width, height)) { + const plotData = plotHistogram(histogram); + setPdf(plotData); + yield emptyImage; + } +} + +export default function FlameHistogram() { + const {width, height, setPainter} = useContext(PainterContext); + const [pdfData, setPdfData] = useState<{ x: number, y: number }[]>(null); + + useEffect(() => setPainter(plotChaosGame(width, height, setPdfData, null)), []); + + return ( + + + + ) } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/PlotHistogram.ts b/blog/2024-11-15-playing-with-fire/3-log-density/PlotHistogram.ts deleted file mode 100644 index 7a527e8..0000000 --- a/blog/2024-11-15-playing-with-fire/3-log-density/PlotHistogram.ts +++ /dev/null @@ -1,35 +0,0 @@ -// hidden-start -import {VictoryChart} from "victory"; -import {camera, histIndex} from "../src/camera"; -// hidden-end -export class PlotHistogram { - public readonly pixels: Uint32Array; - - public constructor(private readonly width: number, height: number) { - this.pixels = new Uint32Array(width * height); - } - - public plot(x: number, y: number) { - const [pixelX, pixelY] = camera(x, y, this.width); - const pixelIndex = histIndex(pixelX, pixelY, this.width, 1); - this.pixels[pixelIndex] += 1; - } - - public getHistogram() { - const data = new Map(); - this.pixels.forEach(value => { - const bucket = 32 - Math.clz32(value); - - if (bucket in data) { - data[bucket] += 1; - } else { - data[bucket] = 1; - } - }) - - const output: {x: number, y: number}[] = []; - data.forEach((bucket, value) => - output.push({x: Math.pow(bucket, 2), y: value})); - return output; - } -} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts new file mode 100644 index 0000000..c831353 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts @@ -0,0 +1,34 @@ +import {plot} from "./plotHistogram"; +import {randomBiUnit} from "../src/randomBiUnit"; +import {randomChoice} from "../src/randomChoice"; +import {buildTransform} from "../2-transforms/buildTransform"; +import {transformPost} from "../2-transforms/post"; +import {transforms} from "../2-transforms/FlameFinal"; +import * as params from "../src/params"; + +const finalTransform = buildTransform(params.xformFinalCoefs, params.xformFinalVariations); +const finalTransformPost = transformPost(finalTransform, params.xformFinalCoefsPost); + +const step = 1000; +const quality = 1; + +export function* chaosGameHistogram(width: number, height: number) { + let iterations = quality * width * height; + let histogram = new Uint32Array(width * height); + + let [x, y] = [randomBiUnit(), randomBiUnit()]; + + for (let i = 0; i < iterations; i++) { + const [_, transform] = randomChoice(transforms); + [x, y] = transform(x, y); + [x, y] = finalTransformPost(x, y); + + if (i > 20) + plot(x, y, width, histogram); + + if (i % step === 0) + yield histogram; + } + + yield histogram; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index 37292ec..ce2168c 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -23,6 +23,13 @@ We'll render the reference image again, but this time, counting the times we tried to turn on a pixel. import CodeBlock from "@theme/CodeBlock"; -import plotHistogramSource from "!!raw-loader!./PlotHistogram"; +import plotHistogramSource from "!!raw-loader!./plotHistogram"; {plotHistogramSource} + +import Canvas from "../src/Canvas"; +import FlameHistogram from "./FlameHistogram"; + + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/plotHistogram.ts b/blog/2024-11-15-playing-with-fire/3-log-density/plotHistogram.ts new file mode 100644 index 0000000..479d0ae --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/3-log-density/plotHistogram.ts @@ -0,0 +1,23 @@ +// hidden-start +import {camera, histIndex} from "../src/camera"; +// hidden-end +export function plot(x: number, y: number, width: number, hitCount: Uint32Array) { + const [pixelX, pixelY] = camera(x, y, width); + const pixelIndex = histIndex(pixelX, pixelY, width, 1); + hitCount[pixelIndex] += 1; +} + +export type PlotData = {x: number, y: number}[]; +export function plotHistogram(hitCount: Uint32Array) { + const data = new Map(); + hitCount.forEach(value => { + const bucket = 32 - Math.clz32(value); + const currentCount = data.get(bucket) ?? 0; + data.set(bucket, currentCount + 1); + }) + + const output: PlotData = []; + data.forEach((value, bucket) => + output.push({x: Math.pow(2, bucket), y: value})); + return output; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 5788598..20e6bee 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -1,23 +1,80 @@ import React, {useCallback, useEffect, useState, createContext} from "react"; import {useColorMode} from "@docusaurus/theme-common"; +import BrowserOnly from "@docusaurus/BrowserOnly"; -export interface PainterProps { - readonly width: number; - readonly height: number; - readonly setPainter: (painter: Iterator) => void; +function invertImage(sourceImage: ImageData): ImageData { + const image = new ImageData(sourceImage.width, sourceImage.height); + image.data.forEach((value, index) => + image.data[index] = index % 4 === 3 ? value : 0xff - value) + + return image; +} + +type InvertibleCanvasProps = { + width: number, + height: number, + hidden?: boolean, + // NOTE: Images are provided as a single-element array + //so we can allow re-painting with the same (modified) ImageData reference. + image?: [ImageData], } /** - * Context provider for child elements to submit image iterator functions - * (painters) for rendering + * Draw images to a canvas, automatically inverting colors as needed. + * + * @param width Canvas width + * @param height Canvas height + * @param hidden Hide the canvas element + * @param image Image data to draw on the canvas */ +const InvertibleCanvas: React.FC = ({width, height, hidden, image}) => { + const [canvasCtx, setCanvasCtx] = useState(null); + const canvasRef = useCallback(node => { + if (node !== null) { + setCanvasCtx(node.getContext("2d")); + } + }, []); + + const [paintImage, setPaintImage] = useState<[ImageData]>(null); + useEffect(() => { + if (canvasCtx && paintImage) { + canvasCtx.putImageData(paintImage[0], 0, 0); + } + }, [canvasCtx, paintImage]); + + const {colorMode} = useColorMode(); + useEffect(() => { + if (image) { + setPaintImage(colorMode === 'light' ? image : [invertImage(image[0])]); + } + }, [image, colorMode]); + + return ( +
    diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx index 0a80624..c125281 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx @@ -1,41 +1,15 @@ import React, {useContext, useEffect, useMemo, useRef, useState} from "react"; import * as params from "../src/params"; -import {PainterContext} from "../src/Canvas"; -import {chaosGameColor} from "./chaosGameColor"; +import {InvertibleCanvas, PainterContext} from "../src/Canvas"; +import {chaosGameColor, ChaosGameColorProps, TransformColor} from "./chaosGameColor"; import styles from "../src/css/styles.module.css"; -import {palette} from "../src/params"; - -const colorSwatch = (width: number, height: number, palette: number[], color: number): ImageData => { - return new ImageData(width, height); -} - -type ColorSliderProps = { - title: string; - palette: number[]; - color: number; - setColor: (color: number) => void; - children?: React.ReactNode; -} -const ColorSlider: React.FC = ({title, palette, color, setColor, children}) => { - const swatch = useMemo(() => colorSwatch(50, 20, palette, color), [palette, color]); - - return ( - <> -
    -

    {title}: {color}

    - setColor(Number(e.currentTarget.value))}/> -
    - {children} - - ) -} +import {colorFromPalette} from "@site/blog/2024-11-15-playing-with-fire/3-log-density/color"; type PaletteBarProps = { height: number; palette: number[]; - sizingStyle: any; + sizingStyle?: any; children?: React.ReactNode; } const PaletteBar: React.FC = ({height, palette, sizingStyle, children}) => { @@ -61,6 +35,76 @@ const PaletteBar: React.FC = ({height, palette, sizingStyle, ch ) } +type AutoSizingCanvasProps = { + painter: (width: number, height: number) => ImageData; +} +const AutoSizingCanvas: React.FC = ({painter}) => { + const sizingRef = useRef(null); + const [width, setWidth] = useState(0); + const [height, setHeight] = useState(0); + + useEffect(() => { + if (sizingRef) { + setWidth(sizingRef.current.offsetWidth); + setHeight(sizingRef.current.offsetHeight) + } + }, [sizingRef]); + + const image: [ImageData] = useMemo(() => (width && height) ? [painter(width, height)] : null, [painter, width, height]); + + return ( +
    + ) +} + +const colorSwatchPainter = (palette: number[], color: number) => + (width: number, height: number) => { + const [r, g, b] = colorFromPalette(palette, color); + const image = new ImageData(width, height); + for (let i = 0; i < image.data.length; i += 4) { + image.data[i] = r * 0xff; + image.data[i + 1] = g * 0xff; + image.data[i + 2] = b * 0xff; + image.data[i + 3] = 0xff; + } + + return image; + } + +type ColorEditorProps = { + title: string; + palette: number[]; + transformColor: TransformColor; + setTransformColor: (transformColor: TransformColor) => void; + resetTransformColor: () => void; + children?: React.ReactNode; +} +const ColorEditor: React.FC = ({title, palette, transformColor, setTransformColor, resetTransformColor, children}) => { + const painter = useMemo(() => colorSwatchPainter(palette, transformColor.color), [palette, transformColor]); + const resetButton = + + return ( + <> +
    +

    {title} {resetButton}

    +
    +

    Color: {transformColor.color}

    + setTransformColor({...transformColor, color: Number(e.currentTarget.value)})}/> +
    +
    +

    Color speed: {transformColor.colorSpeed}

    + setTransformColor({...transformColor, colorSpeed: Number(e.currentTarget.value)})}/> +
    +
    + +
    +
    + + ) +} + type Props = { quality?: number; children?: React.ReactElement; @@ -68,36 +112,64 @@ type Props = { export default function FlameColor({quality, children}: Props) { const {width, height, setPainter} = useContext(PainterContext); - const [xform1Color, setXform1Color] = useState(params.xform1Color); - const [xform2Color, setXform2Color] = useState(params.xform2Color); - const [xform3Color, setXform3Color] = useState(params.xform3Color); - const resetColor = () => { - setXform1Color(params.xform1Color); - setXform2Color(params.xform2Color); - setXform3Color(params.xform3Color); - } + const xform1ColorDefault: TransformColor = {color: params.xform1Color, colorSpeed: 0.5}; + const [xform1Color, setXform1Color] = useState(xform1ColorDefault); + const resetXform1Color = () => setXform1Color(xform1ColorDefault); + + const xform2ColorDefault: TransformColor = {color: params.xform2Color, colorSpeed: 0.5}; + const [xform2Color, setXform2Color] = useState(xform2ColorDefault); + const resetXform2Color = () => setXform2Color(xform2ColorDefault); + + const xform3ColorDefault: TransformColor = {color: params.xform3Color, colorSpeed: 0.5}; + const [xform3Color, setXform3Color] = useState(xform3ColorDefault); + const resetXform3Color = () => setXform3Color(xform3ColorDefault); + + const xformFinalColorDefault: TransformColor = {color: params.xformFinalColor, colorSpeed: 0}; + const [xformFinalColor, setXformFinalColor] = useState(xformFinalColorDefault); + const resetXformFinalColor = () => setXformFinalColor(xformFinalColorDefault); useEffect(() => { - const gameParams = { + const gameParams: ChaosGameColorProps = { width, height, transforms: params.xforms, final: params.xformFinal, quality, palette: params.palette, - colors: [xform1Color, xform2Color, xform3Color] + colors: [xform1Color, xform2Color, xform3Color], + finalColor: xformFinalColor } setPainter(chaosGameColor(gameParams)); - }, [xform1Color, xform2Color, xform3Color]); + }, [xform1Color, xform2Color, xform3Color, xformFinalColor]); - const resetButton = return ( -
    -

    Transform Colors {resetButton}

    - - - - -
    + <> + + + + + + {children} + ); } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts index cb02bc1..11b6ed6 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts @@ -4,11 +4,21 @@ import {randomChoice} from "../src/randomChoice"; import {camera, histIndex} from "../src/camera"; import {colorFromPalette, paintColor} from "./color"; -type ChaosGameHistogramProps = ChaosGameFinalProps & { - palette: number[]; - colors: number[]; +export type TransformColor = { + color: number; + colorSpeed: number; } -export function* chaosGameColor({width, height, transforms, final, palette, colors, quality, step}: ChaosGameHistogramProps) { + +function mixColor(color1: number, color2: number, colorSpeed: number) { + return color1 * (1 - colorSpeed) + color2 * colorSpeed; +} + +export type ChaosGameColorProps = ChaosGameFinalProps & { + palette: number[]; + colors: TransformColor[]; + finalColor: TransformColor; +} +export function* chaosGameColor({width, height, transforms, final, palette, colors, finalColor, quality, step}: ChaosGameColorProps) { let iterations = (quality ?? 1) * width * height; step = step ?? 100_000; @@ -33,8 +43,11 @@ export function* chaosGameColor({width, height, transforms, final, palette, colo if (pixelIndex < 0 || pixelIndex >= alpha.length) continue; - currentColor = (currentColor + colors[transformIndex]) / 2; - const [r, g, b] = colorFromPalette(palette, currentColor); + const transformColor = colors[transformIndex]; + currentColor = mixColor(currentColor, transformColor.color, transformColor.colorSpeed); + + const colorFinal = mixColor(currentColor, finalColor.color, finalColor.colorSpeed); + const [r, g, b] = colorFromPalette(palette, colorFinal); red[pixelIndex] += r; green[pixelIndex] += g; blue[pixelIndex] += b; diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 9a9c998..e4b8fbe 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -26,7 +26,7 @@ type InvertibleCanvasProps = { * @param hidden Hide the canvas element * @param image Image data to draw on the canvas */ -const InvertibleCanvas: React.FC = ({width, height, image}) => { +export const InvertibleCanvas: React.FC = ({width, height, image}) => { const [canvasCtx, setCanvasCtx] = useState(null); const canvasRef = useCallback(node => { if (node !== null) { diff --git a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css index 4ceecaf..6c16604 100644 --- a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css +++ b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css @@ -22,6 +22,10 @@ margin: 0 } +.inputElement > input { + width: 100%; +} + .inputReset { display: flex; float: right; From 137dcc675d7fb93cf778c54722afb7c7ed24427f Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Wed, 4 Dec 2024 22:45:48 -0500 Subject: [PATCH 30/51] Fix color swatch paint area Still hate the code, but at least it's sized correctly now --- .../3-log-density/FlameColor.tsx | 3 ++- blog/2024-11-15-playing-with-fire/3-log-density/index.mdx | 4 ++-- blog/2024-11-15-playing-with-fire/src/Canvas.tsx | 5 +---- 3 files changed, 5 insertions(+), 7 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx index c125281..5064ebf 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx @@ -45,6 +45,7 @@ const AutoSizingCanvas: React.FC = ({painter}) => { useEffect(() => { if (sizingRef) { + console.log(`Sizing; width=${sizingRef.current.offsetWidth} height=${sizingRef.current.offsetHeight}`) setWidth(sizingRef.current.offsetWidth); setHeight(sizingRef.current.offsetHeight) } @@ -53,7 +54,7 @@ const AutoSizingCanvas: React.FC = ({painter}) => { const image: [ImageData] = useMemo(() => (width && height) ? [painter(width, height)] : null, [painter, width, height]); return ( -
    +
    ) } diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index df0efa2..b4d552c 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -32,13 +32,13 @@ import Canvas from "../src/Canvas"; import FlameHistogram from "./FlameHistogram"; import {paintLinear} from "./paintLinear"; - + ## Log display import {paintLogarithmic} from './paintLogarithmic' - + ## Color diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index e4b8fbe..41c851a 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -53,10 +53,7 @@ export const InvertibleCanvas: React.FC = ({width, height ref={canvasRef} width={width} height={height} - style={{ - aspectRatio: width / height, - width: '75%' - }} + style={{aspectRatio: width / height}} /> ) } From 845e7fb4f764bb5579ee65703b95925e55ffca72 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sat, 7 Dec 2024 15:18:12 -0500 Subject: [PATCH 31/51] Palette bar implementation --- .../3-log-density/FlameColor.tsx | 74 +++++++++++-------- 1 file changed, 42 insertions(+), 32 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx index 5064ebf..2498e68 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx @@ -1,39 +1,11 @@ import React, {useContext, useEffect, useMemo, useRef, useState} from "react"; import * as params from "../src/params"; import {InvertibleCanvas, PainterContext} from "../src/Canvas"; +import {colorFromPalette} from "./color"; import {chaosGameColor, ChaosGameColorProps, TransformColor} from "./chaosGameColor"; import styles from "../src/css/styles.module.css"; -import {colorFromPalette} from "@site/blog/2024-11-15-playing-with-fire/3-log-density/color"; - -type PaletteBarProps = { - height: number; - palette: number[]; - sizingStyle?: any; - children?: React.ReactNode; -} -const PaletteBar: React.FC = ({height, palette, sizingStyle, children}) => { - const sizingRef = useRef(null); - const [width, setWidth] = useState(0); - useEffect(() => { - if (!sizingRef.current) { - return; - } - - setWidth(sizingRef.current.offsetWidth); - }, [sizingRef.current]); - - const canvasRef = useRef(null); - useEffect(() => { - if (!canvasRef.current) { - return; - } - }, [canvasRef.current]); - - return ( -
    - ) -} +import {histIndex} from "../src/camera"; type AutoSizingCanvasProps = { painter: (width: number, height: number) => ImageData; @@ -45,7 +17,6 @@ const AutoSizingCanvas: React.FC = ({painter}) => { useEffect(() => { if (sizingRef) { - console.log(`Sizing; width=${sizingRef.current.offsetWidth} height=${sizingRef.current.offsetHeight}`) setWidth(sizingRef.current.offsetWidth); setHeight(sizingRef.current.offsetHeight) } @@ -54,7 +25,45 @@ const AutoSizingCanvas: React.FC = ({painter}) => { const image: [ImageData] = useMemo(() => (width && height) ? [painter(width, height)] : null, [painter, width, height]); return ( -
    +
    + +
    + ) +} + +const paletteBarPainter = (palette: number[]) => + (width: number, height: number) => { + const image = new ImageData(width, height); + for (let x = 0; x < width; x++) { + const colorIndex = x / width; + const [r, g, b] = colorFromPalette(palette, colorIndex); + + for (let y = 0; y < height; y++) { + const pixelIndex = histIndex(x, y, width, 4); + image.data[pixelIndex] = r * 0xff; + image.data[pixelIndex + 1] = g * 0xff; + image.data[pixelIndex + 2] = b * 0xff; + image.data[pixelIndex + 3] = 0xff; + } + } + return image; + } + +type PaletteBarProps = { + height: number; + palette: number[]; + children?: React.ReactNode; +} +const PaletteBar: React.FC = ({height, palette, children}) => { + const painter = useMemo(() => paletteBarPainter(palette), [palette]); + + return ( + <> +
    + +
    + {children} + ) } @@ -102,6 +111,7 @@ const ColorEditor: React.FC = ({title, palette, transformColor
    + {children} ) } From 3c583705f805c7f06d4ec86cc26e1211b8086854 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 8 Dec 2024 15:35:27 -0500 Subject: [PATCH 32/51] Fix final transform modifying coordinates --- .../2-transforms/CoefEditor.tsx | 12 ++++++------ .../3-log-density/FlameColor.tsx | 2 +- .../3-log-density/FlameHistogram.tsx | 2 +- .../3-log-density/chaosGameColor.ts | 3 +-- .../3-log-density/chaosGameHistogram.ts | 12 ++++++------ .../3-log-density/index.mdx | 14 +++++++++++--- .../3-log-density/{color.ts => paintColor.ts} | 0 .../src/css/styles.module.css | 2 +- 8 files changed, 27 insertions(+), 20 deletions(-) rename blog/2024-11-15-playing-with-fire/3-log-density/{color.ts => paintColor.ts} (100%) diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx index 4a91a38..53080c3 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx @@ -18,32 +18,32 @@ export const CoefEditor = ({title, isPost, coefs, setCoefs, resetCoefs}: Props)

    {title} {resetButton}

    {isPost ? \alpha : 'a'}: {coefs.a}

    - setCoefs({...coefs, a: Number(e.currentTarget.value)})}/>

    {isPost ? \beta : 'b'}: {coefs.b}

    - setCoefs({...coefs, b: Number(e.currentTarget.value)})}/>

    {isPost ? \gamma : 'c'}: {coefs.c}

    - setCoefs({...coefs, c: Number(e.currentTarget.value)})}/>

    {isPost ? \delta : 'd'}: {coefs.d}

    - setCoefs({...coefs, d: Number(e.currentTarget.value)})}/>

    {isPost ? \epsilon : 'e'}: {coefs.e}

    - setCoefs({...coefs, e: Number(e.currentTarget.value)})}/>

    {isPost ? \zeta : 'f'}: {coefs.f}

    - setCoefs({...coefs, f: Number(e.currentTarget.value)})}/>
    diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx index 2498e68..22461b2 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx @@ -1,7 +1,7 @@ import React, {useContext, useEffect, useMemo, useRef, useState} from "react"; import * as params from "../src/params"; import {InvertibleCanvas, PainterContext} from "../src/Canvas"; -import {colorFromPalette} from "./color"; +import {colorFromPalette} from "./paintColor"; import {chaosGameColor, ChaosGameColorProps, TransformColor} from "./chaosGameColor"; import styles from "../src/css/styles.module.css"; diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx index 9ed60fa..8db4119 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx @@ -1,7 +1,7 @@ import React, {useContext, useEffect} from "react"; import * as params from "../src/params"; import {PainterContext} from "../src/Canvas"; -import {chaosGameHistogram} from "@site/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram"; +import {chaosGameHistogram} from "./chaosGameHistogram"; type Props = { quality?: number; diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts index 11b6ed6..dd3a1aa 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts @@ -2,7 +2,7 @@ import {ChaosGameFinalProps} from "../2-transforms/chaosGameFinal"; import {randomBiUnit} from "../src/randomBiUnit"; import {randomChoice} from "../src/randomChoice"; import {camera, histIndex} from "../src/camera"; -import {colorFromPalette, paintColor} from "./color"; +import {colorFromPalette, paintColor} from "./paintColor"; export type TransformColor = { color: number; @@ -33,7 +33,6 @@ export function* chaosGameColor({width, height, transforms, final, palette, colo for (let i = 0; i < iterations; i++) { const [transformIndex, transform] = randomChoice(transforms); [x, y] = transform(x, y); - const [finalX, finalY] = final(x, y); if (i > 20) { diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts index 828f31e..76025ab 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts @@ -5,9 +5,9 @@ import {ChaosGameFinalProps} from "../2-transforms/chaosGameFinal"; import {camera, histIndex} from "../src/camera"; // hidden-end export type ChaosGameHistogramProps = ChaosGameFinalProps & { - painter: (width: number, histogram: Uint32Array) => ImageData; + paint: (width: number, histogram: Uint32Array) => ImageData; } -export function* chaosGameHistogram({width, height, transforms, final, quality, step, painter}: ChaosGameHistogramProps) { +export function* chaosGameHistogram({width, height, transforms, final, quality, step, paint}: ChaosGameHistogramProps) { let iterations = (quality ?? 1) * width * height; step = step ?? 100_000; @@ -18,17 +18,17 @@ export function* chaosGameHistogram({width, height, transforms, final, quality, for (let i = 0; i < iterations; i++) { const [_, transform] = randomChoice(transforms); [x, y] = transform(x, y); - [x, y] = final(x, y); + const [finalX, finalY] = final(x, y); if (i > 20) { - const [pixelX, pixelY] = camera(x, y, width); + const [pixelX, pixelY] = camera(finalX, finalY, width); const pixelIndex = histIndex(pixelX, pixelY, width, 1); histogram[pixelIndex] += 1; } if (i % step === 0) - yield painter(width, histogram); + yield paint(width, histogram); } - yield painter(width, histogram); + yield paint(width, histogram); } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index b4d552c..495d47c 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -32,16 +32,24 @@ import Canvas from "../src/Canvas"; import FlameHistogram from "./FlameHistogram"; import {paintLinear} from "./paintLinear"; - + ## Log display +import paintLogarithmicSource from "!!raw-loader!./paintLogarithmic" + +{paintLogarithmicSource} + import {paintLogarithmic} from './paintLogarithmic' - + ## Color +import paintColorSource from "!!raw-loader!./paintColor" + +{paintColorSource} + import FlameColor from "./FlameColor"; - \ No newline at end of file + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/color.ts b/blog/2024-11-15-playing-with-fire/3-log-density/paintColor.ts similarity index 100% rename from blog/2024-11-15-playing-with-fire/3-log-density/color.ts rename to blog/2024-11-15-playing-with-fire/3-log-density/paintColor.ts diff --git a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css index 6c16604..f83b7cf 100644 --- a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css +++ b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css @@ -22,7 +22,7 @@ margin: 0 } -.inputElement > input { +.inputElement > input[type=range] { width: 100%; } From 78d71cbc7b20ad5da314b86713a8d9a91354e7f8 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 8 Dec 2024 16:17:21 -0500 Subject: [PATCH 33/51] View detection --- .../3-log-density/FlameColor.tsx | 2 +- .../3-log-density/FlameHistogram.tsx | 12 +++---- .../3-log-density/chaosGameColor.ts | 2 +- .../3-log-density/chaosGameHistogram.ts | 2 +- .../3-log-density/index.mdx | 4 +-- .../src/Canvas.tsx | 32 ++++++++++++++++--- package.json | 2 +- 7 files changed, 40 insertions(+), 16 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx index 22461b2..bf75f31 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx @@ -103,7 +103,7 @@ const ColorEditor: React.FC = ({title, palette, transformColor onInput={e => setTransformColor({...transformColor, color: Number(e.currentTarget.value)})}/>
    -

    Color speed: {transformColor.colorSpeed}

    +

    Speed: {transformColor.colorSpeed}

    setTransformColor({...transformColor, colorSpeed: Number(e.currentTarget.value)})}/>
    diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx index 8db4119..d0b11de 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx @@ -1,24 +1,24 @@ import React, {useContext, useEffect} from "react"; -import * as params from "../src/params"; +import {xforms as transforms, xformFinal as final} from "../src/params"; import {PainterContext} from "../src/Canvas"; import {chaosGameHistogram} from "./chaosGameHistogram"; type Props = { quality?: number; - paintFn: (width: number, histogram: Uint32Array) => ImageData; + paint: (width: number, histogram: Uint32Array) => ImageData; children?: React.ReactElement; } -export default function FlameHistogram({quality, paintFn, children}: Props) { +export default function FlameHistogram({quality, paint, children}: Props) { const {width, height, setPainter} = useContext(PainterContext); useEffect(() => { const gameParams = { width, height, - transforms: params.xforms, - final: params.xformFinal, + transforms, + final, quality, - painter: paintFn + paint } setPainter(chaosGameHistogram(gameParams)); }, []); diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts index dd3a1aa..71902e8 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts @@ -20,7 +20,7 @@ export type ChaosGameColorProps = ChaosGameFinalProps & { } export function* chaosGameColor({width, height, transforms, final, palette, colors, finalColor, quality, step}: ChaosGameColorProps) { let iterations = (quality ?? 1) * width * height; - step = step ?? 100_000; + step = step ?? 10_000; let currentColor = Math.random(); const red = Array(width * height).fill(0); diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts index 76025ab..b35980d 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts @@ -9,7 +9,7 @@ export type ChaosGameHistogramProps = ChaosGameFinalProps & { } export function* chaosGameHistogram({width, height, transforms, final, quality, step, paint}: ChaosGameHistogramProps) { let iterations = (quality ?? 1) * width * height; - step = step ?? 100_000; + step = step ?? 10_000; const histogram = new Uint32Array(width * height); diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index 495d47c..515451f 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -32,7 +32,7 @@ import Canvas from "../src/Canvas"; import FlameHistogram from "./FlameHistogram"; import {paintLinear} from "./paintLinear"; - + ## Log display @@ -42,7 +42,7 @@ import paintLogarithmicSource from "!!raw-loader!./paintLogarithmic" import {paintLogarithmic} from './paintLogarithmic' - + ## Color diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 41c851a..c6afae3 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -1,4 +1,4 @@ -import React, {useCallback, useEffect, useState, createContext} from "react"; +import React, {useCallback, useEffect, useState, createContext, useRef} from "react"; import {useColorMode} from "@docusaurus/theme-common"; import BrowserOnly from "@docusaurus/BrowserOnly"; @@ -100,10 +100,32 @@ interface CanvasProps { * a good way to make those generic. */ export default function Canvas({width, height, children}: CanvasProps) { + const viewportDetectionRef = useRef(null); + const [isVisible, setIsVisible] = useState(false); + useEffect(() => { + if (!viewportDetectionRef) { + return; + } + + const observer = new IntersectionObserver(([entry]) => { + if (entry.isIntersecting) { + setIsVisible(true); + } + }, {root: null, threshold: .1}); + observer.observe(viewportDetectionRef.current); + + return () => { + if (viewportDetectionRef.current) { + observer.unobserve(viewportDetectionRef.current); + } + } + }, [viewportDetectionRef]); + const [image, setImage] = useState<[ImageData]>(null); const [painterHolder, setPainterHolder] = useState<[Iterator]>(null); useEffect(() => { - if (!painterHolder) { + if (!isVisible || !painterHolder) { + console.log("Skipping, not visible"); return; } @@ -115,7 +137,7 @@ export default function Canvas({width, height, children}: CanvasProps) { } else { setPainterHolder(null); } - }, [painterHolder]); + }, [isVisible, painterHolder]); const [painter, setPainter] = useState>(null); useEffect(() => { @@ -129,7 +151,9 @@ export default function Canvas({width, height, children}: CanvasProps) { return ( <>
    - +
    + +
    {() => children} diff --git a/package.json b/package.json index 47f0fda..8a0c59f 100644 --- a/package.json +++ b/package.json @@ -4,7 +4,7 @@ "private": true, "scripts": { "docusaurus": "docusaurus", - "start": "docusaurus start", + "start": "docusaurus start --host 0.0.0.0", "build": "docusaurus build", "swizzle": "docusaurus swizzle", "deploy": "docusaurus deploy", From 5ae6b82d2628d7d6e4f70e12ef948915d33a8b68 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 8 Dec 2024 19:53:06 -0500 Subject: [PATCH 34/51] Auto-sizing canvas, starting cleanup for display on mobile browsers --- .../1-introduction/Gasket.tsx | 17 +- .../1-introduction/GasketWeighted.tsx | 6 +- .../1-introduction/chaosGame.js | 43 ++--- .../1-introduction/chaosGameWeighted.ts | 36 ++-- .../1-introduction/index.mdx | 20 +-- .../1-introduction/plot.ts | 78 +++++---- .../2-transforms/index.mdx | 6 +- .../3-log-density/index.mdx | 6 +- .../src/Canvas.tsx | 155 ++++++------------ .../src/css/styles.module.css | 5 +- .../src/randomChoice.ts | 27 +-- .../src/randomInteger.ts | 8 +- src/css/custom.css | 13 ++ 13 files changed, 206 insertions(+), 214 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx index 1b96395..c1d848b 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx @@ -1,16 +1,21 @@ -import Canvas, {PainterContext} from "../src/Canvas"; -import {useContext} from "react"; +import {SquareCanvas, PainterContext} from "../src/Canvas"; +import {useContext, useEffect} from "react"; export function Render({f}) { - const {setPainter} = useContext(PainterContext); - setPainter(f); + const {width, height, setPainter} = useContext(PainterContext); + useEffect(() => { + if (width && height) { + const painter = f({width, height}); + setPainter(painter); + } + }, [width, height]); return <>; } export default function Gasket({f}) { return ( - + - + ) } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx index 40d5a3b..326b7f1 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx @@ -1,4 +1,4 @@ -import {useEffect, useState, useContext} from "react"; +import {useEffect, useState, useContext, useRef} from "react"; import {PainterContext} from "../src/Canvas"; import {chaosGameWeighted} from "./chaosGameWeighted"; import TeX from '@matejmazur/react-katex'; @@ -30,7 +30,7 @@ export default function GasketWeighted() { const weightInput = (title, weight, setWeight) => ( <>
    -

    {title} weight: {weight}

    +

    {title}: {weight}

    setWeight(Number(e.currentTarget.value))}/>
    @@ -39,7 +39,7 @@ export default function GasketWeighted() { return ( <> -
    +
    {weightInput("F_0", f0Weight, setF0Weight)} {weightInput("F_1", f1Weight, setF1Weight)} {weightInput("F_2", f2Weight, setF2Weight)} diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js index 2644edf..42ff413 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js @@ -1,30 +1,33 @@ -// Hint: try increasing the iteration count -const iterations = 10000; +// Hint: try changing the iteration count +const iterations = 100000; -// Hint: negating `x` and `y` creates some interesting images -const transforms = [ - (x, y) => [x / 2, y / 2], - (x, y) => [(x + 1) / 2, y / 2], - (x, y) => [x / 2, (y + 1) / 2] +// Hint: negating `x` and `y` creates some cool images +const xforms = [ + (x, y) => [x / 2, y / 2], + (x, y) => [(x + 1) / 2, y / 2], + (x, y) => [x / 2, (y + 1) / 2] ] -function* chaosGame() { - let image = new ImageData(500, 500); - let [x, y] = [randomBiUnit(), randomBiUnit()]; +function* chaosGame({width, height}) { + let img = new ImageData(width, height); + let [x, y] = [ + randomBiUnit(), + randomBiUnit() + ]; - for (var count = 0; count < iterations; count++) { - const i = randomInteger(0, transforms.length); - [x, y] = transforms[i](x, y); + for (let c = 0; c < iterations; c++) { + const i = randomInteger(0, xforms.length); + [x, y] = xforms[i](x, y); - if (count > 20) - plot(x, y, image); + if (c > 20) + plot(x, y, img); - if (count % 1000 === 0) - yield image; - } + if (c % 1000 === 0) + yield img; + } - yield image; + yield img; } // Wiring so the code above displays properly -render() +render() diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts index 35b00f5..a8d4c7e 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts @@ -6,27 +6,33 @@ import {Transform} from "../src/transform"; const iterations = 50_000; const step = 1000; // hidden-end -export type ChaosGameWeightedProps = { +type Props = { width: number, height: number, transforms: [number, Transform][] } -export function* chaosGameWeighted({width, height, transforms}: ChaosGameWeightedProps) { - let image = new ImageData(width, height); - var [x, y] = [randomBiUnit(), randomBiUnit()]; +export function* chaosGameWeighted( + {width, height, transforms}: Props +) { + let img = new ImageData(width, height); + let [x, y] = [ + randomBiUnit(), + randomBiUnit() + ]; - for (let i = 0; i < iterations; i++) { - // highlight-start - const [_, transform] = randomChoice(transforms); - // highlight-end - [x, y] = transform(x, y); + const iterations = width * height * 0.5; + for (let c = 0; c < iterations; c++) { + // highlight-start + const [_, xform] = randomChoice(transforms); + // highlight-end + [x, y] = xform(x, y); - if (i > 20) - plot(x, y, image); + if (c > 20) + plot(x, y, img); - if (i % step === 0) - yield image; - } + if (c % step === 0) + yield img; + } - yield image; + yield img; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index e4f1988..e9c8ec9 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -101,7 +101,7 @@ export const shiftData = simpleData.map(({x, y}) => { return {x: x + 1, y} }) This is a simple example designed to illustrate the principle. In general, $F_i$ functions have the form: $$ -F_i(x,y) = (a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) +F_i(x,y) = (a_i \cdot x + b_i \cdot y + c_i, d_i \cdot x + e_i \cdot y + f_i) $$ The parameters ($a_i$, $b_i$, etc.) are values we get to choose. In the example above, we can represent our shift @@ -126,10 +126,10 @@ Fractal flames use more complex functions to produce a wide variety of images, b Using these definitions, we can build the first image. The paper defines a function system for us: $$ -F_0(x, y) = \left({x \over 2}, {y \over 2} \right) -\hspace{0.8cm} -F_1(x, y) = \left({{x + 1} \over 2}, {y \over 2} \right) -\hspace{0.8cm} +F_0(x, y) = \left({x \over 2}, {y \over 2} \right) \\ +~\\ +F_1(x, y) = \left({{x + 1} \over 2}, {y \over 2} \right) \\ +~\\ F_2(x, y) = \left({x \over 2}, {{y + 1} \over 2} \right) $$ @@ -141,11 +141,11 @@ Next, how do we find out all the points in $S$? The paper lays out an algorithm $$ \begin{align*} -&(x, y) = \text{a random point in the bi-unit square} \\ +&(x, y) = \text{random point in the bi-unit square} \\ &\text{iterate } \{ \\ -&\hspace{1cm} i = \text{a random integer from 0 to } n - 1 \text{ inclusive} \\ +&\hspace{1cm} i = \text{random integer from 0 to } n - 1 \\ &\hspace{1cm} (x,y) = F_i(x,y) \\ -&\hspace{1cm} \text{plot}(x,y) \text{ except during the first 20 iterations} \\ +&\hspace{1cm} \text{plot}(x,y) \text{ if iterations} > 20 \\ \} \end{align*} $$ @@ -199,6 +199,6 @@ import chaosGameWeightedSource from "!!raw-loader!./chaosGameWeighted"; {chaosGameWeightedSource} import GasketWeighted from "./GasketWeighted"; -import Canvas from "../src/Canvas"; +import {SquareCanvas} from "../src/Canvas"; - \ No newline at end of file + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts index 23f0b2f..a30eaf3 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts @@ -1,34 +1,52 @@ -export function plot(x: number, y: number, image: ImageData) { - // Translate (x,y) coordinates to pixel coordinates; - // also known as a "camera" function. - // - // The display range we care about is x=[0, 1], y=[0, 1], - // so our pixelX and pixelY coordinates are easy to calculate: - const pixelX = Math.floor(x * image.width); - const pixelY = Math.floor(y * image.height); +/** + * ImageData is an array that contains + * four elements per pixel (one for each + * red, green, blue, and alpha value). + * This maps from pixel coordinates + * to the array index + */ +function imageIndex( + width: number, + x: number, + y: number +) { + return y * (width * 4) + x * 4; +} - // If we have an (x,y) coordinate outside the display range, - // skip it - if ( - pixelX < 0 || - pixelX > image.width || - pixelY < 0 || - pixelY > image.height - ) { - return; - } +export function plot( + x: number, + y: number, + img: ImageData +) { + // Translate (x,y) coordinates + // to pixel coordinates. + // Also known as a "camera" function. + // + // The display range is: + // x=[0, 1] + // y=[0, 1] + let pixelX = Math.floor(x * img.width); + let pixelY = Math.floor(y * img.height); - // ImageData is an array that contains four bytes per pixel - // (one for each of the red, green, blue, and alpha values). - // The (pixelX, pixelY) coordinates are used to find where - // in the image we need to write. - const index = pixelY * (image.width * 4) + pixelX * 4; + const index = imageIndex( + img.width, + pixelX, + pixelY + ); - // Set the pixel to black by writing a 0 to the first three - // bytes (red, green, blue), and 256 to the last byte (alpha), - // starting at our index: - image.data[index] = 0; - image.data[index + 1] = 0; - image.data[index + 2] = 0; - image.data[index + 3] = 0xff; + // Skip pixels outside the display range + if ( + index < 0 || + index > img.data.length + ) { + return; + } + + // Set the pixel to black by writing 0 + // to the first three elements, + // and 255 to the last element + img.data[index] = 0; + img.data[index + 1] = 0; + img.data[index + 2] = 0; + img.data[index + 3] = 0xff; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 944243d..64f778f 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -145,7 +145,7 @@ each transform. import Canvas from "../src/Canvas"; import FlameBlend from "./FlameBlend"; - + ## Post transforms @@ -160,10 +160,10 @@ $$ import FlamePost from "./FlamePost"; - + ## Final transform import FlameFinal from "./FlameFinal"; - \ No newline at end of file + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index 515451f..69dbca5 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -32,7 +32,7 @@ import Canvas from "../src/Canvas"; import FlameHistogram from "./FlameHistogram"; import {paintLinear} from "./paintLinear"; - + ## Log display @@ -42,7 +42,7 @@ import paintLogarithmicSource from "!!raw-loader!./paintLogarithmic" import {paintLogarithmic} from './paintLogarithmic' - + ## Color @@ -52,4 +52,4 @@ import paintColorSource from "!!raw-loader!./paintColor" import FlameColor from "./FlameColor"; - \ No newline at end of file + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index c6afae3..0b262d7 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -1,138 +1,68 @@ -import React, {useCallback, useEffect, useState, createContext, useRef} from "react"; +import React, {useEffect, useState, createContext, useRef} from "react"; import {useColorMode} from "@docusaurus/theme-common"; import BrowserOnly from "@docusaurus/BrowserOnly"; -function invertImage(sourceImage: ImageData): ImageData { - const image = new ImageData(sourceImage.width, sourceImage.height); - sourceImage.data.forEach((value, index) => - image.data[index] = index % 4 === 3 ? value : 0xff - value) - - return image; -} - -type InvertibleCanvasProps = { - width: number, - height: number, - // NOTE: Images are provided as a single-element array - //so we can allow re-painting with the same (modified) ImageData reference. - image?: [ImageData], -} - -/** - * Draw images to a canvas, automatically inverting colors as needed. - * - * @param width Canvas width - * @param height Canvas height - * @param hidden Hide the canvas element - * @param image Image data to draw on the canvas - */ -export const InvertibleCanvas: React.FC = ({width, height, image}) => { - const [canvasCtx, setCanvasCtx] = useState(null); - const canvasRef = useCallback(node => { - if (node !== null) { - setCanvasCtx(node.getContext("2d")); - } - }, []); - - const [paintImage, setPaintImage] = useState<[ImageData]>(null); - useEffect(() => { - if (canvasCtx && paintImage) { - canvasCtx.putImageData(paintImage[0], 0, 0); - } - }, [canvasCtx, paintImage]); - - const {colorMode} = useColorMode(); - useEffect(() => { - if (image) { - setPaintImage(colorMode === 'light' ? image : [invertImage(image[0])]); - } - }, [image, colorMode]); - - return ( - - ) -} - type PainterProps = { width: number; height: number; setPainter: (painter: Iterator) => void; } -export const PainterContext = createContext(null); +export const PainterContext = createContext(null) -interface CanvasProps { - width?: number; - height?: number; - children?: React.ReactElement; +type CanvasProps = { + style?: any; + children?: React.ReactElement } +export const Canvas: React.FC = ({style, children}) => { + const canvasRef = useRef(null); -/** - * Draw fractal flames to a canvas. - * - * This component is a bit involved because it attempts to solve - * a couple problems at once: - * - Incrementally drawing an image to the canvas - * - Interrupting drawing with new parameters - * - * Running a full render is labor-intensive, so we model it - * as an iterator that yields an image of the current system. - * Internally, that iterator is re-queued on each new image; - * so long as retrieving each image happens quickly, - * we keep the main loop running even with CPU-heavy code. - * As a side benefit, this also animates the chaos game nicely. - * TODO(bspeice): This also causes React to complain about maximum update depth - * Would this be better off spawning a `useEffect` animator - * that has access to a `setState` queue? - * - * To interrupt drawing, children set the active iterator - * through the context provider. This component doesn't care - * about which iterator is in progress, it exists only - * to fetch the next image and paint it to our canvas. - * - * TODO(bspeice): Can we make this "re-queueing iterator" pattern generic? - * It would be nice to have iterators returning arbitrary objects, - * but we rely on contexts to manage the iterator, and I can't find - * a good way to make those generic. - */ -export default function Canvas({width, height, children}: CanvasProps) { - const viewportDetectionRef = useRef(null); const [isVisible, setIsVisible] = useState(false); useEffect(() => { - if (!viewportDetectionRef) { + if (!canvasRef.current) { return; } - const observer = new IntersectionObserver(([entry]) => { + const observer = new IntersectionObserver((entries) => { + const [entry] = entries; if (entry.isIntersecting) { setIsVisible(true); } - }, {root: null, threshold: .1}); - observer.observe(viewportDetectionRef.current); + }); + observer.observe(canvasRef.current); return () => { - if (viewportDetectionRef.current) { - observer.unobserve(viewportDetectionRef.current); + if (canvasRef.current) { + observer.unobserve(canvasRef.current); } } - }, [viewportDetectionRef]); + }, [canvasRef]); + + const [width, setWidth] = useState(0); + const [height, setHeight] = useState(0); + useEffect(() => { + if (canvasRef.current) { + setWidth(canvasRef.current.offsetWidth); + setHeight(canvasRef.current.offsetHeight); + } + }, [canvasRef]); + + const [imageHolder, setImageHolder] = useState<[ImageData]>(null); + useEffect(() => { + if (canvasRef.current && imageHolder) { + canvasRef.current.getContext("2d").putImageData(imageHolder[0], 0, 0); + } + }, [canvasRef, imageHolder]); - const [image, setImage] = useState<[ImageData]>(null); const [painterHolder, setPainterHolder] = useState<[Iterator]>(null); useEffect(() => { if (!isVisible || !painterHolder) { - console.log("Skipping, not visible"); return; } const painter = painterHolder[0]; const nextImage = painter.next().value; if (nextImage) { - setImage([nextImage]); + setImageHolder([nextImage]); setPainterHolder([painter]); } else { setPainterHolder(null); @@ -146,18 +76,25 @@ export default function Canvas({width, height, children}: CanvasProps) { } }, [painter]); - width = width ?? 500; - height = height ?? 500; + const {colorMode} = useColorMode(); return ( <> -
    -
    - -
    -
    + {() => children} ) +} + +export const SquareCanvas: React.FC = ({style, children}) => { + return } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css index f83b7cf..d769283 100644 --- a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css +++ b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css @@ -1,6 +1,7 @@ .inputGroup { - padding: .5em; - margin: .5em; + padding: .2em; + margin-top: .2em; + margin-bottom: .2em; border: 1px solid; border-radius: var(--ifm-global-radius); border-color: var(--ifm-color-emphasis-500); diff --git a/blog/2024-11-15-playing-with-fire/src/randomChoice.ts b/blog/2024-11-15-playing-with-fire/src/randomChoice.ts index 0494924..58cf17e 100644 --- a/blog/2024-11-15-playing-with-fire/src/randomChoice.ts +++ b/blog/2024-11-15-playing-with-fire/src/randomChoice.ts @@ -1,15 +1,20 @@ -export function randomChoice(choices: [number, T][]): [number, T] { - const weightSum = choices.reduce((sum, [weight, _]) => sum + weight, 0); - let choice = Math.random() * weightSum; +export function randomChoice( + choices: [number, T][] +): [number, T] { + const weightSum = choices.reduce( + (sum, [weight, _]) => sum + weight, + 0 + ); + let choice = Math.random() * weightSum; - for (const [index, element] of choices.entries()) { - const [weight, t] = element; - if (choice < weight) { - return [index, t]; - } - choice -= weight; + for (const [idx, elem] of choices.entries()) { + const [weight, t] = elem; + if (choice < weight) { + return [idx, t]; } + choice -= weight; + } - const index = choices.length - 1; - return [index, choices[index][1]]; + const index = choices.length - 1; + return [index, choices[index][1]]; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/randomInteger.ts b/blog/2024-11-15-playing-with-fire/src/randomInteger.ts index c3a6719..39e99b2 100644 --- a/blog/2024-11-15-playing-with-fire/src/randomInteger.ts +++ b/blog/2024-11-15-playing-with-fire/src/randomInteger.ts @@ -1,3 +1,7 @@ -export function randomInteger(min: number, max: number) { - return Math.floor(Math.random() * (max - min)) + min; +export function randomInteger( + min: number, + max: number +) { + let v = Math.random() * (max - min); + return Math.floor(v) + min; } \ No newline at end of file diff --git a/src/css/custom.css b/src/css/custom.css index 9a455f7..5030f55 100644 --- a/src/css/custom.css +++ b/src/css/custom.css @@ -3,6 +3,19 @@ --ifm-container-width-xl: 1440px; --ifm-footer-padding-vertical: .5rem; --ifm-spacing-horizontal: .8rem; + + /* Reduce padding on code blocks */ + --ifm-pre-padding: .6rem; + + /* More readable code highlight background */ + --docusaurus-highlighted-code-line-bg: var(--ifm-color-emphasis-300); + + /*--ifm-code-font-size: 85%;*/ +} + +.katex { + /* Default is 1.21, this helps with fitting on mobile screens */ + font-size: 1.16em; } .header-github-link:hover { From b608a25146e1d5e9c55b65a659a4f68a99c54fe3 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 8 Dec 2024 22:50:46 -0500 Subject: [PATCH 35/51] Actually doing some writing --- .../1-introduction/chaosGame.js | 3 +- .../1-introduction/chaosGameWeighted.ts | 3 +- .../1-introduction/index.mdx | 56 +++++++++++-------- .../1-introduction/plot.ts | 12 ++-- .../2-transforms/CoefEditor.tsx | 2 +- .../2-transforms/FlameBlend.tsx | 5 +- .../2-transforms/FlamePost.tsx | 2 +- .../2-transforms/VariationEditor.tsx | 2 +- .../2-transforms/chaosGameFinal.ts | 15 +++-- .../2-transforms/index.mdx | 8 +-- .../3-log-density/FlameColor.tsx | 44 +++++---------- .../3-log-density/index.mdx | 8 +-- 12 files changed, 78 insertions(+), 82 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js index 42ff413..75f0d5f 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js @@ -9,6 +9,7 @@ const xforms = [ ] function* chaosGame({width, height}) { + const step = 1000; let img = new ImageData(width, height); let [x, y] = [ randomBiUnit(), @@ -22,7 +23,7 @@ function* chaosGame({width, height}) { if (c > 20) plot(x, y, img); - if (c % 1000 === 0) + if (c % step === 0) yield img; } diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts index a8d4c7e..e219ed9 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts @@ -6,7 +6,7 @@ import {Transform} from "../src/transform"; const iterations = 50_000; const step = 1000; // hidden-end -type Props = { +export type Props = { width: number, height: number, transforms: [number, Transform][] @@ -20,6 +20,7 @@ export function* chaosGameWeighted( randomBiUnit() ]; + // TODO: Explain quality const iterations = width * height * 0.5; for (let c = 0; c < iterations; c++) { // highlight-start diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index e9c8ec9..de3897b 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -6,11 +6,11 @@ authors: [bspeice] tags: [] --- -Wikipedia [describes](https://en.wikipedia.org/wiki/Fractal_flame) fractal flames as: +Wikipedia describes fractal flames fractal flames as: > a member of the iterated function system class of fractals -I think of them a different way: beauty in mathematics. +It's a bit tedious, but technically correct. I choose to think of them a different way: beauty in mathematics. import isDarkMode from '@site/src/isDarkMode' import banner from '../banner.png' @@ -21,37 +21,38 @@ import banner from '../banner.png' -I don't remember exactly when or how I originally came across fractal flames, but I do remember becoming entranced by the images they created. -I also remember their unique appeal to my young engineering mind; this was an art form I could actively participate in. +I don't remember exactly when I first learned about fractal flames, but I do remember becoming entranced by the images they created. +I also remember their unique appeal to my young engineering mind; this was an art form I could participate in. -The [paper](https://flam3.com/flame_draves.pdf) describing their mathematical structure was too much -for me to handle at the time (I was ~12 years old), and I was content to play around and enjoy the pictures. -But the desire to understand it stuck with me, so I wanted to try again. With a graduate degree in Financial Engineering under my belt, -maybe it would be easier this time. +The original [Fractal Flame](https://flam3.com/flame_draves.pdf) describing their structure was too much +for me to handle at the time (I was ~12 years old), so I was content to play around and enjoy the pictures. +But the desire to understand it stuck around. Now, with a graduate degree under my belt, maybe I can make some progress. + +This guide is my attempt to explain fractal flames in a way that younger me — and others interested in the art — +can understand without too much prior knowledge. --- ## Iterated function systems -Let's begin by defining an "[iterated function system](https://en.wikipedia.org/wiki/Iterated_function_system)" (IFS). -We'll start at the end and work backwards to build a practical understanding. In mathematical notation, an IFS is: +As mentioned above, fractal flames are a type of "[iterated function system](https://en.wikipedia.org/wiki/Iterated_function_system)," +or IFS. Their mathematical foundations come from a paper written by [John E. Hutchinson](https://maths-people.anu.edu.au/~john/Assets/Research%20Papers/fractals_self-similarity.pdf), +but reading that paper isn't critical for our purposes. Instead, we'll focus on building a practical understanding +of how they work. The formula for an IFS is short, but will take some time to unpack: $$ -S = \bigcup_{i=0}^{n-1} F_i(S) \\[0.6cm] -S \in \mathbb{R}^2 \\ -F_i(S) \in \mathbb{R}^2 \rightarrow \mathbb{R}^2 +S = \bigcup_{i=0}^{n-1} F_i(S) $$ -### Stationary point +### Fixed set -First, $S$. We're generating images, so everything is in two dimensions: $S \in \mathbb{R}^2$. The set $S$ is -all points that are "in the system." To generate our final image, we just plot every point in the system -like a coordinate chart. - -TODO: What is a stationary point? How does it relate to the chaos game? Why does the chaos game work? +First, $S$. $S$ is the set of points in two dimensions (in math terms, $S \in \mathbb{R}^2$) that represent +a "solution" of some kind. Our goal is to find all points in the set $S$, plot them, and display that image. For example, if we say $S = \{(0,0), (1, 1), (2, 2)\}$, there are three points to plot: + + import {VictoryChart, VictoryTheme, VictoryScatter, VictoryLegend} from "victory"; export const simpleData = [ {x: 0, y: 0}, @@ -63,8 +64,18 @@ export const simpleData = [ -For fractal flames, we just need to figure out which points are in $S$ and plot them. While there are -technically an infinite number of points, if we find _enough_ points and plot them, we end up with a nice picture. +However, this is a pretty boring image. With fractal flames, rather than listing individual points, +we use functions to describe which points are part of the solution. This means there are an infinite +number of points, but if we find _enough_ points to plot, we'll end up with a nice picture. +And if we choose different functions to start with, our solution set changes, and we'll end up +with a new picture. + +However, it's not clear which points belong in the solution just by staring at the functions. +We'll need a computer to figure it out. + +TODO: Other topics worth covering in this section? Maybe in a `details` block?: +- Fixed sets: https://en.wiktionary.org/wiki/fixed_set +- Compact sets ### Transformation functions @@ -182,7 +193,8 @@ import chaosGameSource from '!!raw-loader!./chaosGame'
    -Note: The image here is different than the fractal flame paper, but I think the paper has an error. +Note: The image here is slightly different than the fractal flame paper; I think the paper has an error, +so I'm choosing to plot the image in a way that's consistent with [`flam3` itself](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L440-L441). ## Weights diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts index a30eaf3..2364330 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts @@ -29,17 +29,17 @@ export function plot( let pixelY = Math.floor(y * img.height); const index = imageIndex( - img.width, - pixelX, - pixelY + img.width, + pixelX, + pixelY ); // Skip pixels outside the display range if ( - index < 0 || - index > img.data.length + index < 0 || + index > img.data.length ) { - return; + return; } // Set the pixel to black by writing 0 diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx index 53080c3..fc4d782 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx @@ -14,7 +14,7 @@ export const CoefEditor = ({title, isPost, coefs, setCoefs, resetCoefs}: Props) const resetButton = return ( -
    +

    {title} {resetButton}

    {isPost ? \alpha : 'a'}: {coefs.a}

    diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx index b4792d4..a05dcf8 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx @@ -4,9 +4,8 @@ import * as params from "../src/params" import {PainterContext} from "../src/Canvas" import {chaosGameFinal} from "./chaosGameFinal" import {VariationEditor, VariationProps} from "./VariationEditor" -import {xform1Weight} from "../src/params"; -import {applyTransform} from "@site/blog/2024-11-15-playing-with-fire/src/applyTransform"; -import {buildBlend} from "@site/blog/2024-11-15-playing-with-fire/2-transforms/buildBlend"; +import {applyTransform} from "../src/applyTransform"; +import {buildBlend} from "./buildBlend"; export default function FlameBlend() { const {width, height, setPainter} = useContext(PainterContext); diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx index 33e0664..539114e 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx @@ -3,7 +3,7 @@ import {Coefs} from "../src/coefs" import {Transform} from "../src/transform"; import * as params from "../src/params"; import {PainterContext} from "../src/Canvas" -import {chaosGameFinal, ChaosGameFinalProps} from "./chaosGameFinal" +import {chaosGameFinal, Props as ChaosGameFinalProps} from "./chaosGameFinal" import {CoefEditor} from "./CoefEditor" import {applyPost, applyTransform} from "@site/blog/2024-11-15-playing-with-fire/src/applyTransform"; diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx index 1785ea7..57a3159 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx @@ -18,7 +18,7 @@ export const VariationEditor = ({title, variations, setVariations, resetVariatio const resetButton = return ( -
    +

    {title} {resetButton}

    Linear: {variations.linear} diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts b/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts index 638846d..147b02b 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts +++ b/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts @@ -3,20 +3,19 @@ import { randomBiUnit } from "../src/randomBiUnit"; import { randomChoice } from "../src/randomChoice"; import { plotBinary as plot } from "../src/plotBinary" import {Transform} from "../src/transform"; -import {ChaosGameWeightedProps} from "../1-introduction/chaosGameWeighted"; +import {Props as ChaosGameWeightedProps} from "../1-introduction/chaosGameWeighted"; + +const quality = 0.5; +const step = 1000; // hidden-end -export type ChaosGameFinalProps = ChaosGameWeightedProps & { +export type Props = ChaosGameWeightedProps & { final: Transform, - quality?: number, - step?: number, } -export function* chaosGameFinal({width, height, transforms, final, quality, step}: ChaosGameFinalProps) { +export function* chaosGameFinal({width, height, transforms, final}: Props) { let image = new ImageData(width, height); let [x, y] = [randomBiUnit(), randomBiUnit()]; - const iterations = (quality ?? 0.5) * width * height; - step = step ?? 1000; - + const iterations = width * height * quality; for (let i = 0; i < iterations; i++) { const [_, transform] = randomChoice(transforms); [x, y] = transform(x, y); diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 64f778f..47c60c2 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -142,10 +142,10 @@ The sliders below change the variation weights for each transform (the $v_{ij}$ try changing them around to see which parts of the image are controlled by each transform. -import Canvas from "../src/Canvas"; +import {SquareCanvas} from "../src/Canvas"; import FlameBlend from "./FlameBlend"; - + ## Post transforms @@ -160,10 +160,10 @@ $$ import FlamePost from "./FlamePost"; - + ## Final transform import FlameFinal from "./FlameFinal"; - \ No newline at end of file + \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx index bf75f31..84a0db1 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx @@ -1,35 +1,12 @@ import React, {useContext, useEffect, useMemo, useRef, useState} from "react"; import * as params from "../src/params"; -import {InvertibleCanvas, PainterContext} from "../src/Canvas"; +import {PainterContext} from "../src/Canvas"; import {colorFromPalette} from "./paintColor"; import {chaosGameColor, ChaosGameColorProps, TransformColor} from "./chaosGameColor"; import styles from "../src/css/styles.module.css"; import {histIndex} from "../src/camera"; - -type AutoSizingCanvasProps = { - painter: (width: number, height: number) => ImageData; -} -const AutoSizingCanvas: React.FC = ({painter}) => { - const sizingRef = useRef(null); - const [width, setWidth] = useState(0); - const [height, setHeight] = useState(0); - - useEffect(() => { - if (sizingRef) { - setWidth(sizingRef.current.offsetWidth); - setHeight(sizingRef.current.offsetHeight) - } - }, [sizingRef]); - - const image: [ImageData] = useMemo(() => (width && height) ? [painter(width, height)] : null, [painter, width, height]); - - return ( -
    - -
    - ) -} +import {useColorMode} from "@docusaurus/theme-common"; const paletteBarPainter = (palette: number[]) => (width: number, height: number) => { @@ -60,7 +37,7 @@ const PaletteBar: React.FC = ({height, palette, children}) => { return ( <>
    - + {/**/}
    {children} @@ -90,9 +67,13 @@ type ColorEditorProps = { children?: React.ReactNode; } const ColorEditor: React.FC = ({title, palette, transformColor, setTransformColor, resetTransformColor, children}) => { - const painter = useMemo(() => colorSwatchPainter(palette, transformColor.color), [palette, transformColor]); const resetButton = + const [r, g, b] = colorFromPalette(palette, transformColor.color); + const colorCss = `rgb(${Math.floor(r * 0xff)},${Math.floor(g * 0xff)},${Math.floor(b * 0xff)})`; + + const {colorMode} = useColorMode(); + return ( <>
    @@ -107,9 +88,12 @@ const ColorEditor: React.FC = ({title, palette, transformColor setTransformColor({...transformColor, colorSpeed: Number(e.currentTarget.value)})}/>
    -
    - -
    +
    {children} diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index 69dbca5..7c96033 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -28,11 +28,11 @@ import paintLinearSource from "!!raw-loader!./paintLinear" {paintLinearSource} -import Canvas from "../src/Canvas"; +import {SquareCanvas} from "../src/Canvas"; import FlameHistogram from "./FlameHistogram"; import {paintLinear} from "./paintLinear"; - + ## Log display @@ -42,7 +42,7 @@ import paintLogarithmicSource from "!!raw-loader!./paintLogarithmic" import {paintLogarithmic} from './paintLogarithmic' - + ## Color @@ -52,4 +52,4 @@ import paintColorSource from "!!raw-loader!./paintColor" import FlameColor from "./FlameColor"; - \ No newline at end of file + \ No newline at end of file From 09835586599baa75767cd6103275fb95f804a5cd Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Mon, 9 Dec 2024 22:18:13 -0500 Subject: [PATCH 36/51] More writing for the main posts --- .../1-introduction/chaosGameWeighted.ts | 6 +- .../1-introduction/index.mdx | 20 ++- .../2-transforms/FlameBlend.tsx | 2 - .../2-transforms/FlamePost.tsx | 2 +- .../2-transforms/chaosGameFinal.ts | 2 + .../2-transforms/index.mdx | 133 +++++++++++------- .../2-transforms/post.ts | 2 +- .../3-log-density/FlameColor.tsx | 14 -- .../3-log-density/chaosGameColor.ts | 22 +-- .../3-log-density/chaosGameHistogram.ts | 33 +++-- .../3-log-density/index.mdx | 4 + .../3-log-density/paintLinear.ts | 16 +-- .../3-log-density/paintLogarithmic.ts | 4 +- .../2024-11-15-playing-with-fire/src/blend.ts | 11 +- .../src/plotBinary.ts | 7 +- src/css/custom.css | 2 +- 16 files changed, 155 insertions(+), 125 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts index e219ed9..ef1966a 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts @@ -3,7 +3,8 @@ import { randomBiUnit } from "../src/randomBiUnit"; import { randomChoice } from "../src/randomChoice"; import { plot } from "./plot" import {Transform} from "../src/transform"; -const iterations = 50_000; + +const quality = 0.5; const step = 1000; // hidden-end export type Props = { @@ -20,8 +21,7 @@ export function* chaosGameWeighted( randomBiUnit() ]; - // TODO: Explain quality - const iterations = width * height * 0.5; + const iterations = width * height * quality; for (let c = 0; c < iterations; c++) { // highlight-start const [_, xform] = randomChoice(transforms); diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index de3897b..befe48d 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -24,7 +24,7 @@ import banner from '../banner.png' I don't remember exactly when I first learned about fractal flames, but I do remember becoming entranced by the images they created. I also remember their unique appeal to my young engineering mind; this was an art form I could participate in. -The original [Fractal Flame](https://flam3.com/flame_draves.pdf) describing their structure was too much +The original [Fractal Flame Algorithm paper](https://flam3.com/flame_draves.pdf) describing their structure was too much for me to handle at the time (I was ~12 years old), so I was content to play around and enjoy the pictures. But the desire to understand it stuck around. Now, with a graduate degree under my belt, maybe I can make some progress. @@ -35,7 +35,13 @@ can understand without too much prior knowledge. ## Iterated function systems -As mentioned above, fractal flames are a type of "[iterated function system](https://en.wikipedia.org/wiki/Iterated_function_system)," +:::note + +This post covers section 2 of the Fractal Flame Algorithm paper + +::: + +As mentioned, fractal flames are a type of "[iterated function system](https://en.wikipedia.org/wiki/Iterated_function_system)," or IFS. Their mathematical foundations come from a paper written by [John E. Hutchinson](https://maths-people.anu.edu.au/~john/Assets/Research%20Papers/fractals_self-similarity.pdf), but reading that paper isn't critical for our purposes. Instead, we'll focus on building a practical understanding of how they work. The formula for an IFS is short, but will take some time to unpack: @@ -65,7 +71,11 @@ export const simpleData = [ However, this is a pretty boring image. With fractal flames, rather than listing individual points, -we use functions to describe which points are part of the solution. This means there are an infinite +we use functions to describe which points are part of the solution. + +TODO: Explain characteristics of the solution - fixed set + +This means there are an infinite number of points, but if we find _enough_ points to plot, we'll end up with a nice picture. And if we choose different functions to start with, our solution set changes, and we'll end up with a new picture. @@ -73,10 +83,6 @@ with a new picture. However, it's not clear which points belong in the solution just by staring at the functions. We'll need a computer to figure it out. -TODO: Other topics worth covering in this section? Maybe in a `details` block?: -- Fixed sets: https://en.wiktionary.org/wiki/fixed_set -- Compact sets - ### Transformation functions Second, $F_i(S)$. At their most basic, each $F_i$ is a function that takes in a 2-dimensional point and transforms diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx index a05dcf8..03d83a2 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx @@ -37,8 +37,6 @@ export default function FlameBlend() { const [xform3Variations, setXform3Variations] = useState(xform3VariationsDefault) const resetXform3Variations = () => setXform3Variations(xform3VariationsDefault); - // Cheating a bit here; for purposes of code re-use, use the post- and final-transform-enabled chaos game, - // and swap in identity components for each const identityXform: Transform = (x, y) => [x, y]; useEffect(() => { diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx index 539114e..7402383 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx @@ -17,7 +17,7 @@ export default function FlamePost() { const resetXform2CoefsPost = () => setXform2CoefsPost(params.xform2CoefsPost); const [xform3CoefsPost, setXform3CoefsPost] = useState(params.xform3CoefsPost); - const resetXform3CoefsPost = () => setXform1CoefsPost(params.xform3CoefsPost); + const resetXform3CoefsPost = () => setXform3CoefsPost(params.xform3CoefsPost); const identityXform: Transform = (x, y) => [x, y]; diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts b/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts index 147b02b..caacae1 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts +++ b/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts @@ -25,7 +25,9 @@ export function* chaosGameFinal({width, height, transforms, final}: Props) { // highlight-end if (i > 20) + // highlight-start plot(finalX, finalY, image); + // highlight-end if (i % step === 0) yield image; diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 47c60c2..475b36e 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -7,60 +7,55 @@ tags: [] --- Now that we have a basic chaos game in place, it's time to spice things up. Transforms and variations create the -interesting patterns that fractal flames are known for. +shapes and patterns that fractal flames are known for. -This blog post uses a set of reference parameters ([available here](../params.flame)) to demonstrate a practical -implementation of the fractal flame algorithm. If you're interested in tweaking the parameters, or generating -your own art, [Apophysis](https://sourceforge.net/projects/apophysis/) is a good introductory tool. +:::note -TODO: Include the reference image here +This post uses a set of [reference parameters](../params.flame) to demonstrate a working +implementation of the fractal flame algorithm. If you're interested in tweaking the parameters, +or generating your own art, [Apophysis](https://sourceforge.net/projects/apophysis/) +can load that file and gives full control over the image. + +::: ## Transforms and variations +:::note + +This post covers section 3 of the Fractal Flame Algorithm paper + +::: + import CodeBlock from '@theme/CodeBlock' -We previously introduced "transforms" as the "functions" of an "iterated function system." Their general format is: +We previously introduced transforms as the "functions" of an "iterated function system," and showed how +playing the chaos game leads to an image of Sierpinski's Gasket. Even though we used simple functions, +the image it generates is exciting. But it's still not nearly as exciting as the images the Fractal Flame +algorithm is known for. + +This leads us to the first big innovation of the Fractal Flame algorithm: using non-linear functions +for the transforms. These functions are known as "variations": $$ -F_i(x,y) = (a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) +F_i(x, y) = V_j(a_i \cdot x + b_i \cdot y + c_i, d_i \cdot x + e_i \cdot y + f_i) $$ -import coefsSrc from '!!raw-loader!../src/coefs' +import variationSource from '!!raw-loader!../src/variation' -{coefsSrc} +{variationSource} -We also introduced the Sierpinski Gasket functions ($F_0$, $F_1$, and $F_2$), demonstrating how they are related to -the general format. For example: +Variations, labeled $V_j$ above, are functions just like transforms (we use $j$ to indicate a specific variation). +They take an input point $(x,y)$, and give an output point. However, the sky is the limit for what variation functions do in between +input to output. The Fractal Flame paper lists 49 different variation functions, +and the official `flam3` implementation supports [98 different functions](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/variations.c). -$$ -\begin{align*} -F_0(x,y) &= \left({x \over 2}, {y \over 2}\right) \\ -&= (a_0 \cdot x + b_0 \cdot y + c_0, d_0 \cdot x + e_0 \cdot y + f_0) \\ -& a_0 = 0.5 \hspace{0.2cm} b_0 = 0 \hspace{0.2cm} c_0 = 0 \\ -& d_0 = 0 \hspace{0.2cm} e_0 = 0.5 \hspace{0.2cm} f_0 = 0 -\end{align*} -$$ - -TODO: Explain the applyCoefs function - -However, these transforms are pretty boring. We can build more exciting images by using additional functions -within the transform. These "sub-functions" are called "variations": - -$$ -F_i(x, y) = V_j(a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) -$$ - -The fractal flame paper lists 49 variation functions ($V_j$ above), but the sky's the limit here. -For example, the official `flam3` implementation supports -[98 variations](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/variations.c). - -Our reference image will focus on just four variations: +To draw our reference image, we'll focus on four variations: ### Linear (variation 0) -This variation returns the $x$ and $y$ coordinates as-is: +This variation is dead simple: just return the $x$ and $y$ coordinates as-is. $$ V_0(x,y) = (x,y) @@ -70,11 +65,17 @@ import linearSrc from '!!raw-loader!../src/linear' {linearSrc} +:::tip + +In a way, we've already been using this variation! The functions that define Sierpinski's Gasket +apply the affine coefficients to the input point, and use that as the output point. + +::: + ### Julia (variation 13) -This variation still uses just the $x$ and $y$ coordinates, but does crazy things with them: - -TODO: Is this related to the Julia set? +This variation is a good example of the non-linear functions the Fractal Flame Algorithm introduces. +It still receives an input point $(x, y)$, but does some crazy things with it: $$ \begin{align*} @@ -97,8 +98,8 @@ import juliaSrc from '!!raw-loader!../src/julia' ### Popcorn (variation 17) -This is known as a "dependent variation" because it depends on knowing the transform coefficients -(specifically, $c$ and $f$): +Some variations rely on knowing the transform's affine coefficients; these are known as "dependent variations." +For the popcorn variation, we use the $c$ and $f$ coefficients: $$ V_{17}(x,y) = (x + c \cdot \text{sin}(\text{tan }3y), y + f \cdot \text{sin}(\text{tan }3x)) @@ -110,7 +111,8 @@ import popcornSrc from '!!raw-loader!../src/popcorn' ### PDJ (variation 24) -This is known as a "parametric" variation because it has additional parameters given to it: +Some variations have extra parameters that the designer can choose; these are known as "parametric variations." +For the PDJ variation, there are four extra parameters we can choose: $$ p_1 = \text{pdj.a} \hspace{0.2cm} p_2 = \text{pdj.b} \hspace{0.2cm} p_3 = \text{pdj.c} \hspace{0.2cm} p_4 = \text{pdj.d} \\ @@ -123,9 +125,9 @@ import pdjSrc from '!!raw-loader!../src/pdj' ## Blending -Now, one variation is fun, but we can also combine variations in a single transform by "blending." +Now, one variation is fun, but we can also combine variations in a process called "blending." Each variation receives the same $x$ and $y$ inputs, and we add together each variation's $x$ and $y$ outputs. -We'll also give each variation a weight ($v_{ij}$) to control how much it contributes to the transform: +We'll also give each variation a weight (called $v_{ij}$) that changes how much it contributes to the transform: $$ F_i(x,y) = \sum_{j} v_{ij} V_j(a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) @@ -137,10 +139,15 @@ import blendSource from "!!raw-loader!../src/blend"; {blendSource} -And with that in place, we have enough to render a first full fractal flame. -The sliders below change the variation weights for each transform (the $v_{ij}$ parameters); -try changing them around to see which parts of the image are controlled by -each transform. +With that in place, we have enough to render a first full fractal flame. We'll use the same +chaos game as before, but use our new transforms and variations to produce a dramatically different image: + +:::tip +This image is interactive! The sliders change the variation weights ($v_{ij}$ parameters) +so you can design your own image. + +Try using the sliders to find which parts of the image each transform controls. +::: import {SquareCanvas} from "../src/Canvas"; import FlameBlend from "./FlameBlend"; @@ -149,20 +156,40 @@ import FlameBlend from "./FlameBlend"; ## Post transforms -After variation blending, we apply a second set of transform coordinates. +Post transforms introduce a second affine transform, this time _after_ variation blending. +We'll use introduce some new variables, but the post transform function should look familiar by now: -The fractal flame below starts with the same initial transforms/variations as the previous fractal flame, +$$ +\begin{align*} +P_i(x, y) &= (\alpha_i x + \beta_i y + \gamma_i, \delta_i x + \epsilon_i y + \zeta_i) \\ +F_i(x, y) &= P_i\left(\sum_{j} v_{ij} V_j(x, y)\right) +\end{align*} +$$ + +import postSource from '!!raw-loader!./post' + +{postSource} + +The image below starts with the same initial transforms/variations as the previous fractal flame, but allows modifying the post-transform coefficients. -$$ -P_i(x, y) = (\alpha_i x + \beta_i y + \gamma_i, \delta_i x + \epsilon_i y + \zeta_i) -$$ +
    + If you want a challenge... + + Challenge 1: What post-transform coefficients will give us the previous image? + + Challenge 2: What post-transform coefficients will give us a _mirrored_ image? +
    import FlamePost from "./FlamePost"; -## Final transform +## Final transforms + +import chaosGameFinalSource from "!!raw-loader!./chaosGameFinal" + +{chaosGameFinalSource} import FlameFinal from "./FlameFinal"; diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/post.ts b/blog/2024-11-15-playing-with-fire/2-transforms/post.ts index fc9a777..b79ded1 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/post.ts +++ b/blog/2024-11-15-playing-with-fire/2-transforms/post.ts @@ -4,4 +4,4 @@ import {Transform} from "../src/transform"; import {applyCoefs} from "../src/coefs"; // hidden-end export const transformPost = (transform: Transform, coefs: Coefs): Transform => - (x, y): [number, number] => applyCoefs(...transform(x, y), coefs) \ No newline at end of file + (x, y) => applyCoefs(...transform(x, y), coefs) \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx index 84a0db1..b46418e 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx @@ -44,20 +44,6 @@ const PaletteBar: React.FC = ({height, palette, children}) => { ) } -const colorSwatchPainter = (palette: number[], color: number) => - (width: number, height: number) => { - const [r, g, b] = colorFromPalette(palette, color); - const image = new ImageData(width, height); - for (let i = 0; i < image.data.length; i += 4) { - image.data[i] = r * 0xff; - image.data[i + 1] = g * 0xff; - image.data[i + 2] = b * 0xff; - image.data[i + 3] = 0xff; - } - - return image; - } - type ColorEditorProps = { title: string; palette: number[]; diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts index 71902e8..4d35735 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts @@ -1,9 +1,13 @@ -import {ChaosGameFinalProps} from "../2-transforms/chaosGameFinal"; +// hidden-start +import {Props as ChaosGameFinalProps} from "../2-transforms/chaosGameFinal"; import {randomBiUnit} from "../src/randomBiUnit"; import {randomChoice} from "../src/randomChoice"; import {camera, histIndex} from "../src/camera"; import {colorFromPalette, paintColor} from "./paintColor"; +const quality = 15; +const step = 100_000; +// hidden-end export type TransformColor = { color: number; colorSpeed: number; @@ -13,23 +17,21 @@ function mixColor(color1: number, color2: number, colorSpeed: number) { return color1 * (1 - colorSpeed) + color2 * colorSpeed; } -export type ChaosGameColorProps = ChaosGameFinalProps & { +type Props = ChaosGameFinalProps & { palette: number[]; colors: TransformColor[]; finalColor: TransformColor; } -export function* chaosGameColor({width, height, transforms, final, palette, colors, finalColor, quality, step}: ChaosGameColorProps) { - let iterations = (quality ?? 1) * width * height; - step = step ?? 10_000; - +export function* chaosGameColor({width, height, transforms, final, palette, colors, finalColor}: Props) { let currentColor = Math.random(); - const red = Array(width * height).fill(0); - const green = Array(width * height).fill(0); - const blue = Array(width * height).fill(0); - const alpha = Array(width * height).fill(0); + const red = Array(width * height).fill(0); + const green = Array(width * height).fill(0); + const blue = Array(width * height).fill(0); + const alpha = Array(width * height).fill(0); let [x, y] = [randomBiUnit(), randomBiUnit()]; + const iterations = width * height * quality; for (let i = 0; i < iterations; i++) { const [transformIndex, transform] = randomChoice(transforms); [x, y] = transform(x, y); diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts index b35980d..17e61d6 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts @@ -1,17 +1,19 @@ // hidden-start import {randomBiUnit} from "../src/randomBiUnit"; import {randomChoice} from "../src/randomChoice"; -import {ChaosGameFinalProps} from "../2-transforms/chaosGameFinal"; +import {Props as ChaosGameFinalProps} from "../2-transforms/chaosGameFinal"; import {camera, histIndex} from "../src/camera"; -// hidden-end -export type ChaosGameHistogramProps = ChaosGameFinalProps & { - paint: (width: number, histogram: Uint32Array) => ImageData; -} -export function* chaosGameHistogram({width, height, transforms, final, quality, step, paint}: ChaosGameHistogramProps) { - let iterations = (quality ?? 1) * width * height; - step = step ?? 10_000; - const histogram = new Uint32Array(width * height); +const quality = 10; +const step = 100_000; +// hidden-end +export type Props = ChaosGameFinalProps & { + paint: (width: number, height: number, histogram: number[]) => ImageData; +} +export function* chaosGameHistogram({width, height, transforms, final, paint}: Props) { + let iterations = quality * width * height; + + const histogram = Array(width * height).fill(0); let [x, y] = [randomBiUnit(), randomBiUnit()]; @@ -22,13 +24,18 @@ export function* chaosGameHistogram({width, height, transforms, final, quality, if (i > 20) { const [pixelX, pixelY] = camera(finalX, finalY, width); - const pixelIndex = histIndex(pixelX, pixelY, width, 1); - histogram[pixelIndex] += 1; + const hIndex = histIndex(pixelX, pixelY, width, 1); + + if (hIndex < 0 || hIndex >= histogram.length) { + continue; + } + + histogram[hIndex] += 1; } if (i % step === 0) - yield paint(width, histogram); + yield paint(width, height, histogram); } - yield paint(width, histogram); + yield paint(width, height, histogram); } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index 7c96033..5c435d7 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -18,6 +18,10 @@ Can we do something more intelligent with that information? ## Image histograms +:::note +This post covers sections 4 and 5 of the Fractal Flame Algorithm paper +::: + To start with, it's worth demonstrating how much work is actually "wasted." We'll render the reference image again, but this time, set each pixel's transparency based on how many times we encounter it in the chaos game: diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/paintLinear.ts b/blog/2024-11-15-playing-with-fire/3-log-density/paintLinear.ts index 05d5c91..077b3a6 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/paintLinear.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/paintLinear.ts @@ -1,17 +1,17 @@ -export function paintLinear(width: number, histogram: Uint32Array): ImageData { - const image = new ImageData(width, histogram.length / width); +export function paintLinear(width: number, height: number, histogram: number[]): ImageData { + const image = new ImageData(width, height); - let countMax = 0; + let valueMax = 0; for (let value of histogram) { - countMax = Math.max(countMax, value); + valueMax = Math.max(valueMax, value); } for (let i = 0; i < histogram.length; i++) { const pixelIndex = i * 4; - image.data[pixelIndex] = 0; // red - image.data[pixelIndex + 1] = 0; // green - image.data[pixelIndex + 2] = 0; // blue - image.data[pixelIndex + 3] = Number(histogram[i]) / countMax * 0xff; + image.data[pixelIndex] = 0; + image.data[pixelIndex + 1] = 0; + image.data[pixelIndex + 2] = 0; + image.data[pixelIndex + 3] = histogram[i] / valueMax * 0xff; } return image; diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/paintLogarithmic.ts b/blog/2024-11-15-playing-with-fire/3-log-density/paintLogarithmic.ts index c79bce0..4e18b1d 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/paintLogarithmic.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/paintLogarithmic.ts @@ -1,5 +1,5 @@ -export function paintLogarithmic(width: number, histogram: Uint32Array): ImageData { - const image = new ImageData(width, histogram.length / width); +export function paintLogarithmic(width: number, height: number, histogram: number[]): ImageData { + const image = new ImageData(width, height); const histogramLog = new Array(); histogram.forEach(value => histogramLog.push(Math.log(value))); diff --git a/blog/2024-11-15-playing-with-fire/src/blend.ts b/blog/2024-11-15-playing-with-fire/src/blend.ts index a17e47b..d47f2cc 100644 --- a/blog/2024-11-15-playing-with-fire/src/blend.ts +++ b/blog/2024-11-15-playing-with-fire/src/blend.ts @@ -5,14 +5,15 @@ export type VariationBlend = [number, Variation][]; export function blend( x: number, y: number, - variations: VariationBlend): [number, number] { - let [finalX, finalY] = [0, 0]; + variations: VariationBlend +): [number, number] { + let [outX, outY] = [0, 0]; for (const [weight, variation] of variations) { const [varX, varY] = variation(x, y); - finalX += weight * varX; - finalY += weight * varY; + outX += weight * varX; + outY += weight * varY; } - return [finalX, finalY]; + return [outX, outY]; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/plotBinary.ts b/blog/2024-11-15-playing-with-fire/src/plotBinary.ts index 5b9fb64..fd5b9a8 100644 --- a/blog/2024-11-15-playing-with-fire/src/plotBinary.ts +++ b/blog/2024-11-15-playing-with-fire/src/plotBinary.ts @@ -2,14 +2,11 @@ import { camera, histIndex } from "./camera" export function plotBinary(x: number, y: number, image: ImageData) { const [pixelX, pixelY] = camera(x, y, image.width); - if ( - pixelX < 0 || pixelX >= image.width || pixelY < 0 || pixelY > image.height - ) { + const pixelIndex = histIndex(pixelX, pixelY, image.width, 4); + if (pixelIndex < 0 || pixelIndex > image.data.length) { return; } - const pixelIndex = histIndex(pixelX, pixelY, image.width, 4); - image.data[pixelIndex] = 0; image.data[pixelIndex + 1] = 0; image.data[pixelIndex + 2] = 0; diff --git a/src/css/custom.css b/src/css/custom.css index 5030f55..e4b9fdd 100644 --- a/src/css/custom.css +++ b/src/css/custom.css @@ -8,7 +8,7 @@ --ifm-pre-padding: .6rem; /* More readable code highlight background */ - --docusaurus-highlighted-code-line-bg: var(--ifm-color-emphasis-300); + --docusaurus-highlighted-code-line-bg: var(--ifm-color-emphasis-200); /*--ifm-code-font-size: 85%;*/ } From 6c32f0c24912a8dc8a0ed0e447edb915494da66b Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Wed, 11 Dec 2024 08:10:07 -0500 Subject: [PATCH 37/51] Remove plotly dependency --- package.json | 2 -- 1 file changed, 2 deletions(-) diff --git a/package.json b/package.json index 8a0c59f..036d5cb 100644 --- a/package.json +++ b/package.json @@ -23,12 +23,10 @@ "@mdx-js/react": "^3.0.0", "clsx": "^2.0.0", "docusaurus-lunr-search": "^3.5.0", - "plotly.js": "^2.35.2", "prism-react-renderer": "^2.3.0", "raw-loader": "^4.0.2", "react": "^18.0.0", "react-dom": "^18.0.0", - "react-plotly.js": "^2.6.0", "rehype-katex": "^7.0.1", "remark-math": "^6.0.0", "victory": "^37.3.2" From c3c3c65614445c335ff6d7f29a762c9fc7dc7ca2 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Wed, 11 Dec 2024 08:12:19 -0500 Subject: [PATCH 38/51] Don't track IDE folders --- .gitignore | 2 ++ 1 file changed, 2 insertions(+) diff --git a/.gitignore b/.gitignore index deef8ab..91c45ad 100644 --- a/.gitignore +++ b/.gitignore @@ -10,11 +10,13 @@ # Misc .DS_Store +.idea .env.local .env.development.local .env.test.local .env.production.local .styles +.vscode npm-debug.log* yarn-debug.log* From f6439961281d7db4021fd6ac0d5f7efa4ad6816f Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Wed, 11 Dec 2024 17:28:04 -0500 Subject: [PATCH 39/51] Use a sizing ref to avoid resizing the canvas --- .../3-log-density/FlameColor.tsx | 46 +++++++++++++------ .../3-log-density/FlameHistogram.tsx | 8 ++-- .../3-log-density/chaosGameColor.ts | 2 +- .../src/Canvas.tsx | 43 ++++++++--------- 4 files changed, 55 insertions(+), 44 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx index b46418e..88453f4 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx @@ -2,14 +2,32 @@ import React, {useContext, useEffect, useMemo, useRef, useState} from "react"; import * as params from "../src/params"; import {PainterContext} from "../src/Canvas"; import {colorFromPalette} from "./paintColor"; -import {chaosGameColor, ChaosGameColorProps, TransformColor} from "./chaosGameColor"; +import {chaosGameColor, Props as ChaosGameColorProps, TransformColor} from "./chaosGameColor"; import styles from "../src/css/styles.module.css"; import {histIndex} from "../src/camera"; import {useColorMode} from "@docusaurus/theme-common"; -const paletteBarPainter = (palette: number[]) => - (width: number, height: number) => { +type PaletteBarProps = { + height: number; + palette: number[]; + children?: React.ReactNode; +} +const PaletteBar: React.FC = ({height, palette, children}) => { + const sizingRef = useRef(null); + const [width, setWidth] = useState(0); + useEffect(() => { + if (sizingRef) { + setWidth(sizingRef.current.offsetWidth); + } + }, [sizingRef]); + + const canvasRef = useRef(null); + const paletteImage = useMemo(() => { + if (width === 0) { + return; + } + const image = new ImageData(width, height); for (let x = 0; x < width; x++) { const colorIndex = x / width; @@ -23,21 +41,20 @@ const paletteBarPainter = (palette: number[]) => image.data[pixelIndex + 3] = 0xff; } } - return image; - } -type PaletteBarProps = { - height: number; - palette: number[]; - children?: React.ReactNode; -} -const PaletteBar: React.FC = ({height, palette, children}) => { - const painter = useMemo(() => paletteBarPainter(palette), [palette]); + return image; + }, [width, height, palette]); + + useEffect(() => { + if (canvasRef && paletteImage) { + canvasRef.current.getContext("2d").putImageData(paletteImage, 0, 0); + } + }, [canvasRef, paletteImage]); return ( <> -
    - {/**/} +
    + {width > 0 ? : null}
    {children} @@ -115,7 +132,6 @@ export default function FlameColor({quality, children}: Props) { height, transforms: params.xforms, final: params.xformFinal, - quality, palette: params.palette, colors: [xform1Color, xform2Color, xform3Color], finalColor: xformFinalColor diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx index d0b11de..3ac3a86 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx @@ -4,11 +4,10 @@ import {PainterContext} from "../src/Canvas"; import {chaosGameHistogram} from "./chaosGameHistogram"; type Props = { - quality?: number; - paint: (width: number, histogram: Uint32Array) => ImageData; + paint: (width: number, height: number, histogram: number[]) => ImageData; children?: React.ReactElement; } -export default function FlameHistogram({quality, paint, children}: Props) { +export default function FlameHistogram({paint, children}: Props) { const {width, height, setPainter} = useContext(PainterContext); useEffect(() => { @@ -17,11 +16,10 @@ export default function FlameHistogram({quality, paint, children}: Props) { height, transforms, final, - quality, paint } setPainter(chaosGameHistogram(gameParams)); - }, []); + }, [width, height]); return children; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts index 4d35735..58b253b 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts @@ -17,7 +17,7 @@ function mixColor(color1: number, color2: number, colorSpeed: number) { return color1 * (1 - colorSpeed) + color2 * colorSpeed; } -type Props = ChaosGameFinalProps & { +export type Props = ChaosGameFinalProps & { palette: number[]; colors: TransformColor[]; finalColor: TransformColor; diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 0b262d7..012c540 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -14,8 +14,17 @@ type CanvasProps = { children?: React.ReactElement } export const Canvas: React.FC = ({style, children}) => { - const canvasRef = useRef(null); + const sizingRef = useRef(null); + const [width, setWidth] = useState(0); + const [height, setHeight] = useState(0); + useEffect(() => { + if (sizingRef.current) { + setWidth(sizingRef.current.offsetWidth); + setHeight(sizingRef.current.offsetHeight); + } + }, [sizingRef]); + const canvasRef = useRef(null); const [isVisible, setIsVisible] = useState(false); useEffect(() => { if (!canvasRef.current) { @@ -35,16 +44,7 @@ export const Canvas: React.FC = ({style, children}) => { observer.unobserve(canvasRef.current); } } - }, [canvasRef]); - - const [width, setWidth] = useState(0); - const [height, setHeight] = useState(0); - useEffect(() => { - if (canvasRef.current) { - setWidth(canvasRef.current.offsetWidth); - setHeight(canvasRef.current.offsetHeight); - } - }, [canvasRef]); + }, [canvasRef.current]); const [imageHolder, setImageHolder] = useState<[ImageData]>(null); useEffect(() => { @@ -76,25 +76,22 @@ export const Canvas: React.FC = ({style, children}) => { } }, [painter]); - const {colorMode} = useColorMode(); + const filter = useColorMode().colorMode === 'dark' ? 'invert(1)' : ''; + return ( <> - +
    +
    + {width > 0 ? : null} +
    +
    - {() => children} + {width > 0 ? children : null} ) } export const SquareCanvas: React.FC = ({style, children}) => { - return + return
    } \ No newline at end of file From 192286a86a8fab52a4a83f7821c33ba4698c627e Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Wed, 11 Dec 2024 17:31:34 -0500 Subject: [PATCH 40/51] Formatting tweak --- blog/2024-11-15-playing-with-fire/src/Canvas.tsx | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 012c540..45e0a64 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -1,6 +1,5 @@ import React, {useEffect, useState, createContext, useRef} from "react"; import {useColorMode} from "@docusaurus/theme-common"; -import BrowserOnly from "@docusaurus/BrowserOnly"; type PainterProps = { width: number; @@ -76,13 +75,18 @@ export const Canvas: React.FC = ({style, children}) => { } }, [painter]); - const filter = useColorMode().colorMode === 'dark' ? 'invert(1)' : ''; + const canvasProps = { + ref: canvasRef, + width, + height, + style: {filter: useColorMode().colorMode === 'dark' ? 'invert(1)' : ''} + } return ( <>
    - {width > 0 ? : null} + {width > 0 ? : null}
    From 538cc2eb47bc5a206e79013c733ee82a42a682ba Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Wed, 11 Dec 2024 19:56:39 -0500 Subject: [PATCH 41/51] More writing for the math and browser APIs --- .../1-introduction/GasketWeighted.tsx | 2 +- .../1-introduction/cameraGasket.ts | 10 ++ .../1-introduction/chaosGame.js | 1 - .../1-introduction/index.mdx | 145 ++++++++++++------ .../1-introduction/plot.ts | 39 ++--- .../2-transforms/index.mdx | 15 +- .../src/applyTransform.ts | 3 +- .../2024-11-15-playing-with-fire/src/coefs.ts | 11 -- .../src/transform.ts | 14 +- 9 files changed, 138 insertions(+), 102 deletions(-) create mode 100644 blog/2024-11-15-playing-with-fire/1-introduction/cameraGasket.ts delete mode 100644 blog/2024-11-15-playing-with-fire/src/coefs.ts diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx index 326b7f1..1d0776c 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx @@ -31,7 +31,7 @@ export default function GasketWeighted() { <>

    {title}: {weight}

    - setWeight(Number(e.currentTarget.value))}/>
    diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/cameraGasket.ts b/blog/2024-11-15-playing-with-fire/1-introduction/cameraGasket.ts new file mode 100644 index 0000000..8f729cc --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/1-introduction/cameraGasket.ts @@ -0,0 +1,10 @@ +export function camera( + size: number, + x: number, + y: number +): [number, number] { + return [ + Math.floor(x * size), + Math.floor(y * size) + ]; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js index 75f0d5f..17f6962 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js @@ -30,5 +30,4 @@ function* chaosGame({width, height}) { yield img; } -// Wiring so the code above displays properly render() diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index befe48d..eeb18f9 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -36,9 +36,7 @@ can understand without too much prior knowledge. ## Iterated function systems :::note - This post covers section 2 of the Fractal Flame Algorithm paper - ::: As mentioned, fractal flames are a type of "[iterated function system](https://en.wikipedia.org/wiki/Iterated_function_system)," @@ -50,15 +48,18 @@ $$ S = \bigcup_{i=0}^{n-1} F_i(S) $$ -### Fixed set +TODO: I'm not sure what the intuitive explanation here is. Is the idea that the solution is all points +produced by applying each function to all points in the solution? And the purpose of the chaos game is +that if we find one point in the solution set, we can effectively discover all the other points? -First, $S$. $S$ is the set of points in two dimensions (in math terms, $S \in \mathbb{R}^2$) that represent -a "solution" of some kind. Our goal is to find all points in the set $S$, plot them, and display that image. +### Solution set + +First, $S$. $S$ is the set of points in two dimensions (in math terms, $S \in \mathbb{R}^2$) +that represent a "solution" of some kind to our equation. +Our goal is to find all points in $S$, plot them, and display that image. For example, if we say $S = \{(0,0), (1, 1), (2, 2)\}$, there are three points to plot: - - import {VictoryChart, VictoryTheme, VictoryScatter, VictoryLegend} from "victory"; export const simpleData = [ {x: 0, y: 0}, @@ -71,35 +72,52 @@ export const simpleData = [ However, this is a pretty boring image. With fractal flames, rather than listing individual points, -we use functions to describe which points are part of the solution. - -TODO: Explain characteristics of the solution - fixed set - -This means there are an infinite +we use functions to describe which points are part of the solution. This means there are an infinite number of points, but if we find _enough_ points to plot, we'll end up with a nice picture. -And if we choose different functions to start with, our solution set changes, and we'll end up -with a new picture. +And if we change the functions, our solution changes, and we'll get a new picture. -However, it's not clear which points belong in the solution just by staring at the functions. -We'll need a computer to figure it out. +### Transform functions -### Transformation functions +Second, the $F_i(S)$ functions, also known as "transforms." +At their most basic, each $F_i$ takes in a 2-dimensional point and gives back a new point +(in math terms, $F_i \in \mathbb{R}^2 \rightarrow \mathbb{R}^2$). +While you could theoretically use any function, we'll focus on a specific kind of function +known as an "[affine transformation](https://en.wikipedia.org/wiki/Affine_transformation)." -Second, $F_i(S)$. At their most basic, each $F_i$ is a function that takes in a 2-dimensional point and transforms -it into a new 2-dimensional point: $F_i \in \mathbb{R}^2 \rightarrow \mathbb{R}^2$. It's worth discussing -these functions, but not critical, so **this section is optional**. - -In mathematical terms, each $F_i$ is a special kind of function called an [affine transformation](https://en.wikipedia.org/wiki/Affine_transformation). -We can think of them like mapping from one coordinate system to another. For example, we can define a coordinate system -where everything is shifted over: +The general form of an affine transformation is: $$ -F_{shift}(x, y) = (x + 1, y) +F_i(a_i \cdot x + b_i \cdot y + c_i, d_i \cdot x + e_i \cdot y + f_i) $$ -That is, for an input point $(x, y)$, the output point will be $(x + 1, y)$: +import transformSource from "!!raw-loader!../src/transform" -export const shiftData = simpleData.map(({x, y}) => { return {x: x + 1, y} }) +{transformSource} + +The parameters ($a_i$, $b_i$, etc.) are values we get to choose. +For example, we can represent a "shift" function like this: + +$$ +\begin{align*} +a &= 1 \\ +b &= 0 \\ +c &= 0.5 \\ +d &= 0 \\ +e &= 1 \\ +f &= 1.5 \\ +F_{shift}(x,y) &= (1 \cdot x + 0 \cdot y + 0.5, 0 \cdot x + 1 \cdot y + 0.5) \\ +F_{shift}(x, y) &= (x + 0.5, y + 0.5) +\end{align*} +$$ + +Applying this function to our original points will give us a new set of points: + +import {applyCoefs} from "../src/transform" + +export const coefs = {a: 1, b: 0, c: 0.5, d: 0, e: 1, f: 1.5} +export const toData = ([x, y]) => ({x, y}) + +export const shiftData = simpleData.map(({x, y}) => toData(applyCoefs(x, y, coefs))) @@ -115,32 +133,37 @@ export const shiftData = simpleData.map(({x, y}) => { return {x: x + 1, y} }) /> -This is a simple example designed to illustrate the principle. In general, $F_i$ functions have the form: +Fractal flames use more complex functions, but they all start with this structure. + +
    + If you're interested in more math... + + TODO: Contractive functions, attractors, etc.? +
    + +### Fixed set + +With those definitions in place, we can try stating the original problem in +a more natural way: $$ -F_i(x,y) = (a_i \cdot x + b_i \cdot y + c_i, d_i \cdot x + e_i \cdot y + f_i) +S = \bigcup_{i=0}^{n-1} F_i(S) $$ -The parameters ($a_i$, $b_i$, etc.) are values we get to choose. In the example above, we can represent our shift -function using these parameters: +> The solution, $S$, is the union of all sets produced by applying each function, $F_i$, +> to points in the solution. -$$ -a_i = 1 \hspace{0.5cm} b_i = 0 \hspace{0.5cm} c_i = 1 \\ -d_i = 0 \hspace{0.5cm} e_i = 1 \hspace{0.5cm} f_i = 0 \\ -$$ +There's just one small problem: to solve the equation, we must already know what the solution is? -$$ -\begin{align*} -F_{shift}(x,y) &= (1 \cdot x + 0 \cdot y + 1, 0 \cdot x + 1 \cdot y + 0) \\ -F_{shift}(x,y) &= (x + 1, y) -\end{align*} -$$ - -Fractal flames use more complex functions to produce a wide variety of images, but all follow this same format. +TODO: Phrase it another way? +A point is in the solution if it can be reached by applying +one of the functions to another point in the solution? +Is that the definition of a fixed set? ## Sierpinski's gasket -Using these definitions, we can build the first image. The paper defines a function system for us: +With the math out of the way, we're ready to build our first IFS. +The Fractal Flame paper provides us three functions we can use for our system: $$ F_0(x, y) = \left({x \over 2}, {y \over 2} \right) \\ @@ -169,7 +192,7 @@ $$ Let's turn this into code, one piece at a time. -First, the "bi-unit square" is the range $[-1, 1]$. We can pick a random point like this: +First, the "bi-unit square" is the range $[-1, 1]$. We can : import biunitSource from '!!raw-loader!../src/randomBiUnit' @@ -181,14 +204,36 @@ import randintSource from '!!raw-loader!../src/randomInteger' {randintSource} -Finally, implementing the `plot` function. Web browsers have a [Canvas API](https://developer.mozilla.org/en-US/docs/Web/API/Canvas_API) -we can use for 2D graphics. In our case, the plot function will take an $(x,y)$ coordinate and plot it by -coloring the corresponding pixel in an [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData): +### Plotting + +Finally, implementing the `plot` function. This blog series +is designed to be interactive, so everything shows +real-time directly in the browser. As an alternative, +software like `flam3` an Apophysis can also save an image. + +To display the results, we'll use the [Canvas API](https://developer.mozilla.org/en-US/docs/Web/API/Canvas_API). +This allows us to manipulate individual pixels an image, +and display it on screen. + +First, we need to convert from Fractal Flame coordinates to pixel coordinates. +To simplify things, we'll assume that we're plotting a square image, +and we'll focus on the range $[0, 1]$ for both $x$ and $y$: + +import cameraSource from "!!raw-loader!./cameraGasket" + +{cameraSource} + +Next, we'll use an [`ImageData` object](https://developer.mozilla.org/en-US/docs/Web/API/ImageData) +to store the pixel data. +Each pixel in the image on screen has a corresponding index in the `data` array. +To plot our image, we set that pixel to be black: import plotSource from '!!raw-loader!./plot' {plotSource} +Putting it all together, we have our first image: + import Playground from '@theme/Playground' import Scope from './scope' @@ -199,8 +244,8 @@ import chaosGameSource from '!!raw-loader!./chaosGame'
    -Note: The image here is slightly different than the fractal flame paper; I think the paper has an error, -so I'm choosing to plot the image in a way that's consistent with [`flam3` itself](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L440-L441). +Note: The image here is slightly different than the one in the paper. +I think the paper has an error, so I'm choosing to plot the image in a way that's consistent with [`flam3` itself](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L440-L441). ## Weights diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts index 2364330..ef386f5 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts @@ -1,10 +1,6 @@ -/** - * ImageData is an array that contains - * four elements per pixel (one for each - * red, green, blue, and alpha value). - * This maps from pixel coordinates - * to the array index - */ +// hidden-start +import {camera} from "./cameraGasket" +// hidden-end function imageIndex( width: number, x: number, @@ -18,17 +14,9 @@ export function plot( y: number, img: ImageData ) { - // Translate (x,y) coordinates - // to pixel coordinates. - // Also known as a "camera" function. - // - // The display range is: - // x=[0, 1] - // y=[0, 1] - let pixelX = Math.floor(x * img.width); - let pixelY = Math.floor(y * img.height); + let [pixelX, pixelY] = camera(img.width, x, y); - const index = imageIndex( + const i = imageIndex( img.width, pixelX, pixelY @@ -36,17 +24,18 @@ export function plot( // Skip pixels outside the display range if ( - index < 0 || - index > img.data.length + i < 0 || + i > img.data.length ) { return; } // Set the pixel to black by writing 0 - // to the first three elements, - // and 255 to the last element - img.data[index] = 0; - img.data[index + 1] = 0; - img.data[index + 2] = 0; - img.data[index + 3] = 0xff; + // to the first three elements at the index + // (red, green, and blue, respectively), + // and 255 to the last element (alpha) + img.data[i] = 0; + img.data[i + 1] = 0; + img.data[i + 2] = 0; + img.data[i + 3] = 0xff; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 475b36e..1979e4f 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -12,22 +12,15 @@ shapes and patterns that fractal flames are known for. :::note +This post uses a set of [reference parameters](../params.flame) to demonstrate the fractal flame algorithm. +If you're interested in tweaking the parameters, or generating your own art, [Apophysis](https://sourceforge.net/projects/apophysis/) +can load that file and you can try tweaking things yourself! -This post uses a set of [reference parameters](../params.flame) to demonstrate a working -implementation of the fractal flame algorithm. If you're interested in tweaking the parameters, -or generating your own art, [Apophysis](https://sourceforge.net/projects/apophysis/) -can load that file and gives full control over the image. - +This post covers section 3 of the Fractal Flame Algorithm paper ::: ## Transforms and variations -:::note - -This post covers section 3 of the Fractal Flame Algorithm paper - -::: - import CodeBlock from '@theme/CodeBlock' We previously introduced transforms as the "functions" of an "iterated function system," and showed how diff --git a/blog/2024-11-15-playing-with-fire/src/applyTransform.ts b/blog/2024-11-15-playing-with-fire/src/applyTransform.ts index 0b28ae0..92b2165 100644 --- a/blog/2024-11-15-playing-with-fire/src/applyTransform.ts +++ b/blog/2024-11-15-playing-with-fire/src/applyTransform.ts @@ -1,5 +1,4 @@ -import {Transform} from "./transform"; -import {applyCoefs, Coefs} from "./coefs"; +import {Transform, Coefs, applyCoefs} from "./transform"; import {blend, VariationBlend} from "./blend"; export const applyTransform = (coefs: Coefs, variations: VariationBlend): Transform => diff --git a/blog/2024-11-15-playing-with-fire/src/coefs.ts b/blog/2024-11-15-playing-with-fire/src/coefs.ts deleted file mode 100644 index da7e129..0000000 --- a/blog/2024-11-15-playing-with-fire/src/coefs.ts +++ /dev/null @@ -1,11 +0,0 @@ -export interface Coefs { - a: number, b: number, c: number, - d: number, e: number, f: number -} - -export function applyCoefs(x: number, y: number, coefs: Coefs): [number, number] { - return [ - (x * coefs.a + y * coefs.b + coefs.c), - (x * coefs.d + y * coefs.e + coefs.f) - ] -} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/transform.ts b/blog/2024-11-15-playing-with-fire/src/transform.ts index ce099a0..9b7e783 100644 --- a/blog/2024-11-15-playing-with-fire/src/transform.ts +++ b/blog/2024-11-15-playing-with-fire/src/transform.ts @@ -1 +1,13 @@ -export type Transform = (x: number, y: number) => [number, number]; \ No newline at end of file +export type Transform = (x: number, y: number) => [number, number]; + +export interface Coefs { + a: number, b: number, c: number, + d: number, e: number, f: number +} + +export function applyCoefs(x: number, y: number, coefs: Coefs): [number, number] { + return [ + (x * coefs.a + y * coefs.b + coefs.c), + (x * coefs.d + y * coefs.e + coefs.f) + ] +} \ No newline at end of file From a5e620f6031abe3fa82f391dda8e9d2c4dacacd1 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Thu, 12 Dec 2024 17:14:08 -0500 Subject: [PATCH 42/51] More writing for the math --- .../1-introduction/index.mdx | 80 ++++++++++++------- 1 file changed, 52 insertions(+), 28 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index eeb18f9..c9ecc16 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -6,6 +6,7 @@ authors: [bspeice] tags: [] --- + Wikipedia describes fractal flames fractal flames as: > a member of the iterated function system class of fractals @@ -40,18 +41,12 @@ This post covers section 2 of the Fractal Flame Algorithm paper ::: As mentioned, fractal flames are a type of "[iterated function system](https://en.wikipedia.org/wiki/Iterated_function_system)," -or IFS. Their mathematical foundations come from a paper written by [John E. Hutchinson](https://maths-people.anu.edu.au/~john/Assets/Research%20Papers/fractals_self-similarity.pdf), -but reading that paper isn't critical for our purposes. Instead, we'll focus on building a practical understanding -of how they work. The formula for an IFS is short, but will take some time to unpack: +or IFS. The formula for an IFS is short, but will take some time to unpack: $$ S = \bigcup_{i=0}^{n-1} F_i(S) $$ -TODO: I'm not sure what the intuitive explanation here is. Is the idea that the solution is all points -produced by applying each function to all points in the solution? And the purpose of the chaos game is -that if we find one point in the solution set, we can effectively discover all the other points? - ### Solution set First, $S$. $S$ is the set of points in two dimensions (in math terms, $S \in \mathbb{R}^2$) @@ -91,6 +86,7 @@ F_i(a_i \cdot x + b_i \cdot y + c_i, d_i \cdot x + e_i \cdot y + f_i) $$ import transformSource from "!!raw-loader!../src/transform" +import CodeBlock from '@theme/CodeBlock' {transformSource} @@ -135,35 +131,63 @@ export const shiftData = simpleData.map(({x, y}) => toData(applyCoefs(x, y, coef Fractal flames use more complex functions, but they all start with this structure. -
    - If you're interested in more math... - - TODO: Contractive functions, attractors, etc.? -
    - ### Fixed set -With those definitions in place, we can try stating the original problem in -a more natural way: +With those definitions in place, let's revisit the initial problem: $$ S = \bigcup_{i=0}^{n-1} F_i(S) $$ -> The solution, $S$, is the union of all sets produced by applying each function, $F_i$, +Or, to put it in English, we would get something like this: + +> Our solution, $S$, is the union of all sets produced by applying each function, $F_i$, > to points in the solution. -There's just one small problem: to solve the equation, we must already know what the solution is? +There's just one small problem: to find the solution, we must apply these functions to points +we know are in the solution. But how do we know which points are in the solution to start with? -TODO: Phrase it another way? -A point is in the solution if it can be reached by applying -one of the functions to another point in the solution? -Is that the definition of a fixed set? +John E. Hutchinson provides an answer in the [original paper](https://maths-people.anu.edu.au/~john/Assets/Research%20Papers/fractals_self-similarity.pdf) +explaining the mathematics of iterated function systems: + +> Furthermore, $S$ is compact and is the closure of the set of fixed points $s_{i_1...i_p}$ +> of finite compositions $F_{i_1...i_p}$ of members of $F$. + +:::note +I've tweaked the wording slightly to match the conventions in the Fractal Flame paper +::: + +Before your eyes glaze over, let's unpack this explanation: + +- **$S$ is [compact](https://en.wikipedia.org/wiki/Compact_space)...**: All points in our solution will be in a finite range +- **...and is the [closure](https://en.wikipedia.org/wiki/Closure_(mathematics)) of the set of [fixed points](https://en.wikipedia.org/wiki/Fixed_point_(mathematics))**: + Applying our functions to these points does not change them +- **...of finite compositions $F_{i_1...i_p}$ of members of $F$**: By composing our functions (that is, + using the output of one function as input to the next function), we will arrive at the points we care about + +Thus, by applying the functions in our system to "fixed points," we will find the other points we care about. + +However, this is all a bit vague, so let's work through an example. + +
    + But if you want a bit more math... + + ...then it's worth mentioning some information I've skipped over. + + First, the Hutchinson paper explains that the functions $F_i$ must be _contractive_ for this result to hold. + That is, applying the function to a point must bring it closer to other points. However, as the Fractal Flame + algorithm demonstrates, we only need functions to be contractive _on average_. At worst, the system will + degenerate and produce a bad image. + + Second, we're focused $\mathbb{R}^2$ because we're generating images, but the Hutchinson paper + allows for arbitrary dimensions - which means you could also have 3-dimensional fractal flames. + + TODO: Mention attractors? https://en.wikipedia.org/wiki/Chaos_game +
    ## Sierpinski's gasket -With the math out of the way, we're ready to build our first IFS. -The Fractal Flame paper provides us three functions we can use for our system: +The Fractal Flame paper gives us three functions we can use for our function system: $$ F_0(x, y) = \left({x \over 2}, {y \over 2} \right) \\ @@ -175,9 +199,8 @@ $$ ### The chaos game -import CodeBlock from '@theme/CodeBlock' - -Next, how do we find out all the points in $S$? The paper lays out an algorithm called the "chaos game": +Next, how do we find the "fixed points" we mentioned earlier? The paper lays out an algorithm called the "[chaos game](https://en.wikipedia.org/wiki/Chaos_game)" +that will give us points in the solution set: $$ \begin{align*} @@ -244,8 +267,9 @@ import chaosGameSource from '!!raw-loader!./chaosGame'
    -Note: The image here is slightly different than the one in the paper. -I think the paper has an error, so I'm choosing to plot the image in a way that's consistent with [`flam3` itself](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L440-L441). +The image here is slightly different than the one in the paper. +I think the paper has an error, so I'm choosing to plot the image + in a way that's consistent with [`flam3` itself](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L440-L441). ## Weights From b526b02e7be4eab7c9d4feac0ceb6f53f605ff2b Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Fri, 13 Dec 2024 20:03:53 -0500 Subject: [PATCH 43/51] More writing --- .../1-introduction/index.mdx | 34 ++++++--- .../2-transforms/index.mdx | 72 +++++++++++-------- .../3-log-density/index.mdx | 30 ++++++-- 3 files changed, 93 insertions(+), 43 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index c9ecc16..fc88bb5 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -170,11 +170,11 @@ Thus, by applying the functions in our system to "fixed points," we will find th However, this is all a bit vague, so let's work through an example.
    - But if you want a bit more math... + If you want a bit more math first... - ...then it's worth mentioning some information I've skipped over. + ...then there are some details worth mentioning that I've glossed over so far. - First, the Hutchinson paper explains that the functions $F_i$ must be _contractive_ for this result to hold. + First, the Hutchinson paper requires that the functions $F_i$ be _contractive_ tor the solution set to exist. That is, applying the function to a point must bring it closer to other points. However, as the Fractal Flame algorithm demonstrates, we only need functions to be contractive _on average_. At worst, the system will degenerate and produce a bad image. @@ -200,7 +200,7 @@ $$ ### The chaos game Next, how do we find the "fixed points" we mentioned earlier? The paper lays out an algorithm called the "[chaos game](https://en.wikipedia.org/wiki/Chaos_game)" -that will give us points in the solution set: +that will give us points in the solution set. $$ \begin{align*} @@ -213,7 +213,11 @@ $$ \end{align*} $$ -Let's turn this into code, one piece at a time. +:::note +In effect, the chaos game algorithm implements the "finite compositions of $F_{i_1..i_p}$ mentioned earlier. +::: + +Now, let's turn this into code, one piece at a time. First, the "bi-unit square" is the range $[-1, 1]$. We can : @@ -272,10 +276,13 @@ I think the paper has an error, so I'm choosing to plot the image in a way that's consistent with [`flam3` itself](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L440-L441). -## Weights +### Weights -Finally, we'll introduce a "weight" parameter ($w_i$) assigned to each function, which controls -how often that function is used: +Finally, we'll introduce a "weight" ($w_i$) for each function that controls how often we choose +that function during the chaos game relative to each other function. + +For Sierpinski's Gasket, we start with equal weighting, +but you can see how changing the function weights affects the image below: import randomChoiceSource from '!!raw-loader!../src/randomChoice' @@ -288,4 +295,13 @@ import chaosGameWeightedSource from "!!raw-loader!./chaosGameWeighted"; import GasketWeighted from "./GasketWeighted"; import {SquareCanvas} from "../src/Canvas"; - \ No newline at end of file + + +## Summary + +Studying the foundations of fractal flames is challenging, +but we now have an understanding of both the mathematics +and implementation of iterated function systems. + +In the next post, we'll study the first innovation that fractal flames +bring: variations. \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 1979e4f..6dfa42f 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -6,20 +6,22 @@ authors: [bspeice] tags: [] --- -Now that we have a basic chaos game in place, it's time to spice things up. Transforms and variations create the +Now that we have a basic chaos game in place, it's time to spice things up. Variations create the shapes and patterns that fractal flames are known for. -:::note +:::info This post uses a set of [reference parameters](../params.flame) to demonstrate the fractal flame algorithm. If you're interested in tweaking the parameters, or generating your own art, [Apophysis](https://sourceforge.net/projects/apophysis/) can load that file and you can try tweaking things yourself! - -This post covers section 3 of the Fractal Flame Algorithm paper ::: -## Transforms and variations +## Variations + +:::note +This post covers section 3 for the Fractal Flame Algorithm paper +::: import CodeBlock from '@theme/CodeBlock' @@ -28,8 +30,8 @@ playing the chaos game leads to an image of Sierpinski's Gasket. Even though we the image it generates is exciting. But it's still not nearly as exciting as the images the Fractal Flame algorithm is known for. -This leads us to the first big innovation of the Fractal Flame algorithm: using non-linear functions -for the transforms. These functions are known as "variations": +This leads us to the first big innovation of the Fractal Flame algorithm: applying non-linear functions +after the affine transform has happened. These functions are called "variations": $$ F_i(x, y) = V_j(a_i \cdot x + b_i \cdot y + c_i, d_i \cdot x + e_i \cdot y + f_i) @@ -39,10 +41,10 @@ import variationSource from '!!raw-loader!../src/variation' {variationSource} -Variations, labeled $V_j$ above, are functions just like transforms (we use $j$ to indicate a specific variation). -They take an input point $(x,y)$, and give an output point. However, the sky is the limit for what variation functions do in between -input to output. The Fractal Flame paper lists 49 different variation functions, -and the official `flam3` implementation supports [98 different functions](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/variations.c). +Just like transforms, variations ($V_j$) are functions that map $(x, y)$ coordinates to new coordinates. +However, the sky is the limit for what we can do in between input and output. +The Fractal Flame paper lists 49 different variation functions, +and the official `flam3` implementation supports [98 different variations](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/variations.c). To draw our reference image, we'll focus on four variations: @@ -59,16 +61,16 @@ import linearSrc from '!!raw-loader!../src/linear' {linearSrc} :::tip - -In a way, we've already been using this variation! The functions that define Sierpinski's Gasket +In a way, we've already been using this variation! The transforms that define Sierpinski's Gasket apply the affine coefficients to the input point, and use that as the output point. - ::: ### Julia (variation 13) -This variation is a good example of the non-linear functions the Fractal Flame Algorithm introduces. -It still receives an input point $(x, y)$, but does some crazy things with it: +This variation is a good example of the non-linear functions we can use. It uses both trigonometry +and probability to produce interesting shapes: + +TODO: Connection with the julia set? $$ \begin{align*} @@ -91,8 +93,8 @@ import juliaSrc from '!!raw-loader!../src/julia' ### Popcorn (variation 17) -Some variations rely on knowing the transform's affine coefficients; these are known as "dependent variations." -For the popcorn variation, we use the $c$ and $f$ coefficients: +Some variations rely on knowing their transform's affine coefficients; they're known as "dependent variations." +For the popcorn variation, we use $c$ and $f$: $$ V_{17}(x,y) = (x + c \cdot \text{sin}(\text{tan }3y), y + f \cdot \text{sin}(\text{tan }3x)) @@ -104,7 +106,7 @@ import popcornSrc from '!!raw-loader!../src/popcorn' ### PDJ (variation 24) -Some variations have extra parameters that the designer can choose; these are known as "parametric variations." +Some variations have extra parameters we can choose; these are known as "parametric variations." For the PDJ variation, there are four extra parameters we can choose: $$ @@ -132,14 +134,11 @@ import blendSource from "!!raw-loader!../src/blend"; {blendSource} -With that in place, we have enough to render a first full fractal flame. We'll use the same -chaos game as before, but use our new transforms and variations to produce a dramatically different image: +With that in place, we have enough to render a first fractal flame. We'll use the same +chaos game as before, but our new transforms and variations produce a dramatically different image: :::tip -This image is interactive! The sliders change the variation weights ($v_{ij}$ parameters) -so you can design your own image. - -Try using the sliders to find which parts of the image each transform controls. +Try using the variation weight sliders to figure out which parts of the image each transform controls. ::: import {SquareCanvas} from "../src/Canvas"; @@ -149,8 +148,8 @@ import FlameBlend from "./FlameBlend"; ## Post transforms -Post transforms introduce a second affine transform, this time _after_ variation blending. -We'll use introduce some new variables, but the post transform function should look familiar by now: +Next, we'll introduce a second affine transform, known as a post transform, that is applied _after_ variation blending. +We'll use some new variables, but the post transform function should look familiar: $$ \begin{align*} @@ -163,11 +162,11 @@ import postSource from '!!raw-loader!./post' {postSource} -The image below starts with the same initial transforms/variations as the previous fractal flame, +The image below uses the same transforms/variations as the previous fractal flame, but allows modifying the post-transform coefficients.
    - If you want a challenge... + If you want to test your understanding... Challenge 1: What post-transform coefficients will give us the previous image? @@ -180,10 +179,23 @@ import FlamePost from "./FlamePost"; ## Final transforms +Our last step is to introduce a "final transform" ($F_{final}$) that is applied +regardless of which transform function we're using. It works just like a normal transform +(composition of affine transform, variation blend, and post transform), +but it doesn't change the chaos game state: + import chaosGameFinalSource from "!!raw-loader!./chaosGameFinal" {chaosGameFinalSource} import FlameFinal from "./FlameFinal"; - \ No newline at end of file + + +## Summary + +Variations are the fractal flame algorithm's first major innovation over previous IFS's. +Blending variation functions and post/final transforms allows us to generate interesting images. + +However, the images themselves are grainy and unappealing. In the next post, we'll clean up +the quality and add color. \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index 5c435d7..924bbec 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -11,8 +11,8 @@ to a specific pixel, and color in that pixel. This works well for simple function systems (like Sierpinski's Gasket), but more complex systems (like our reference parameters) produce grainy images. -Every time we "turn on" pixels that have already been enabled, we're wasting work. -Can we do something more intelligent with that information? +Every additional time we plot a pixel, we're wasting work. +Can we do something more intelligent instead? @@ -23,8 +23,12 @@ This post covers sections 4 and 5 of the Fractal Flame Algorithm paper ::: To start with, it's worth demonstrating how much work is actually "wasted." -We'll render the reference image again, but this time, set each pixel's transparency -based on how many times we encounter it in the chaos game: +Previously, pixels would be either transparent or opaque depending on whether +we encountered them while running the chaos game. + +We'll render the reference image again, but this time, keep track of how many times +we encounter each pixel during the chaos game. At the end, we'll "paint" our final image +by setting each pixel's transparency based on how frequently we encounter it: import CodeBlock from "@theme/CodeBlock"; @@ -40,6 +44,24 @@ import {paintLinear} from "./paintLinear"; ## Log display +Using a histogram to paint our image is definitely a quality improvement, +but it produces "ghostly" images. In our reference parameters, the outer circle +is preserved, but the interior appears to be missing! + +To fix this, we'll introduce the second major innovation of the fractal flame algorithm: tone mapping. +This technique is used in computer graphics to adjust for the fact that +people perceive brightness on a logarithmic scale. + +As a concrete example, high dynamic range (HDR) photography uses this technique to capture +nice images of scenes with very different brightness levels. If you want to take a picture of something dark, +you need a long exposure time. However, long exposures lead to bright spots that "wash out" and become nothing but white. +If we take multiple images using different exposure times, we can blend them together to create +a final image where everything is visible. + +TODO: HDR link? + +In fractal flames, this "tone map" is accomplished + import paintLogarithmicSource from "!!raw-loader!./paintLogarithmic" {paintLogarithmicSource} From 9b1a3895d020c10238f2f10be1ef51af37483242 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Fri, 13 Dec 2024 23:28:35 -0500 Subject: [PATCH 44/51] More writing. Hopefully can finish the first draft soon --- .../1-introduction/index.mdx | 4 +- .../3-log-density/FlameColor.tsx | 6 +- .../3-log-density/index.mdx | 77 +++++++++++++------ .../3-log-density/paintLogarithmic.ts | 2 +- .../src/Canvas.tsx | 11 ++- docusaurus.config.ts | 5 +- 6 files changed, 71 insertions(+), 34 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index fc88bb5..5620f3c 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -243,8 +243,8 @@ This allows us to manipulate individual pixels an image, and display it on screen. First, we need to convert from Fractal Flame coordinates to pixel coordinates. -To simplify things, we'll assume that we're plotting a square image, -and we'll focus on the range $[0, 1]$ for both $x$ and $y$: +To simplify things, we'll assume that we're plotting a square image +with range $[0, 1]$ for both $x$ and $y$: import cameraSource from "!!raw-loader!./cameraGasket" diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx index 88453f4..e306b46 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx @@ -13,7 +13,7 @@ type PaletteBarProps = { palette: number[]; children?: React.ReactNode; } -const PaletteBar: React.FC = ({height, palette, children}) => { +export const PaletteBar: React.FC = ({height, palette, children}) => { const sizingRef = useRef(null); const [width, setWidth] = useState(0); useEffect(() => { @@ -51,10 +51,12 @@ const PaletteBar: React.FC = ({height, palette, children}) => { } }, [canvasRef, paletteImage]); + const canvasStyle = {filter: useColorMode().colorMode === 'dark' ? 'invert(1)' : ''}; + return ( <>
    - {width > 0 ? : null} + {width > 0 ? : null}
    {children} diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index 924bbec..b740246 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -6,13 +6,11 @@ authors: [bspeice] tags: [] --- -So far, our `plot()` function has been fairly simple; map an input coordinate -to a specific pixel, and color in that pixel. -This works well for simple function systems (like Sierpinski's Gasket), +So far, our `plot()` function has been fairly simple; map an input coordinate to a specific pixel, +and color in that pixel. This works well for simple function systems (like Sierpinski's Gasket), but more complex systems (like our reference parameters) produce grainy images. -Every additional time we plot a pixel, we're wasting work. -Can we do something more intelligent instead? +In this post, we'll refine the image quality and add color to really make things shine. @@ -22,13 +20,14 @@ Can we do something more intelligent instead? This post covers sections 4 and 5 of the Fractal Flame Algorithm paper ::: -To start with, it's worth demonstrating how much work is actually "wasted." -Previously, pixels would be either transparent or opaque depending on whether -we encountered them while running the chaos game. +To start, it's worth demonstrating how much work is actually "wasted" +when we treat pixels as a binary "on" (opaque) or "off" (transparent). -We'll render the reference image again, but this time, keep track of how many times -we encounter each pixel during the chaos game. At the end, we'll "paint" our final image -by setting each pixel's transparency based on how frequently we encounter it: +We'll render the reference image again, but this time, track each time +we encounter each pixel during the chaos game. When the chaos game finishes, +find the pixel we encountered most frequently. Finally, "paint" the image +by setting each pixel's transparency to ratio of times encountered +divided by the maximum value: import CodeBlock from "@theme/CodeBlock"; @@ -40,27 +39,40 @@ import {SquareCanvas} from "../src/Canvas"; import FlameHistogram from "./FlameHistogram"; import {paintLinear} from "./paintLinear"; - + ## Log display -Using a histogram to paint our image is definitely a quality improvement, -but it produces "ghostly" images. In our reference parameters, the outer circle +While using a histogram to paint the image improves the quality, +it also leads to some parts vanishing entirely. +In the reference parameters, the outer circle is preserved, but the interior appears to be missing! -To fix this, we'll introduce the second major innovation of the fractal flame algorithm: tone mapping. -This technique is used in computer graphics to adjust for the fact that -people perceive brightness on a logarithmic scale. +To fix this, we'll introduce the second major innovation of the fractal flame algorithm: [tone mapping](https://en.wikipedia.org/wiki/Tone_mapping). +This is a technique used in computer graphics to compensate for differences in how +computers represent color, and how color is perceived by people. As a concrete example, high dynamic range (HDR) photography uses this technique to capture -nice images of scenes with very different brightness levels. If you want to take a picture of something dark, -you need a long exposure time. However, long exposures lead to bright spots that "wash out" and become nothing but white. -If we take multiple images using different exposure times, we can blend them together to create +nice images of scenes with wide brightness ranges. To take a picture of something dark, +you need a long exposure time. However, long exposures can lead to images that "wash out" and become pure white. +By taking multiple pictures using different exposure times, we can combine them to create a final image where everything is visible. -TODO: HDR link? +In fractal flames, this "tone map" is accomplished by scaling brightness according to the _logarithm_ +of how many times we encounter a pixel. This way, "dark spots" (pixels the chaos game visits infrequently) +will still be visible, and "bright spots" (pixels the chaos game visits frequently) won't wash out. -In fractal flames, this "tone map" is accomplished +
    + Log-scale vibrancy is also why fractal flames appear to be 3D... + + As explained in the Fractal Flame paper: + + > Where one branch of the fractal crosses another, one may appear to occlude the other + > if their densities are different enough because the lesser density is inconsequential in sum. + > For example, branches of densities 1000 and 100 might have brightnesses of 30 and 20. + > Where they cross the density is 1100, whose brightness is 30.4, which is + > hardly distinguishable from 30. +
    import paintLogarithmicSource from "!!raw-loader!./paintLogarithmic" @@ -68,10 +80,29 @@ import paintLogarithmicSource from "!!raw-loader!./paintLogarithmic" import {paintLogarithmic} from './paintLogarithmic' - + ## Color +Finally, we'll spice things up with the last innovation introduced by +the fractal flame algorithm: color. By including a color coordinate +in the chaos game, we can illustrate the transforms that are responsible +for each part of an image. + +### Palette + +Our first step is to define a color palette for the image. Fractal flames +typically use a palette of 256 colors that transition smoothly +from one to another. In the diagram below, each color in our palette is plotted +on a small strip. Putting the strips side by side shows the palette for our image: + +import * as params from "../src/params" +import {PaletteBar} from "./FlameColor" + + + +### Color coordinate + import paintColorSource from "!!raw-loader!./paintColor" {paintColorSource} diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/paintLogarithmic.ts b/blog/2024-11-15-playing-with-fire/3-log-density/paintLogarithmic.ts index 4e18b1d..eacad34 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/paintLogarithmic.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/paintLogarithmic.ts @@ -1,7 +1,7 @@ export function paintLogarithmic(width: number, height: number, histogram: number[]): ImageData { const image = new ImageData(width, height); - const histogramLog = new Array(); + const histogramLog: number[] = []; histogram.forEach(value => histogramLog.push(Math.log(value))); let histogramLogMax = -Infinity; diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 45e0a64..515b14c 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -1,4 +1,4 @@ -import React, {useEffect, useState, createContext, useRef} from "react"; +import React, {useEffect, useState, createContext, useRef, MouseEvent} from "react"; import {useColorMode} from "@docusaurus/theme-common"; type PainterProps = { @@ -8,6 +8,13 @@ type PainterProps = { } export const PainterContext = createContext(null) +const downloadImage = (e: MouseEvent) => { + const link = document.createElement("a"); + link.download = "flame.png"; + link.href = (e.target as HTMLCanvasElement).toDataURL("image/png"); + link.click(); +} + type CanvasProps = { style?: any; children?: React.ReactElement @@ -86,7 +93,7 @@ export const Canvas: React.FC = ({style, children}) => { <>
    - {width > 0 ? : null} + {width > 0 ? : null}
    diff --git a/docusaurus.config.ts b/docusaurus.config.ts index 72d1a9c..184cf6e 100644 --- a/docusaurus.config.ts +++ b/docusaurus.config.ts @@ -99,11 +99,8 @@ const config: Config = { plugins: [require.resolve('docusaurus-lunr-search')], stylesheets: [ { - href: 'https://cdn.jsdelivr.net/npm/katex@0.13.24/dist/katex.min.css', + href: '/katex/katex.min.css', type: 'text/css', - integrity: - 'sha384-odtC+0UGzzFL/6PNoE8rX/SPcQDXBJ+uRepguP4QkPCm2LBxH3FA3y+fKSiJ+AmM', - crossorigin: 'anonymous', }, ], future: { From a05acf67486594bd413159418c0bd8a106666b95 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sat, 14 Dec 2024 16:55:54 -0500 Subject: [PATCH 45/51] Finish a first draft --- .../2-transforms/index.mdx | 20 ++- .../3-log-density/FlameColor.tsx | 2 +- .../3-log-density/chaosGameColor.ts | 43 ++--- .../3-log-density/chaosGameHistogram.ts | 4 + .../3-log-density/colorFromPalette.ts | 4 + .../3-log-density/index.mdx | 155 +++++++++++++++--- .../3-log-density/mixColor.ts | 3 + .../3-log-density/paintColor.ts | 8 +- 8 files changed, 184 insertions(+), 55 deletions(-) create mode 100644 blog/2024-11-15-playing-with-fire/3-log-density/colorFromPalette.ts create mode 100644 blog/2024-11-15-playing-with-fire/3-log-density/mixColor.ts diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 6dfa42f..26d0c31 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -180,9 +180,23 @@ import FlamePost from "./FlamePost"; ## Final transforms Our last step is to introduce a "final transform" ($F_{final}$) that is applied -regardless of which transform function we're using. It works just like a normal transform +regardless of which transform the chaos game selects. It works just like a normal transform (composition of affine transform, variation blend, and post transform), -but it doesn't change the chaos game state: +but it doesn't change the chaos game state. + +With that in place, our chaos game algorithm changes slightly: + +$$ +\begin{align*} +&(x, y) = \text{random point in the bi-unit square} \\ +&\text{iterate } \{ \\ +&\hspace{1cm} i = \text{random integer from 0 to } n - 1 \\ +&\hspace{1cm} (x,y) = F_i(x,y) \\ +&\hspace{1cm} (x_f,y_f) = F_{final}(x,y) \\ +&\hspace{1cm} \text{plot}(x_f,y_f) \text{ if iterations} > 20 \\ +\} +\end{align*} +$$ import chaosGameFinalSource from "!!raw-loader!./chaosGameFinal" @@ -198,4 +212,4 @@ Variations are the fractal flame algorithm's first major innovation over previou Blending variation functions and post/final transforms allows us to generate interesting images. However, the images themselves are grainy and unappealing. In the next post, we'll clean up -the quality and add color. \ No newline at end of file +the image quality and add some color. \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx index e306b46..f6cc860 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx @@ -1,7 +1,7 @@ import React, {useContext, useEffect, useMemo, useRef, useState} from "react"; import * as params from "../src/params"; import {PainterContext} from "../src/Canvas"; -import {colorFromPalette} from "./paintColor"; +import {colorFromPalette} from "./colorFromPalette"; import {chaosGameColor, Props as ChaosGameColorProps, TransformColor} from "./chaosGameColor"; import styles from "../src/css/styles.module.css"; diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts index 58b253b..4b75409 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts @@ -3,7 +3,9 @@ import {Props as ChaosGameFinalProps} from "../2-transforms/chaosGameFinal"; import {randomBiUnit} from "../src/randomBiUnit"; import {randomChoice} from "../src/randomChoice"; import {camera, histIndex} from "../src/camera"; -import {colorFromPalette, paintColor} from "./paintColor"; +import {colorFromPalette} from "./colorFromPalette"; +import {mixColor} from "./mixColor"; +import {paintColor} from "./paintColor"; const quality = 15; const step = 100_000; @@ -13,51 +15,50 @@ export type TransformColor = { colorSpeed: number; } -function mixColor(color1: number, color2: number, colorSpeed: number) { - return color1 * (1 - colorSpeed) + color2 * colorSpeed; -} - export type Props = ChaosGameFinalProps & { palette: number[]; colors: TransformColor[]; finalColor: TransformColor; } export function* chaosGameColor({width, height, transforms, final, palette, colors, finalColor}: Props) { - let currentColor = Math.random(); - const red = Array(width * height).fill(0); - const green = Array(width * height).fill(0); - const blue = Array(width * height).fill(0); - const alpha = Array(width * height).fill(0); + const imgRed = Array(width * height).fill(0); + const imgGreen = Array(width * height).fill(0); + const imgBlue = Array(width * height).fill(0); + const imgAlpha = Array(width * height).fill(0); let [x, y] = [randomBiUnit(), randomBiUnit()]; + let c = Math.random(); const iterations = width * height * quality; for (let i = 0; i < iterations; i++) { const [transformIndex, transform] = randomChoice(transforms); [x, y] = transform(x, y); + + // highlight-start + const transformColor = colors[transformIndex]; + c = mixColor(c, transformColor.color, transformColor.colorSpeed); + // highlight-end + const [finalX, finalY] = final(x, y); if (i > 20) { const [pixelX, pixelY] = camera(finalX, finalY, width); const pixelIndex = histIndex(pixelX, pixelY, width, 1); - if (pixelIndex < 0 || pixelIndex >= alpha.length) + if (pixelIndex < 0 || pixelIndex >= imgAlpha.length) continue; - const transformColor = colors[transformIndex]; - currentColor = mixColor(currentColor, transformColor.color, transformColor.colorSpeed); - - const colorFinal = mixColor(currentColor, finalColor.color, finalColor.colorSpeed); + const colorFinal = mixColor(c, finalColor.color, finalColor.colorSpeed); const [r, g, b] = colorFromPalette(palette, colorFinal); - red[pixelIndex] += r; - green[pixelIndex] += g; - blue[pixelIndex] += b; - alpha[pixelIndex] += 1; + imgRed[pixelIndex] += r; + imgGreen[pixelIndex] += g; + imgBlue[pixelIndex] += b; + imgAlpha[pixelIndex] += 1; } if (i % step === 0) - yield paintColor(width, height, red, green, blue, alpha); + yield paintColor(width, height, imgRed, imgGreen, imgBlue, imgAlpha); } - yield paintColor(width, height, red, green, blue, alpha); + yield paintColor(width, height, imgRed, imgGreen, imgBlue, imgAlpha); } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts index 17e61d6..0f122a4 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts @@ -13,7 +13,9 @@ export type Props = ChaosGameFinalProps & { export function* chaosGameHistogram({width, height, transforms, final, paint}: Props) { let iterations = quality * width * height; + // highlight-start const histogram = Array(width * height).fill(0); + // highlight-end let [x, y] = [randomBiUnit(), randomBiUnit()]; @@ -23,6 +25,7 @@ export function* chaosGameHistogram({width, height, transforms, final, paint}: P const [finalX, finalY] = final(x, y); if (i > 20) { + // highlight-start const [pixelX, pixelY] = camera(finalX, finalY, width); const hIndex = histIndex(pixelX, pixelY, width, 1); @@ -31,6 +34,7 @@ export function* chaosGameHistogram({width, height, transforms, final, paint}: P } histogram[hIndex] += 1; + // highlight-end } if (i % step === 0) diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/colorFromPalette.ts b/blog/2024-11-15-playing-with-fire/3-log-density/colorFromPalette.ts new file mode 100644 index 0000000..a039313 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/3-log-density/colorFromPalette.ts @@ -0,0 +1,4 @@ +export function colorFromPalette(palette: number[], colorIndex: number): [number, number, number] { + const paletteIndex = Math.floor(colorIndex * (palette.length / 3)) * 3; + return [palette[paletteIndex], palette[paletteIndex + 1], palette[paletteIndex + 2]]; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index b740246..613e707 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -1,6 +1,6 @@ --- slug: 2024/11/playing-with-fire-log-density -title: "Playing with fire: Log-density and color" +title: "Playing with fire: Tone mapping and color" date: 2024-11-15 14:00:00 authors: [bspeice] tags: [] @@ -23,11 +23,17 @@ This post covers sections 4 and 5 of the Fractal Flame Algorithm paper To start, it's worth demonstrating how much work is actually "wasted" when we treat pixels as a binary "on" (opaque) or "off" (transparent). -We'll render the reference image again, but this time, track each time -we encounter each pixel during the chaos game. When the chaos game finishes, -find the pixel we encountered most frequently. Finally, "paint" the image -by setting each pixel's transparency to ratio of times encountered -divided by the maximum value: +We'll render the reference image again, but this time, count each time +we encounter a pixel during the chaos game. This gives us a kind of "histogram" +of the image: + +import chaosGameHistogramSource from "!!raw-loader!./chaosGameHistogram" + +{chaosGameHistogramSource} + +When the chaos game finishes, find the pixel we encountered most frequently. +Finally, "paint" the image by setting each pixel's alpha value (transparency) +to the ratio of times encountered, divided by the maximum value: import CodeBlock from "@theme/CodeBlock"; @@ -39,22 +45,20 @@ import {SquareCanvas} from "../src/Canvas"; import FlameHistogram from "./FlameHistogram"; import {paintLinear} from "./paintLinear"; - + -## Log display +## Tone mapping -While using a histogram to paint the image improves the quality, -it also leads to some parts vanishing entirely. -In the reference parameters, the outer circle -is preserved, but the interior appears to be missing! +While using a histogram to paint the image improves the quality, it also leads to some parts vanishing entirely. +In the reference parameters, the outer circle is preserved, but the interior appears to be missing! To fix this, we'll introduce the second major innovation of the fractal flame algorithm: [tone mapping](https://en.wikipedia.org/wiki/Tone_mapping). This is a technique used in computer graphics to compensate for differences in how -computers represent color, and how color is perceived by people. +computers represent color, and how people see color. As a concrete example, high dynamic range (HDR) photography uses this technique to capture nice images of scenes with wide brightness ranges. To take a picture of something dark, -you need a long exposure time. However, long exposures can lead to images that "wash out" and become pure white. +you need a long exposure time. However, long exposures can lead to "hot spots" in images that are pure white. By taking multiple pictures using different exposure times, we can combine them to create a final image where everything is visible. @@ -80,33 +84,134 @@ import paintLogarithmicSource from "!!raw-loader!./paintLogarithmic" import {paintLogarithmic} from './paintLogarithmic' - + ## Color -Finally, we'll spice things up with the last innovation introduced by -the fractal flame algorithm: color. By including a color coordinate -in the chaos game, we can illustrate the transforms that are responsible -for each part of an image. +Finally, we'll introduce the last innovation of the fractal flame algorithm: color. +By including a color coordinate ($c$) in the chaos game, we can illustrate the transforms +responsible for each part of the image. + +### Color coordinate + +Color in a fractal flame uses a range of $[0, 1]$. This is important for two reasons: + +- It helps blend colors together in the final image +- It allows us to swap in new color palettes easily + +We'll give each transform a color value ($c_i$) in the $[0, 1]$ range. +Then, at each step in the chaos game, we'll set the current color +by blending it with the previous color and the current transform: + +$$ +\begin{align*} +&(x, y) = \text{random point in the bi-unit square} \\ +&c = \text{random point from [0,1]} \\ +&\text{iterate } \{ \\ +&\hspace{1cm} i = \text{random integer from 0 to } n - 1 \\ +&\hspace{1cm} (x,y) = F_i(x,y) \\ +&\hspace{1cm} (x_f,y_f) = F_{final}(x,y) \\ +&\hspace{1cm} c = (c + c_i) / 2 \\ +&\hspace{1cm} \text{plot}(x_f,y_f,c_f) \text{ if iterations} > 20 \\ +\} +\end{align*} +$$ + +### Color speed + +:::warning +Color speed as a concept isn't introduced in the Fractal Flame Algorithm paper. + +It is included here because [`flam3` implements it](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/variations.c#L2140), +and because it's fun to play with. +::: + +Next, we'll add a parameter to each transform that controls how much it affects the current color. +This is known as the "color speed" ($s_i$): + +$$ +c = c \cdot (1 - s_i) + c_i \cdot s_i +$$ + +import mixColorSource from "!!raw-loader!./mixColor" + +{mixColorSource} + +Color speed values work just like transform weights. A value of 1 +means we take the transform color and ignore the previous color state. +Similarly, a value of 0 means we keep the current color state and ignore the +transform color. ### Palette -Our first step is to define a color palette for the image. Fractal flames -typically use a palette of 256 colors that transition smoothly -from one to another. In the diagram below, each color in our palette is plotted -on a small strip. Putting the strips side by side shows the palette for our image: +Now, we need to map the color coordinate to a pixel color. Fractal flames typically use +256 colors (each color has 3 values - red, green, blue) to define a palette. +Then, the color coordinate becomes an index into the palette. + +There's one small complication: the color coordinate is continuous, but the palette +uses discrete colors. How do we handle situations where the color coordinate is +"in between" the colors of our palette? + +One way is to use a step function. In the code below, we multiply the color coordinate +by the number of colors in the palette, then truncate that value. This gives us a discrete index: + +import colorFromPaletteSource from "!!raw-loader!./colorFromPalette"; + +{colorFromPaletteSource} + +
    + As an alternative... + + ...you could also interpolate between colors in the palette. + For example: [`flam3` code](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L483-L486) +
    + +In the diagram below, each color in our palette is plotted on a small vertical strip. +Putting the strips side by side shows the palette used by our reference image: import * as params from "../src/params" import {PaletteBar} from "./FlameColor" -### Color coordinate +### Plotting + +We're now ready to plot our $(x_f,y_f,c_f)$ coordinates. After translating from color coordinate ($c_f$) +to RGB value, add that value to the image histogram: + +import chaosGameColorSource from "!!raw-loader!./chaosGameColor" + +{chaosGameColorSource} + +Finally, painting the image. With tone mapping, logarithms scale the image brightness to match +how it is perceived. When using color, we scale each color channel by the alpha channel: import paintColorSource from "!!raw-loader!./paintColor" {paintColorSource} +And now, at long last, a full-color fractal flame: + import FlameColor from "./FlameColor"; - \ No newline at end of file + + +## Summary + +Tone mapping is the second major innovation of the fractal flame algorithm. +By tracking how often the chaos game encounters each pixel, we can adjust +brightness/transparency to reduce the visual "graining" of previous images. + +Next, introducing a third coordinate to the chaos game makes color images possible, +the third major innovation of the fractal flame algorithm. Using a continuous +color scale and color palette adds a splash of color to our transforms. + +The Fractal Flame Algorithm paper goes on to describe more techniques +not covered here. Image quality can be improved with density estimation +and filtering. New parameters can be generated by "mutating" existing +fractal flames. Fractal flames can even be animated to produce videos! + +That said, I think this is a good place to wrap up. We were able to go from +an introduction to the mathematics of fractal systems all the way to +generating full-color images. Fractal flames are a challenging topic, +but it's extremely rewarding to learn more about how they work. diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/mixColor.ts b/blog/2024-11-15-playing-with-fire/3-log-density/mixColor.ts new file mode 100644 index 0000000..f27b175 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/3-log-density/mixColor.ts @@ -0,0 +1,3 @@ +export function mixColor(color1: number, color2: number, colorSpeed: number) { + return color1 * (1 - colorSpeed) + color2 * colorSpeed; +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/paintColor.ts b/blog/2024-11-15-playing-with-fire/3-log-density/paintColor.ts index eb1c094..33b0470 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/paintColor.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/paintColor.ts @@ -1,8 +1,6 @@ -export function colorFromPalette(palette: number[], colorIndex: number): [number, number, number] { - const paletteIndex = Math.floor(colorIndex * (palette.length / 3)) * 3; - return [palette[paletteIndex], palette[paletteIndex + 1], palette[paletteIndex + 2]]; -} - +// hidden-start +import {colorFromPalette} from "./colorFromPalette"; +// hidden-end export function paintColor( width: number, height: number, From 1ce6137c174830d9ff02b2df2b224967b5838ee7 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 15 Dec 2024 15:55:27 -0500 Subject: [PATCH 46/51] First pass proof-reading --- .../1-introduction/Gasket.tsx | 2 +- .../1-introduction/GasketWeighted.tsx | 2 +- .../1-introduction/index.mdx | 105 +++++++++--------- .../2-transforms/index.mdx | 41 ++++--- .../3-log-density/index.mdx | 70 ++++++------ .../src/Canvas.tsx | 22 ++-- .../src/css/styles.module.css | 8 +- 7 files changed, 132 insertions(+), 118 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx index c1d848b..e1fdf7a 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx @@ -14,7 +14,7 @@ export function Render({f}) { export default function Gasket({f}) { return ( - + ) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx index 1d0776c..3381c56 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx @@ -31,7 +31,7 @@ export default function GasketWeighted() { <>

    {title}: {weight}

    - setWeight(Number(e.currentTarget.value))}/>
    diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index 5620f3c..60a7645 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -7,11 +7,11 @@ tags: [] --- -Wikipedia describes fractal flames fractal flames as: +Wikipedia describes [fractal flames](https://en.wikipedia.org/wiki/Fractal_flame) as: > a member of the iterated function system class of fractals -It's a bit tedious, but technically correct. I choose to think of them a different way: beauty in mathematics. +It's tedious, but technically correct. I choose to think of them a different way: beauty in mathematics. import isDarkMode from '@site/src/isDarkMode' import banner from '../banner.png' @@ -22,14 +22,15 @@ import banner from '../banner.png' -I don't remember exactly when I first learned about fractal flames, but I do remember becoming entranced by the images they created. +I don't remember exactly when I first learned about fractal flames, but I do remember being entranced by the images they created. I also remember their unique appeal to my young engineering mind; this was an art form I could participate in. The original [Fractal Flame Algorithm paper](https://flam3.com/flame_draves.pdf) describing their structure was too much for me to handle at the time (I was ~12 years old), so I was content to play around and enjoy the pictures. -But the desire to understand it stuck around. Now, with a graduate degree under my belt, maybe I can make some progress. +But the desire to understand it stuck around. Now, with a graduate degree under my belt, I want to revisit it +and try to make some progress. -This guide is my attempt to explain fractal flames in a way that younger me — and others interested in the art — +This guide is my attempt to explain how fractal flames work in a way that younger me — and others interested in the art — can understand without too much prior knowledge. --- @@ -41,7 +42,7 @@ This post covers section 2 of the Fractal Flame Algorithm paper ::: As mentioned, fractal flames are a type of "[iterated function system](https://en.wikipedia.org/wiki/Iterated_function_system)," -or IFS. The formula for an IFS is short, but will take some time to unpack: +or IFS. The formula for an IFS is short, but takes some time to unpack: $$ S = \bigcup_{i=0}^{n-1} F_i(S) @@ -69,15 +70,15 @@ export const simpleData = [ However, this is a pretty boring image. With fractal flames, rather than listing individual points, we use functions to describe which points are part of the solution. This means there are an infinite number of points, but if we find _enough_ points to plot, we'll end up with a nice picture. -And if we change the functions, our solution changes, and we'll get a new picture. +And if the functions change, the solution also changes, and we get a new picture. ### Transform functions Second, the $F_i(S)$ functions, also known as "transforms." At their most basic, each $F_i$ takes in a 2-dimensional point and gives back a new point (in math terms, $F_i \in \mathbb{R}^2 \rightarrow \mathbb{R}^2$). -While you could theoretically use any function, we'll focus on a specific kind of function -known as an "[affine transformation](https://en.wikipedia.org/wiki/Affine_transformation)." +While you could theoretically use any function, we'll start with a specific kind of function +called an "[affine transformation](https://en.wikipedia.org/wiki/Affine_transformation)." The general form of an affine transformation is: @@ -102,7 +103,7 @@ d &= 0 \\ e &= 1 \\ f &= 1.5 \\ F_{shift}(x,y) &= (1 \cdot x + 0 \cdot y + 0.5, 0 \cdot x + 1 \cdot y + 0.5) \\ -F_{shift}(x, y) &= (x + 0.5, y + 0.5) +F_{shift}(x, y) &= (x + 0.5, y + 1.5) \end{align*} $$ @@ -139,7 +140,7 @@ $$ S = \bigcup_{i=0}^{n-1} F_i(S) $$ -Or, to put it in English, we would get something like this: +Or, to put it in English, we might say: > Our solution, $S$, is the union of all sets produced by applying each function, $F_i$, > to points in the solution. @@ -154,40 +155,41 @@ explaining the mathematics of iterated function systems: > of finite compositions $F_{i_1...i_p}$ of members of $F$. :::note -I've tweaked the wording slightly to match the conventions in the Fractal Flame paper +I've tweaked the wording slightly to match the conventions of the Fractal Flame paper ::: -Before your eyes glaze over, let's unpack this explanation: +Before your eyes glaze over, let's unpack this: - **$S$ is [compact](https://en.wikipedia.org/wiki/Compact_space)...**: All points in our solution will be in a finite range - **...and is the [closure](https://en.wikipedia.org/wiki/Closure_(mathematics)) of the set of [fixed points](https://en.wikipedia.org/wiki/Fixed_point_(mathematics))**: - Applying our functions to these points does not change them + Applying our functions to points in the solution will give us other points that are in the solution - **...of finite compositions $F_{i_1...i_p}$ of members of $F$**: By composing our functions (that is, - using the output of one function as input to the next function), we will arrive at the points we care about + using the output of one function as input to the next function), we will arrive at the points in the solution -Thus, by applying the functions in our system to "fixed points," we will find the other points we care about. - -However, this is all a bit vague, so let's work through an example. +Thus, by applying the functions to fixed points of our system, we will find the other points we care about.
    - If you want a bit more math first... + If you want a bit more math... - ...then there are some details worth mentioning that I've glossed over so far. + ...then there are some extra details I've glossed over so far. - First, the Hutchinson paper requires that the functions $F_i$ be _contractive_ tor the solution set to exist. + First, the Hutchinson paper requires that the functions $F_i$ be _contractive_ for the solution set to exist. That is, applying the function to a point must bring it closer to other points. However, as the Fractal Flame algorithm demonstrates, we only need functions to be contractive _on average_. At worst, the system will degenerate and produce a bad image. Second, we're focused $\mathbb{R}^2$ because we're generating images, but the Hutchinson paper - allows for arbitrary dimensions - which means you could also have 3-dimensional fractal flames. + allows for arbitrary dimensions; you could also have 3-dimensional fractal flames. - TODO: Mention attractors? https://en.wikipedia.org/wiki/Chaos_game + Finally, there's a close relationship between fractal flames and [attractors](https://en.wikipedia.org/wiki/Attractor). + Specifically, the fixed points of $S$ act as attractors for the chaos game (explained in detail below).
    -## Sierpinski's gasket +This is still a bit vague, so let's work through an example. -The Fractal Flame paper gives us three functions we can use for our function system: +## [Sierpinski's gasket](https://www.britannica.com/biography/Waclaw-Sierpinski) + +The Fractal Flame paper gives us three functions to use for our first IFS: $$ F_0(x, y) = \left({x \over 2}, {y \over 2} \right) \\ @@ -200,7 +202,7 @@ $$ ### The chaos game Next, how do we find the "fixed points" we mentioned earlier? The paper lays out an algorithm called the "[chaos game](https://en.wikipedia.org/wiki/Chaos_game)" -that will give us points in the solution set. +that gives us points in the solution set: $$ \begin{align*} @@ -214,12 +216,13 @@ $$ $$ :::note -In effect, the chaos game algorithm implements the "finite compositions of $F_{i_1..i_p}$ mentioned earlier. +The chaos game algorithm is effectively the "finite compositions of $F_{i_1..i_p}$" mentioned earlier. ::: Now, let's turn this into code, one piece at a time. -First, the "bi-unit square" is the range $[-1, 1]$. We can : +First, we need to generate some random numbers. The "bi-unit square" is the range $[-1, 1]$, +so we generate a random point using an existing API: import biunitSource from '!!raw-loader!../src/randomBiUnit' @@ -233,14 +236,12 @@ import randintSource from '!!raw-loader!../src/randomInteger' ### Plotting -Finally, implementing the `plot` function. This blog series -is designed to be interactive, so everything shows -real-time directly in the browser. As an alternative, -software like `flam3` an Apophysis can also save an image. +Finally, implementing the `plot` function. This blog series is designed to be interactive, +so everything displays directly in the browser. As an alternative, +software like `flam3` and Apophysis can "plot" by saving an image to disk. -To display the results, we'll use the [Canvas API](https://developer.mozilla.org/en-US/docs/Web/API/Canvas_API). -This allows us to manipulate individual pixels an image, -and display it on screen. +To show the results, we'll use the [Canvas API](https://developer.mozilla.org/en-US/docs/Web/API/Canvas_API). +This allows us to manipulate individual pixels in an image and display it on screen. First, we need to convert from Fractal Flame coordinates to pixel coordinates. To simplify things, we'll assume that we're plotting a square image @@ -250,10 +251,9 @@ import cameraSource from "!!raw-loader!./cameraGasket" {cameraSource} -Next, we'll use an [`ImageData` object](https://developer.mozilla.org/en-US/docs/Web/API/ImageData) -to store the pixel data. +Next, we'll store the pixel data in an [`ImageData` object](https://developer.mozilla.org/en-US/docs/Web/API/ImageData). Each pixel in the image on screen has a corresponding index in the `data` array. -To plot our image, we set that pixel to be black: +To plot a point, we set that pixel to be black: import plotSource from '!!raw-loader!./plot' @@ -271,18 +271,16 @@ import chaosGameSource from '!!raw-loader!./chaosGame'
    -The image here is slightly different than the one in the paper. -I think the paper has an error, so I'm choosing to plot the image - in a way that's consistent with [`flam3` itself](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L440-L441). + The image here is slightly different than in the paper. + I think the paper has an error, so I'm choosing to plot the image + the same way as the [reference implementation](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L440-L441). ### Weights -Finally, we'll introduce a "weight" ($w_i$) for each function that controls how often we choose -that function during the chaos game relative to each other function. - -For Sierpinski's Gasket, we start with equal weighting, -but you can see how changing the function weights affects the image below: +There's one last step before we finish the introduction. So far, each function $F_i$ has +the same chance of being chosen. We can change that by introducing a "weight" ($w_i$) +to each transform in the chaos game: import randomChoiceSource from '!!raw-loader!../src/randomChoice' @@ -292,16 +290,23 @@ import chaosGameWeightedSource from "!!raw-loader!./chaosGameWeighted"; {chaosGameWeightedSource} +For Sierpinski's Gasket, we start with equal weighting, +but changing the transform weights affects how often +the chaos game "visits" parts of the image: + +:::tip +Double-click the image if you want to save a copy! +::: + import GasketWeighted from "./GasketWeighted"; import {SquareCanvas} from "../src/Canvas"; - + ## Summary Studying the foundations of fractal flames is challenging, but we now have an understanding of both the mathematics -and implementation of iterated function systems. +and implementations of iterated function systems. -In the next post, we'll study the first innovation that fractal flames -bring: variations. \ No newline at end of file +In the next post, we'll study the first innovation of fractal flames: variations. \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 26d0c31..d01750e 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -12,9 +12,9 @@ shapes and patterns that fractal flames are known for. :::info -This post uses a set of [reference parameters](../params.flame) to demonstrate the fractal flame algorithm. +This post uses [reference parameters](../params.flame) to demonstrate the fractal flame algorithm. If you're interested in tweaking the parameters, or generating your own art, [Apophysis](https://sourceforge.net/projects/apophysis/) -can load that file and you can try tweaking things yourself! +can load that file to play around with! ::: ## Variations @@ -30,8 +30,8 @@ playing the chaos game leads to an image of Sierpinski's Gasket. Even though we the image it generates is exciting. But it's still not nearly as exciting as the images the Fractal Flame algorithm is known for. -This leads us to the first big innovation of the Fractal Flame algorithm: applying non-linear functions -after the affine transform has happened. These functions are called "variations": +This leads us to the first big innovation of the Fractal Flame algorithm: adding non-linear functions +after the affine transform. These functions are called "variations": $$ F_i(x, y) = V_j(a_i \cdot x + b_i \cdot y + c_i, d_i \cdot x + e_i \cdot y + f_i) @@ -41,8 +41,9 @@ import variationSource from '!!raw-loader!../src/variation' {variationSource} -Just like transforms, variations ($V_j$) are functions that map $(x, y)$ coordinates to new coordinates. -However, the sky is the limit for what we can do in between input and output. +Just like transforms, variations ($V_j$) are functions that take in $(x, y)$ coordinates +and give back new $(x, y)$ coordinates. +However, the sky is the limit for what happens between input and output. The Fractal Flame paper lists 49 different variation functions, and the official `flam3` implementation supports [98 different variations](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/variations.c). @@ -70,8 +71,6 @@ apply the affine coefficients to the input point, and use that as the output poi This variation is a good example of the non-linear functions we can use. It uses both trigonometry and probability to produce interesting shapes: -TODO: Connection with the julia set? - $$ \begin{align*} r &= \sqrt{x^2 + y^2} \\ @@ -93,7 +92,7 @@ import juliaSrc from '!!raw-loader!../src/julia' ### Popcorn (variation 17) -Some variations rely on knowing their transform's affine coefficients; they're known as "dependent variations." +Some variations rely on knowing the transform's affine coefficients; they're called "dependent variations." For the popcorn variation, we use $c$ and $f$: $$ @@ -106,7 +105,7 @@ import popcornSrc from '!!raw-loader!../src/popcorn' ### PDJ (variation 24) -Some variations have extra parameters we can choose; these are known as "parametric variations." +Some variations have extra parameters; they're called "parametric variations." For the PDJ variation, there are four extra parameters we can choose: $$ @@ -122,7 +121,7 @@ import pdjSrc from '!!raw-loader!../src/pdj' Now, one variation is fun, but we can also combine variations in a process called "blending." Each variation receives the same $x$ and $y$ inputs, and we add together each variation's $x$ and $y$ outputs. -We'll also give each variation a weight (called $v_{ij}$) that changes how much it contributes to the transform: +We'll also give each variation a weight ($v_{ij}$) that changes how much it contributes to the result: $$ F_i(x,y) = \sum_{j} v_{ij} V_j(a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) @@ -144,11 +143,12 @@ Try using the variation weight sliders to figure out which parts of the image ea import {SquareCanvas} from "../src/Canvas"; import FlameBlend from "./FlameBlend"; - + ## Post transforms -Next, we'll introduce a second affine transform, known as a post transform, that is applied _after_ variation blending. +Next, we'll introduce a second affine transform, applied _after_ variation blending. This is called a "post transform." + We'll use some new variables, but the post transform function should look familiar: $$ @@ -163,19 +163,18 @@ import postSource from '!!raw-loader!./post' {postSource} The image below uses the same transforms/variations as the previous fractal flame, -but allows modifying the post-transform coefficients. +but allows modifying the post-transform coefficients:
    If you want to test your understanding... - Challenge 1: What post-transform coefficients will give us the previous image? - - Challenge 2: What post-transform coefficients will give us a _mirrored_ image? + - What post-transform coefficients will give us the previous image? + - What post-transform coefficients will give us a _mirrored_ image?
    import FlamePost from "./FlamePost"; - + ## Final transforms @@ -204,12 +203,12 @@ import chaosGameFinalSource from "!!raw-loader!./chaosGameFinal" import FlameFinal from "./FlameFinal"; - + ## Summary -Variations are the fractal flame algorithm's first major innovation over previous IFS's. -Blending variation functions and post/final transforms allows us to generate interesting images. +Variations are the fractal flame algorithm's first major innovation. +By blending variation functions, and post/final transforms, we generate unique images. However, the images themselves are grainy and unappealing. In the next post, we'll clean up the image quality and add some color. \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index 613e707..a9356ea 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -6,9 +6,9 @@ authors: [bspeice] tags: [] --- -So far, our `plot()` function has been fairly simple; map an input coordinate to a specific pixel, +So far, our `plot()` function has been fairly simple; map a fractal flame coordinate to a specific pixel, and color in that pixel. This works well for simple function systems (like Sierpinski's Gasket), -but more complex systems (like our reference parameters) produce grainy images. +but more complex systems (like the reference parameters) produce grainy images. In this post, we'll refine the image quality and add color to really make things shine. @@ -20,20 +20,21 @@ In this post, we'll refine the image quality and add color to really make things This post covers sections 4 and 5 of the Fractal Flame Algorithm paper ::: -To start, it's worth demonstrating how much work is actually "wasted" -when we treat pixels as a binary "on" (opaque) or "off" (transparent). +One problem with the existing chaos game is that we waste work +by treating pixels as a binary "on" (opaque) or "off" (transparent). +If the chaos game encounters the same location twice, nothing actually changes. -We'll render the reference image again, but this time, count each time -we encounter a pixel during the chaos game. This gives us a kind of "histogram" -of the image: +To demonstrate how much work is wasted, we'll render the reference image again. +However, we'll also count each time the chaos game encounters a pixel. +This gives us a kind of image "histogram": import chaosGameHistogramSource from "!!raw-loader!./chaosGameHistogram" {chaosGameHistogramSource} -When the chaos game finishes, find the pixel we encountered most frequently. -Finally, "paint" the image by setting each pixel's alpha value (transparency) -to the ratio of times encountered, divided by the maximum value: +When the chaos game finishes, we find the pixel encountered most frequently. +Finally, we "paint" the image by setting each pixel's alpha value (transparency) +to the ratio of times encountered divided by the maximum: import CodeBlock from "@theme/CodeBlock"; @@ -49,27 +50,27 @@ import {paintLinear} from "./paintLinear"; ## Tone mapping -While using a histogram to paint the image improves the quality, it also leads to some parts vanishing entirely. +While using a histogram reduces the "graininess" of the image, it also leads to some parts vanishing entirely. In the reference parameters, the outer circle is preserved, but the interior appears to be missing! To fix this, we'll introduce the second major innovation of the fractal flame algorithm: [tone mapping](https://en.wikipedia.org/wiki/Tone_mapping). This is a technique used in computer graphics to compensate for differences in how -computers represent color, and how people see color. +computers represent brightness, and how people see brightness. As a concrete example, high dynamic range (HDR) photography uses this technique to capture -nice images of scenes with wide brightness ranges. To take a picture of something dark, -you need a long exposure time. However, long exposures can lead to "hot spots" in images that are pure white. -By taking multiple pictures using different exposure times, we can combine them to create +nice images of scenes with a wide range of brightnesses. To take a picture of something dark, +you need a long exposure time. However, long exposures lead to "hot spots" (sections that are pure white). +By taking multiple pictures with different exposure times, we can combine them to create a final image where everything is visible. In fractal flames, this "tone map" is accomplished by scaling brightness according to the _logarithm_ -of how many times we encounter a pixel. This way, "dark spots" (pixels the chaos game visits infrequently) -will still be visible, and "bright spots" (pixels the chaos game visits frequently) won't wash out. +of how many times we encounter a pixel. This way, "cold spots" (pixels the chaos game visits infrequently) +will still be visible, and "hot spots" (pixels the chaos game visits frequently) won't wash out.
    - Log-scale vibrancy is also why fractal flames appear to be 3D... + Log-scale vibrancy also explains fractal flames appear to be 3D... - As explained in the Fractal Flame paper: + As mentioned in the paper: > Where one branch of the fractal crosses another, one may appear to occlude the other > if their densities are different enough because the lesser density is inconsequential in sum. @@ -89,15 +90,17 @@ import {paintLogarithmic} from './paintLogarithmic' ## Color Finally, we'll introduce the last innovation of the fractal flame algorithm: color. -By including a color coordinate ($c$) in the chaos game, we can illustrate the transforms -responsible for each part of the image. +By including a third coordinate ($c$) in the chaos game, we can illustrate the transforms +responsible for the image. ### Color coordinate -Color in a fractal flame uses a range of $[0, 1]$. This is important for two reasons: +Color in a fractal flame is continuous on the range $[0, 1]$. This is important for two reasons: -- It helps blend colors together in the final image -- It allows us to swap in new color palettes easily +- It helps blend colors together in the final image. Slight changes in the color value lead to + slight changes in the actual color +- It allows us to swap in new color palettes easily. We're free to choose what actual colors + each color value represents We'll give each transform a color value ($c_i$) in the $[0, 1]$ range. Then, at each step in the chaos game, we'll set the current color @@ -139,14 +142,14 @@ import mixColorSource from "!!raw-loader!./mixColor" Color speed values work just like transform weights. A value of 1 means we take the transform color and ignore the previous color state. -Similarly, a value of 0 means we keep the current color state and ignore the +A value of 0 means we keep the current color state and ignore the transform color. ### Palette Now, we need to map the color coordinate to a pixel color. Fractal flames typically use 256 colors (each color has 3 values - red, green, blue) to define a palette. -Then, the color coordinate becomes an index into the palette. +The color coordinate then becomes an index into the palette. There's one small complication: the color coordinate is continuous, but the palette uses discrete colors. How do we handle situations where the color coordinate is @@ -163,11 +166,11 @@ import colorFromPaletteSource from "!!raw-loader!./colorFromPalette"; As an alternative... ...you could also interpolate between colors in the palette. - For example: [`flam3` code](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L483-L486) + For example, `flam3` uses [linear interpolation](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L483-L486)
    In the diagram below, each color in our palette is plotted on a small vertical strip. -Putting the strips side by side shows the palette used by our reference image: +Putting the strips side by side shows the full palette used by the reference parameters: import * as params from "../src/params" import {PaletteBar} from "./FlameColor" @@ -177,14 +180,15 @@ import {PaletteBar} from "./FlameColor" ### Plotting We're now ready to plot our $(x_f,y_f,c_f)$ coordinates. After translating from color coordinate ($c_f$) -to RGB value, add that value to the image histogram: +to RGB value, add that to the image histogram: import chaosGameColorSource from "!!raw-loader!./chaosGameColor" {chaosGameColorSource} Finally, painting the image. With tone mapping, logarithms scale the image brightness to match -how it is perceived. When using color, we scale each color channel by the alpha channel: +how it is perceived. With color, we use a similar method, but scale each color channel +by the alpha channel: import paintColorSource from "!!raw-loader!./paintColor" @@ -206,10 +210,10 @@ Next, introducing a third coordinate to the chaos game makes color images possib the third major innovation of the fractal flame algorithm. Using a continuous color scale and color palette adds a splash of color to our transforms. -The Fractal Flame Algorithm paper goes on to describe more techniques -not covered here. Image quality can be improved with density estimation +The Fractal Flame Algorithm paper does go on to describe more techniques +not covered here. For example, Image quality can be improved with density estimation and filtering. New parameters can be generated by "mutating" existing -fractal flames. Fractal flames can even be animated to produce videos! +fractal flames. And fractal flames can even be animated to produce videos! That said, I think this is a good place to wrap up. We were able to go from an introduction to the mathematics of fractal systems all the way to diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index 515b14c..b7ea30c 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -8,18 +8,20 @@ type PainterProps = { } export const PainterContext = createContext(null) -const downloadImage = (e: MouseEvent) => { - const link = document.createElement("a"); - link.download = "flame.png"; - link.href = (e.target as HTMLCanvasElement).toDataURL("image/png"); - link.click(); -} +const downloadImage = (name: string) => + (e: MouseEvent) => { + const link = document.createElement("a"); + link.download = "flame.png"; + link.href = (e.target as HTMLCanvasElement).toDataURL("image/png"); + link.click(); + } type CanvasProps = { + name: string; style?: any; children?: React.ReactElement } -export const Canvas: React.FC = ({style, children}) => { +export const Canvas: React.FC = ({name, style, children}) => { const sizingRef = useRef(null); const [width, setWidth] = useState(0); const [height, setHeight] = useState(0); @@ -93,7 +95,7 @@ export const Canvas: React.FC = ({style, children}) => { <>
    - {width > 0 ? : null} + {width > 0 ? : null}
    @@ -103,6 +105,6 @@ export const Canvas: React.FC = ({style, children}) => { ) } -export const SquareCanvas: React.FC = ({style, children}) => { - return
    +export const SquareCanvas: React.FC = ({name, style, children}) => { + return
    } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css index d769283..6ef2da1 100644 --- a/blog/2024-11-15-playing-with-fire/src/css/styles.module.css +++ b/blog/2024-11-15-playing-with-fire/src/css/styles.module.css @@ -1,7 +1,7 @@ .inputGroup { padding: .2em; - margin-top: .2em; - margin-bottom: .2em; + margin-top: .5em; + margin-bottom: .5em; border: 1px solid; border-radius: var(--ifm-global-radius); border-color: var(--ifm-color-emphasis-500); @@ -25,6 +25,10 @@ .inputElement > input[type=range] { width: 100%; + height: 4px; + appearance: none; + background: var(--ifm-color-emphasis-400); + border-radius: var(--ifm-global-radius); } .inputReset { From 456c3a66e5a399745599574a51e3e0c11a967a73 Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 15 Dec 2024 21:19:09 -0500 Subject: [PATCH 47/51] Mass formatting, fix mobile display, fix issues with image wrap-around --- blog/2024-11-15-playing-with-fire/.prettierrc | 4 + .../1-introduction/Gasket.tsx | 34 +- .../1-introduction/GasketWeighted.tsx | 76 ++--- .../1-introduction/cameraGasket.ts | 14 +- .../1-introduction/chaosGame.js | 21 +- .../1-introduction/chaosGameWeighted.ts | 32 +- .../1-introduction/index.mdx | 22 +- .../1-introduction/plot.ts | 35 ++- .../1-introduction/scope.tsx | 16 +- .../2-transforms/CoefEditor.tsx | 89 +++--- .../2-transforms/FlameBlend.tsx | 116 +++---- .../2-transforms/FlameFinal.tsx | 72 ++--- .../2-transforms/FlamePost.tsx | 72 ++--- .../2-transforms/VariationEditor.tsx | 74 ++--- .../2-transforms/buildBlend.ts | 30 +- .../2-transforms/chaosGameFinal.ts | 60 ++-- .../2-transforms/index.mdx | 10 +- .../2-transforms/post.ts | 14 +- .../3-log-density/FlameColor.tsx | 297 +++++++++--------- .../3-log-density/FlameHistogram.tsx | 38 +-- .../3-log-density/chaosGameColor.ts | 159 +++++++--- .../3-log-density/chaosGameHistogram.ts | 91 ++++-- .../3-log-density/colorFromPalette.ts | 16 +- .../3-log-density/index.mdx | 2 +- .../3-log-density/mixColor.ts | 9 +- .../3-log-density/paintColor.ts | 47 +-- .../3-log-density/paintLinear.ts | 36 ++- .../3-log-density/paintLogarithmic.ts | 40 ++- .../2024-11-15-playing-with-fire/params.flame | 8 +- .../src/Canvas.tsx | 2 +- .../src/applyTransform.ts | 10 +- .../2024-11-15-playing-with-fire/src/blend.ts | 25 +- .../2024-11-15-playing-with-fire/src/julia.ts | 23 +- .../src/linear.ts | 3 +- .../src/params.ts | 161 +++++----- blog/2024-11-15-playing-with-fire/src/pdj.ts | 15 +- .../src/plotBinary.ts | 20 +- .../src/popcorn.ts | 16 +- .../src/randomChoice.ts | 3 +- .../src/transform.ts | 26 +- .../src/variation.ts | 5 +- 41 files changed, 1026 insertions(+), 817 deletions(-) create mode 100644 blog/2024-11-15-playing-with-fire/.prettierrc diff --git a/blog/2024-11-15-playing-with-fire/.prettierrc b/blog/2024-11-15-playing-with-fire/.prettierrc new file mode 100644 index 0000000..b882b19 --- /dev/null +++ b/blog/2024-11-15-playing-with-fire/.prettierrc @@ -0,0 +1,4 @@ +{ + "tabWidth": 2, + "semi": true +} \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx index e1fdf7a..c3aa4d8 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/Gasket.tsx @@ -1,21 +1,21 @@ -import {SquareCanvas, PainterContext} from "../src/Canvas"; -import {useContext, useEffect} from "react"; +import { PainterContext, SquareCanvas } from "../src/Canvas"; +import { useContext, useEffect } from "react"; -export function Render({f}) { - const {width, height, setPainter} = useContext(PainterContext); - useEffect(() => { - if (width && height) { - const painter = f({width, height}); - setPainter(painter); - } - }, [width, height]); - return <>; +export function Render({ f }) { + const { width, height, setPainter } = useContext(PainterContext); + useEffect(() => { + if (width && height) { + const painter = f({ width, height }); + setPainter(painter); + } + }, [width, height]); + return <>; } -export default function Gasket({f}) { - return ( - - - - ) +export default function Gasket({ f }) { + return ( + + + + ); } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx index 3381c56..9d18454 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx @@ -1,49 +1,49 @@ -import {useEffect, useState, useContext, useRef} from "react"; -import {PainterContext} from "../src/Canvas"; -import {chaosGameWeighted} from "./chaosGameWeighted"; -import TeX from '@matejmazur/react-katex'; +import { useContext, useEffect, useState } from "react"; +import { PainterContext } from "../src/Canvas"; +import { chaosGameWeighted } from "./chaosGameWeighted"; +import TeX from "@matejmazur/react-katex"; -import styles from "../src/css/styles.module.css" +import styles from "../src/css/styles.module.css"; type Transform = (x: number, y: number) => [number, number]; export default function GasketWeighted() { - const [f0Weight, setF0Weight] = useState(1); - const [f1Weight, setF1Weight] = useState(1); - const [f2Weight, setF2Weight] = useState(1); + const [f0Weight, setF0Weight] = useState(1); + const [f1Weight, setF1Weight] = useState(1); + const [f2Weight, setF2Weight] = useState(1); - const f0: Transform = (x, y) => [x / 2, y / 2]; - const f1: Transform = (x, y) => [(x + 1) / 2, y / 2]; - const f2: Transform = (x, y) => [x / 2, (y + 1) / 2]; + const f0: Transform = (x, y) => [x / 2, y / 2]; + const f1: Transform = (x, y) => [(x + 1) / 2, y / 2]; + const f2: Transform = (x, y) => [x / 2, (y + 1) / 2]; - const {width, height, setPainter} = useContext(PainterContext); + const { width, height, setPainter } = useContext(PainterContext); - useEffect(() => { - const transforms: [number, Transform][] = [ - [f0Weight, f0], - [f1Weight, f1], - [f2Weight, f2] - ]; - setPainter(chaosGameWeighted({width, height, transforms})); - }, [f0Weight, f1Weight, f2Weight]); + useEffect(() => { + const transforms: [number, Transform][] = [ + [f0Weight, f0], + [f1Weight, f1], + [f2Weight, f2] + ]; + setPainter(chaosGameWeighted({ width, height, transforms })); + }, [f0Weight, f1Weight, f2Weight]); - const weightInput = (title, weight, setWeight) => ( - <> -
    -

    {title}: {weight}

    - setWeight(Number(e.currentTarget.value))}/> -
    - - ) + const weightInput = (title, weight, setWeight) => ( + <> +
    +

    {title}: {weight}

    + setWeight(Number(e.currentTarget.value))} /> +
    + + ); - return ( - <> -
    - {weightInput("F_0", f0Weight, setF0Weight)} - {weightInput("F_1", f1Weight, setF1Weight)} - {weightInput("F_2", f2Weight, setF2Weight)} -
    - - ) + return ( + <> +
    + {weightInput("F_0", f0Weight, setF0Weight)} + {weightInput("F_1", f1Weight, setF1Weight)} + {weightInput("F_2", f2Weight, setF2Weight)} +
    + + ); } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/cameraGasket.ts b/blog/2024-11-15-playing-with-fire/1-introduction/cameraGasket.ts index 8f729cc..47d104c 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/cameraGasket.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/cameraGasket.ts @@ -1,10 +1,10 @@ export function camera( - size: number, - x: number, - y: number + x: number, + y: number, + size: number ): [number, number] { - return [ - Math.floor(x * size), - Math.floor(y * size) - ]; + return [ + Math.floor(x * size), + Math.floor(y * size) + ]; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js index 17f6962..777ccfd 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGame.js @@ -6,28 +6,29 @@ const xforms = [ (x, y) => [x / 2, y / 2], (x, y) => [(x + 1) / 2, y / 2], (x, y) => [x / 2, (y + 1) / 2] -] +]; -function* chaosGame({width, height}) { - const step = 1000; - let img = new ImageData(width, height); +function* chaosGame({ width, height }) { + let img = + new ImageData(width, height); let [x, y] = [ randomBiUnit(), randomBiUnit() ]; - for (let c = 0; c < iterations; c++) { - const i = randomInteger(0, xforms.length); - [x, y] = xforms[i](x, y); + for (let i = 0; i < iterations; i++) { + const index = + randomInteger(0, xforms.length); + [x, y] = xforms[index](x, y); - if (c > 20) + if (i > 20) plot(x, y, img); - if (c % step === 0) + if (i % 1000 === 0) yield img; } yield img; } -render() +render(); diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts index ef1966a..41a9922 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/chaosGameWeighted.ts @@ -1,37 +1,41 @@ // hidden-start import { randomBiUnit } from "../src/randomBiUnit"; import { randomChoice } from "../src/randomChoice"; -import { plot } from "./plot" -import {Transform} from "../src/transform"; +import { plot } from "./plot"; +import { Transform } from "../src/transform"; const quality = 0.5; const step = 1000; // hidden-end export type Props = { - width: number, - height: number, - transforms: [number, Transform][] + width: number, + height: number, + transforms: [number, Transform][] } + export function* chaosGameWeighted( - {width, height, transforms}: Props + { width, height, transforms }: Props ) { - let img = new ImageData(width, height); + let img = + new ImageData(width, height); let [x, y] = [ - randomBiUnit(), - randomBiUnit() + randomBiUnit(), + randomBiUnit() ]; - const iterations = width * height * quality; - for (let c = 0; c < iterations; c++) { + const pixels = width * height; + const iterations = quality * pixels; + for (let i = 0; i < iterations; i++) { // highlight-start - const [_, xform] = randomChoice(transforms); + const [_, xform] = + randomChoice(transforms); // highlight-end [x, y] = xform(x, y); - if (c > 20) + if (i > 20) plot(x, y, img); - if (c % step === 0) + if (i % step === 0) yield img; } diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index 60a7645..dd9dacc 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -83,7 +83,7 @@ called an "[affine transformation](https://en.wikipedia.org/wiki/Affine_transfor The general form of an affine transformation is: $$ -F_i(a_i \cdot x + b_i \cdot y + c_i, d_i \cdot x + e_i \cdot y + f_i) +F_i(a_i x + b_i y + c_i, d_i x + e_i y + f_i) $$ import transformSource from "!!raw-loader!../src/transform" @@ -102,8 +102,7 @@ c &= 0.5 \\ d &= 0 \\ e &= 1 \\ f &= 1.5 \\ -F_{shift}(x,y) &= (1 \cdot x + 0 \cdot y + 0.5, 0 \cdot x + 1 \cdot y + 0.5) \\ -F_{shift}(x, y) &= (x + 0.5, y + 1.5) +F_{shift}(x, y) &= (1 \cdot x + 0.5, 1 \cdot y + 1.5) \end{align*} $$ @@ -155,7 +154,7 @@ explaining the mathematics of iterated function systems: > of finite compositions $F_{i_1...i_p}$ of members of $F$. :::note -I've tweaked the wording slightly to match the conventions of the Fractal Flame paper +I've tweaked the conventions of that paper slightly to match the Fractal Flame paper ::: Before your eyes glaze over, let's unpack this: @@ -174,15 +173,15 @@ Thus, by applying the functions to fixed points of our system, we will find the ...then there are some extra details I've glossed over so far. First, the Hutchinson paper requires that the functions $F_i$ be _contractive_ for the solution set to exist. - That is, applying the function to a point must bring it closer to other points. However, as the Fractal Flame + That is, applying the function to a point must bring it closer to other points. However, as the fractal flame algorithm demonstrates, we only need functions to be contractive _on average_. At worst, the system will degenerate and produce a bad image. - Second, we're focused $\mathbb{R}^2$ because we're generating images, but the Hutchinson paper + Second, we're focused on $\mathbb{R}^2$ because we're generating images, but the Hutchinson paper allows for arbitrary dimensions; you could also have 3-dimensional fractal flames. Finally, there's a close relationship between fractal flames and [attractors](https://en.wikipedia.org/wiki/Attractor). - Specifically, the fixed points of $S$ act as attractors for the chaos game (explained in detail below). + Specifically, the fixed points of $S$ act as attractors for the chaos game (explained in more detail below).
    This is still a bit vague, so let's work through an example. @@ -272,8 +271,8 @@ import chaosGameSource from '!!raw-loader!./chaosGame' The image here is slightly different than in the paper. - I think the paper has an error, so I'm choosing to plot the image - the same way as the [reference implementation](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L440-L441). + I think the paper has an error, so I'm plotting the image + like the [reference implementation](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L440-L441). ### Weights @@ -292,7 +291,10 @@ import chaosGameWeightedSource from "!!raw-loader!./chaosGameWeighted"; For Sierpinski's Gasket, we start with equal weighting, but changing the transform weights affects how often -the chaos game "visits" parts of the image: +the chaos game "visits" parts of the image. If the chaos +were to run forever, we'd get the same image; +but because the iteration count is limited, +some parts may be missing below. :::tip Double-click the image if you want to save a copy! diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts index ef386f5..6db267d 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts +++ b/blog/2024-11-15-playing-with-fire/1-introduction/plot.ts @@ -1,10 +1,11 @@ // hidden-start -import {camera} from "./cameraGasket" +import { camera } from "./cameraGasket"; + // hidden-end function imageIndex( - width: number, x: number, - y: number + y: number, + width: number ) { return y * (width * 4) + x * 4; } @@ -14,24 +15,26 @@ export function plot( y: number, img: ImageData ) { - let [pixelX, pixelY] = camera(img.width, x, y); + let [pixelX, pixelY] = + camera(x, y, img.width); + + // Skip coordinates outside the display + if ( + pixelX < 0 || + pixelX >= img.width || + pixelY < 0 || + pixelY >= img.height + ) + return; const i = imageIndex( - img.width, pixelX, - pixelY + pixelY, + img.width ); - // Skip pixels outside the display range - if ( - i < 0 || - i > img.data.length - ) { - return; - } - - // Set the pixel to black by writing 0 - // to the first three elements at the index + // Set the pixel to black by setting + // the first three elements to 0 // (red, green, and blue, respectively), // and 255 to the last element (alpha) img.data[i] = 0; diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx b/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx index dc05043..4adee1d 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/scope.tsx @@ -1,12 +1,12 @@ import Gasket from "./Gasket"; -import { plot } from './plot'; -import { randomBiUnit } from '../src/randomBiUnit'; -import { randomInteger } from '../src/randomInteger'; +import { plot } from "./plot"; +import { randomBiUnit } from "../src/randomBiUnit"; +import { randomInteger } from "../src/randomInteger"; const Scope = { - Gasket, - plot, - randomBiUnit, - randomInteger, -} + Gasket, + plot, + randomBiUnit, + randomInteger +}; export default Scope; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx index fc4d782..77e0abd 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx @@ -1,51 +1,52 @@ import TeX from "@matejmazur/react-katex"; -import {Coefs} from "../src/coefs"; +import { Coefs } from "../src/transform"; import styles from "../src/css/styles.module.css"; export interface Props { - title: String; - isPost: boolean; - coefs: Coefs; - setCoefs: (coefs: Coefs) => void; - resetCoefs: () => void; + title: String; + isPost: boolean; + coefs: Coefs; + setCoefs: (coefs: Coefs) => void; + resetCoefs: () => void; } -export const CoefEditor = ({title, isPost, coefs, setCoefs, resetCoefs}: Props) => { - const resetButton = - return ( -
    -

    {title} {resetButton}

    -
    -

    {isPost ? \alpha : 'a'}: {coefs.a}

    - setCoefs({...coefs, a: Number(e.currentTarget.value)})}/> -
    -
    -

    {isPost ? \beta : 'b'}: {coefs.b}

    - setCoefs({...coefs, b: Number(e.currentTarget.value)})}/> -
    -
    -

    {isPost ? \gamma : 'c'}: {coefs.c}

    - setCoefs({...coefs, c: Number(e.currentTarget.value)})}/> -
    -
    -

    {isPost ? \delta : 'd'}: {coefs.d}

    - setCoefs({...coefs, d: Number(e.currentTarget.value)})}/> -
    -
    -

    {isPost ? \epsilon : 'e'}: {coefs.e}

    - setCoefs({...coefs, e: Number(e.currentTarget.value)})}/> -
    -
    -

    {isPost ? \zeta : 'f'}: {coefs.f}

    - setCoefs({...coefs, f: Number(e.currentTarget.value)})}/> -
    -
    - ) -} \ No newline at end of file +export const CoefEditor = ({ title, isPost, coefs, setCoefs, resetCoefs }: Props) => { + const resetButton = ; + + return ( +
    +

    {title} {resetButton}

    +
    +

    {isPost ? \alpha : "a"}: {coefs.a}

    + setCoefs({ ...coefs, a: Number(e.currentTarget.value) })} /> +
    +
    +

    {isPost ? \beta : "b"}: {coefs.b}

    + setCoefs({ ...coefs, b: Number(e.currentTarget.value) })} /> +
    +
    +

    {isPost ? \gamma : "c"}: {coefs.c}

    + setCoefs({ ...coefs, c: Number(e.currentTarget.value) })} /> +
    +
    +

    {isPost ? \delta : "d"}: {coefs.d}

    + setCoefs({ ...coefs, d: Number(e.currentTarget.value) })} /> +
    +
    +

    {isPost ? \epsilon : "e"}: {coefs.e}

    + setCoefs({ ...coefs, e: Number(e.currentTarget.value) })} /> +
    +
    +

    {isPost ? \zeta : "f"}: {coefs.f}

    + setCoefs({ ...coefs, f: Number(e.currentTarget.value) })} /> +
    +
    + ); +}; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx index 03d83a2..6d2a7d0 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx @@ -1,68 +1,68 @@ -import {useContext, useEffect, useState} from "react"; -import {Transform} from "../src/transform"; -import * as params from "../src/params" -import {PainterContext} from "../src/Canvas" -import {chaosGameFinal} from "./chaosGameFinal" -import {VariationEditor, VariationProps} from "./VariationEditor" -import {applyTransform} from "../src/applyTransform"; -import {buildBlend} from "./buildBlend"; +import { useContext, useEffect, useState } from "react"; +import { Transform } from "../src/transform"; +import * as params from "../src/params"; +import { PainterContext } from "../src/Canvas"; +import { chaosGameFinal } from "./chaosGameFinal"; +import { VariationEditor, VariationProps } from "./VariationEditor"; +import { applyTransform } from "../src/applyTransform"; +import { buildBlend } from "./buildBlend"; export default function FlameBlend() { - const {width, height, setPainter} = useContext(PainterContext); + const { width, height, setPainter } = useContext(PainterContext); - const xform1VariationsDefault: VariationProps = { - linear: 0, - julia: 1, - popcorn: 0, - pdj: 0, - } - const [xform1Variations, setXform1Variations] = useState(xform1VariationsDefault) - const resetXform1Variations = () => setXform1Variations(xform1VariationsDefault); + const xform1VariationsDefault: VariationProps = { + linear: 0, + julia: 1, + popcorn: 0, + pdj: 0 + }; + const [xform1Variations, setXform1Variations] = useState(xform1VariationsDefault); + const resetXform1Variations = () => setXform1Variations(xform1VariationsDefault); - const xform2VariationsDefault: VariationProps = { - linear: 1, - julia: 0, - popcorn: 1, - pdj: 0 - } - const [xform2Variations, setXform2Variations] = useState(xform2VariationsDefault) - const resetXform2Variations = () => setXform2Variations(xform2VariationsDefault); + const xform2VariationsDefault: VariationProps = { + linear: 1, + julia: 0, + popcorn: 1, + pdj: 0 + }; + const [xform2Variations, setXform2Variations] = useState(xform2VariationsDefault); + const resetXform2Variations = () => setXform2Variations(xform2VariationsDefault); - const xform3VariationsDefault: VariationProps = { - linear: 0, - julia: 0, - popcorn: 0, - pdj: 1 - } - const [xform3Variations, setXform3Variations] = useState(xform3VariationsDefault) - const resetXform3Variations = () => setXform3Variations(xform3VariationsDefault); + const xform3VariationsDefault: VariationProps = { + linear: 0, + julia: 0, + popcorn: 0, + pdj: 1 + }; + const [xform3Variations, setXform3Variations] = useState(xform3VariationsDefault); + const resetXform3Variations = () => setXform3Variations(xform3VariationsDefault); - const identityXform: Transform = (x, y) => [x, y]; + const identityXform: Transform = (x, y) => [x, y]; - useEffect(() => { - const transforms: [number, Transform][] = [ - [params.xform1Weight, applyTransform(params.xform1Coefs, buildBlend(params.xform1Coefs, xform1Variations))], - [params.xform2Weight, applyTransform(params.xform2Coefs, buildBlend(params.xform2Coefs, xform2Variations))], - [params.xform3Weight, applyTransform(params.xform3Coefs, buildBlend(params.xform3Coefs, xform3Variations))] - ] + useEffect(() => { + const transforms: [number, Transform][] = [ + [params.xform1Weight, applyTransform(params.xform1Coefs, buildBlend(params.xform1Coefs, xform1Variations))], + [params.xform2Weight, applyTransform(params.xform2Coefs, buildBlend(params.xform2Coefs, xform2Variations))], + [params.xform3Weight, applyTransform(params.xform3Coefs, buildBlend(params.xform3Coefs, xform3Variations))] + ]; - const gameParams = { - width, - height, - transforms, - final: identityXform - } - setPainter(chaosGameFinal(gameParams)); - }, [xform1Variations, xform2Variations, xform3Variations]); + const gameParams = { + width, + height, + transforms, + final: identityXform + }; + setPainter(chaosGameFinal(gameParams)); + }, [xform1Variations, xform2Variations, xform3Variations]); - return ( - <> - - - - - ) + return ( + <> + + + + + ); } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx index 76b2ecb..530243b 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx @@ -1,46 +1,46 @@ -import {useContext, useEffect, useState} from "react"; -import {Coefs} from "../src/coefs" +import { useContext, useEffect, useState } from "react"; +import { Coefs } from "../src/transform"; import * as params from "../src/params"; -import {PainterContext} from "../src/Canvas" -import {buildBlend} from "./buildBlend"; -import {chaosGameFinal} from "./chaosGameFinal" -import {VariationEditor, VariationProps} from "./VariationEditor"; -import {CoefEditor} from "./CoefEditor"; -import {applyPost, applyTransform} from "../src/applyTransform"; +import { PainterContext } from "../src/Canvas"; +import { buildBlend } from "./buildBlend"; +import { chaosGameFinal } from "./chaosGameFinal"; +import { VariationEditor, VariationProps } from "./VariationEditor"; +import { CoefEditor } from "./CoefEditor"; +import { applyPost, applyTransform } from "../src/applyTransform"; export default function FlameFinal() { - const {width, height, setPainter} = useContext(PainterContext); + const { width, height, setPainter } = useContext(PainterContext); - const [xformFinalCoefs, setXformFinalCoefs] = useState(params.xformFinalCoefs); - const resetXformFinalCoefs = () => setXformFinalCoefs(params.xformFinalCoefs); + const [xformFinalCoefs, setXformFinalCoefs] = useState(params.xformFinalCoefs); + const resetXformFinalCoefs = () => setXformFinalCoefs(params.xformFinalCoefs); - const xformFinalVariationsDefault: VariationProps = { - linear: 0, - julia: 1, - popcorn: 0, - pdj: 0 - } - const [xformFinalVariations, setXformFinalVariations] = useState(xformFinalVariationsDefault); - const resetXformFinalVariations = () => setXformFinalVariations(xformFinalVariationsDefault); + const xformFinalVariationsDefault: VariationProps = { + linear: 0, + julia: 1, + popcorn: 0, + pdj: 0 + }; + const [xformFinalVariations, setXformFinalVariations] = useState(xformFinalVariationsDefault); + const resetXformFinalVariations = () => setXformFinalVariations(xformFinalVariationsDefault); - const [xformFinalCoefsPost, setXformFinalCoefsPost] = useState(params.xformFinalCoefsPost); - const resetXformFinalCoefsPost = () => setXformFinalCoefsPost(params.xformFinalCoefsPost); + const [xformFinalCoefsPost, setXformFinalCoefsPost] = useState(params.xformFinalCoefsPost); + const resetXformFinalCoefsPost = () => setXformFinalCoefsPost(params.xformFinalCoefsPost); - useEffect(() => { - const finalBlend = buildBlend(xformFinalCoefs, xformFinalVariations); - const finalXform = applyPost(xformFinalCoefsPost, applyTransform(xformFinalCoefs, finalBlend)); + useEffect(() => { + const finalBlend = buildBlend(xformFinalCoefs, xformFinalVariations); + const finalXform = applyPost(xformFinalCoefsPost, applyTransform(xformFinalCoefs, finalBlend)); - setPainter(chaosGameFinal({width, height, transforms: params.xforms, final: finalXform})); - }, [xformFinalCoefs, xformFinalVariations, xformFinalCoefsPost]); + setPainter(chaosGameFinal({ width, height, transforms: params.xforms, final: finalXform })); + }, [xformFinalCoefs, xformFinalVariations, xformFinalCoefsPost]); - return ( - <> - - - - - ) + return ( + <> + + + + + ); } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx index 7402383..ef767f9 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx @@ -1,46 +1,46 @@ -import {useContext, useEffect, useState} from "react"; -import {Coefs} from "../src/coefs" -import {Transform} from "../src/transform"; +import { useContext, useEffect, useState } from "react"; +import { applyTransform } from "../src/applyTransform"; +import { Coefs, Transform } from "../src/transform"; import * as params from "../src/params"; -import {PainterContext} from "../src/Canvas" -import {chaosGameFinal, Props as ChaosGameFinalProps} from "./chaosGameFinal" -import {CoefEditor} from "./CoefEditor" -import {applyPost, applyTransform} from "@site/blog/2024-11-15-playing-with-fire/src/applyTransform"; +import { PainterContext } from "../src/Canvas"; +import { chaosGameFinal, Props as ChaosGameFinalProps } from "./chaosGameFinal"; +import { CoefEditor } from "./CoefEditor"; +import { transformPost } from "./post"; export default function FlamePost() { - const {width, height, setPainter} = useContext(PainterContext); + const { width, height, setPainter } = useContext(PainterContext); - const [xform1CoefsPost, setXform1CoefsPost] = useState(params.xform1CoefsPost); - const resetXform1CoefsPost = () => setXform1CoefsPost(params.xform1CoefsPost); + const [xform1CoefsPost, setXform1CoefsPost] = useState(params.xform1CoefsPost); + const resetXform1CoefsPost = () => setXform1CoefsPost(params.xform1CoefsPost); - const [xform2CoefsPost, setXform2CoefsPost] = useState(params.xform2CoefsPost); - const resetXform2CoefsPost = () => setXform2CoefsPost(params.xform2CoefsPost); + const [xform2CoefsPost, setXform2CoefsPost] = useState(params.xform2CoefsPost); + const resetXform2CoefsPost = () => setXform2CoefsPost(params.xform2CoefsPost); - const [xform3CoefsPost, setXform3CoefsPost] = useState(params.xform3CoefsPost); - const resetXform3CoefsPost = () => setXform3CoefsPost(params.xform3CoefsPost); + const [xform3CoefsPost, setXform3CoefsPost] = useState(params.xform3CoefsPost); + const resetXform3CoefsPost = () => setXform3CoefsPost(params.xform3CoefsPost); - const identityXform: Transform = (x, y) => [x, y]; + const identityXform: Transform = (x, y) => [x, y]; - const gameParams: ChaosGameFinalProps = { - width, - height, - transforms: [ - [params.xform1Weight, applyPost(xform1CoefsPost, applyTransform(params.xform1Coefs, params.xform1Variations))], - [params.xform2Weight, applyPost(xform2CoefsPost, applyTransform(params.xform2Coefs, params.xform2Variations))], - [params.xform3Weight, applyPost(xform3CoefsPost, applyTransform(params.xform3Coefs, params.xform3Variations))], - ], - final: identityXform - } - useEffect(() => setPainter(chaosGameFinal(gameParams)), [xform1CoefsPost, xform2CoefsPost, xform3CoefsPost]); + const gameParams: ChaosGameFinalProps = { + width, + height, + transforms: [ + [params.xform1Weight, transformPost(applyTransform(params.xform1Coefs, params.xform1Variations), xform1CoefsPost)], + [params.xform2Weight, transformPost(applyTransform(params.xform2Coefs, params.xform2Variations), xform2CoefsPost)], + [params.xform3Weight, transformPost(applyTransform(params.xform3Coefs, params.xform3Variations), xform3CoefsPost)] + ], + final: identityXform + }; + useEffect(() => setPainter(chaosGameFinal(gameParams)), [xform1CoefsPost, xform2CoefsPost, xform3CoefsPost]); - return ( - <> - - - - - ) + return ( + <> + + + + + ); } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx b/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx index 57a3159..62289b3 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx @@ -1,45 +1,45 @@ -import styles from "../src/css/styles.module.css" +import styles from "../src/css/styles.module.css"; export interface VariationProps { - linear: number; - julia: number; - popcorn: number; - pdj: number; + linear: number; + julia: number; + popcorn: number; + pdj: number; } export interface Props { - title: String; - variations: VariationProps; - setVariations: (variations: VariationProps) => void; - resetVariations: () => void; + title: String; + variations: VariationProps; + setVariations: (variations: VariationProps) => void; + resetVariations: () => void; } -export const VariationEditor = ({title, variations, setVariations, resetVariations}: Props) => { - const resetButton = +export const VariationEditor = ({ title, variations, setVariations, resetVariations }: Props) => { + const resetButton = ; - return ( -
    -

    {title} {resetButton}

    -
    - Linear: {variations.linear} - setVariations({...variations, linear: Number(e.currentTarget.value)})}/> -
    -
    - Julia: {variations.julia} - setVariations({...variations, julia: Number(e.currentTarget.value)})}/> -
    -
    - Popcorn: {variations.popcorn} - setVariations({...variations, popcorn: Number(e.currentTarget.value)})}/> -
    -
    - PDJ: {variations.pdj} - setVariations({...variations, pdj: Number(e.currentTarget.value)})}/> -
    -
    - ) -} \ No newline at end of file + return ( +
    +

    {title} {resetButton}

    +
    + Linear: {variations.linear} + setVariations({ ...variations, linear: Number(e.currentTarget.value) })} /> +
    +
    + Julia: {variations.julia} + setVariations({ ...variations, julia: Number(e.currentTarget.value) })} /> +
    +
    + Popcorn: {variations.popcorn} + setVariations({ ...variations, popcorn: Number(e.currentTarget.value) })} /> +
    +
    + PDJ: {variations.pdj} + setVariations({ ...variations, pdj: Number(e.currentTarget.value) })} /> +
    +
    + ); +}; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/buildBlend.ts b/blog/2024-11-15-playing-with-fire/2-transforms/buildBlend.ts index c2398fd..155ddfb 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/buildBlend.ts +++ b/blog/2024-11-15-playing-with-fire/2-transforms/buildBlend.ts @@ -1,17 +1,17 @@ -import {Coefs} from "../src/coefs"; -import {VariationProps} from "./VariationEditor"; -import {linear} from "../src/linear"; -import {julia} from "../src/julia"; -import {popcorn} from "../src/popcorn"; -import {pdj} from "../src/pdj"; -import {pdjParams} from "../src/params"; -import {VariationBlend} from "../src/blend"; +import { Coefs } from "../src/transform"; +import { VariationProps } from "./VariationEditor"; +import { linear } from "../src/linear"; +import { julia } from "../src/julia"; +import { popcorn } from "../src/popcorn"; +import { pdj } from "../src/pdj"; +import { pdjParams } from "../src/params"; +import { Blend } from "../src/blend"; -export function buildBlend(coefs: Coefs, variations: VariationProps): VariationBlend { - return [ - [variations.linear, linear], - [variations.julia, julia], - [variations.popcorn, popcorn(coefs)], - [variations.pdj, pdj(pdjParams)] - ] +export function buildBlend(coefs: Coefs, variations: VariationProps): Blend { + return [ + [variations.linear, linear], + [variations.julia, julia], + [variations.popcorn, popcorn(coefs)], + [variations.pdj, pdj(pdjParams)] + ]; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts b/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts index caacae1..c653dee 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts +++ b/blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts @@ -1,37 +1,51 @@ // hidden-start import { randomBiUnit } from "../src/randomBiUnit"; import { randomChoice } from "../src/randomChoice"; -import { plotBinary as plot } from "../src/plotBinary" -import {Transform} from "../src/transform"; -import {Props as ChaosGameWeightedProps} from "../1-introduction/chaosGameWeighted"; +import { plotBinary as plot } from "../src/plotBinary"; +import { Transform } from "../src/transform"; +import { Props as WeightedProps } from "../1-introduction/chaosGameWeighted"; const quality = 0.5; const step = 1000; // hidden-end -export type Props = ChaosGameWeightedProps & { - final: Transform, +export type Props = WeightedProps & { + final: Transform, } -export function* chaosGameFinal({width, height, transforms, final}: Props) { - let image = new ImageData(width, height); - let [x, y] = [randomBiUnit(), randomBiUnit()]; - const iterations = width * height * quality; - for (let i = 0; i < iterations; i++) { - const [_, transform] = randomChoice(transforms); - [x, y] = transform(x, y); +export function* chaosGameFinal( + { + width, + height, + transforms, + final + }: Props +) { + let img = + new ImageData(width, height); + let [x, y] = [ + randomBiUnit(), + randomBiUnit() + ]; - // highlight-start - const [finalX, finalY] = final(x, y); - // highlight-end + const pixels = width * height; + const iterations = quality * pixels; + for (let i = 0; i < iterations; i++) { + const [_, transform] = + randomChoice(transforms); + [x, y] = transform(x, y); - if (i > 20) - // highlight-start - plot(finalX, finalY, image); - // highlight-end + // highlight-start + const [finalX, finalY] = final(x, y); + // highlight-end - if (i % step === 0) - yield image; - } + if (i > 20) + // highlight-start + plot(finalX, finalY, img); + // highlight-end - yield image; + if (i % step === 0) + yield img; + } + + yield img; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index d01750e..8c64c7a 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -34,7 +34,7 @@ This leads us to the first big innovation of the Fractal Flame algorithm: adding after the affine transform. These functions are called "variations": $$ -F_i(x, y) = V_j(a_i \cdot x + b_i \cdot y + c_i, d_i \cdot x + e_i \cdot y + f_i) +F_i(x, y) = V_j(a_i x + b_i y + c_i, d_i x + e_i y + f_i) $$ import variationSource from '!!raw-loader!../src/variation' @@ -96,7 +96,7 @@ Some variations rely on knowing the transform's affine coefficients; they're cal For the popcorn variation, we use $c$ and $f$: $$ -V_{17}(x,y) = (x + c \cdot \text{sin}(\text{tan }3y), y + f \cdot \text{sin}(\text{tan }3x)) +V_{17}(x,y) = (x + c\ \text{sin}(\text{tan }3y), y + f\ \text{sin}(\text{tan }3x)) $$ import popcornSrc from '!!raw-loader!../src/popcorn' @@ -109,8 +109,8 @@ Some variations have extra parameters; they're called "parametric variations." For the PDJ variation, there are four extra parameters we can choose: $$ -p_1 = \text{pdj.a} \hspace{0.2cm} p_2 = \text{pdj.b} \hspace{0.2cm} p_3 = \text{pdj.c} \hspace{0.2cm} p_4 = \text{pdj.d} \\ -V_{24} = (\text{sin}(p_1 \cdot y) - \text{cos}(p_2 \cdot x), \text{sin}(p_3 \cdot x) - \text{cos}(p_4 \cdot y)) +p_1 = \text{pdj.a} \hspace{0.1cm} p_2 = \text{pdj.b} \hspace{0.1cm} p_3 = \text{pdj.c} \hspace{0.1cm} p_4 = \text{pdj.d} \\ +V_{24} = (\text{sin}(p_1 y) - \text{cos}(p_2 x), \text{sin}(p_3 x) - \text{cos}(p_4 y)) $$ import pdjSrc from '!!raw-loader!../src/pdj' @@ -124,7 +124,7 @@ Each variation receives the same $x$ and $y$ inputs, and we add together each va We'll also give each variation a weight ($v_{ij}$) that changes how much it contributes to the result: $$ -F_i(x,y) = \sum_{j} v_{ij} V_j(a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i) +F_i(x,y) = \sum_{j} v_{ij} V_j(x, y) $$ The formula looks intimidating, but it's not hard to implement: diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/post.ts b/blog/2024-11-15-playing-with-fire/2-transforms/post.ts index b79ded1..c70c3d6 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/post.ts +++ b/blog/2024-11-15-playing-with-fire/2-transforms/post.ts @@ -1,7 +1,11 @@ // hidden-start -import {Coefs} from "../src/coefs"; -import {Transform} from "../src/transform"; -import {applyCoefs} from "../src/coefs"; +import { applyCoefs, Coefs, Transform } from "../src/transform"; // hidden-end -export const transformPost = (transform: Transform, coefs: Coefs): Transform => - (x, y) => applyCoefs(...transform(x, y), coefs) \ No newline at end of file +export const transformPost = ( + transform: Transform, + coefs: Coefs +): Transform => + (x, y) => { + [x, y] = transform(x, y); + return applyCoefs(x, y, coefs); + } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx index f6cc860..2040b0b 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameColor.tsx @@ -1,174 +1,181 @@ -import React, {useContext, useEffect, useMemo, useRef, useState} from "react"; +import React, { useContext, useEffect, useMemo, useRef, useState } from "react"; import * as params from "../src/params"; -import {PainterContext} from "../src/Canvas"; -import {colorFromPalette} from "./colorFromPalette"; -import {chaosGameColor, Props as ChaosGameColorProps, TransformColor} from "./chaosGameColor"; +import { PainterContext } from "../src/Canvas"; +import { colorFromPalette } from "./colorFromPalette"; +import { chaosGameColor, Props as ChaosGameColorProps, TransformColor } from "./chaosGameColor"; import styles from "../src/css/styles.module.css"; -import {histIndex} from "../src/camera"; -import {useColorMode} from "@docusaurus/theme-common"; +import { histIndex } from "../src/camera"; +import { useColorMode } from "@docusaurus/theme-common"; type PaletteBarProps = { - height: number; - palette: number[]; - children?: React.ReactNode; + height: number; + palette: number[]; + children?: React.ReactNode; } -export const PaletteBar: React.FC = ({height, palette, children}) => { - const sizingRef = useRef(null); - const [width, setWidth] = useState(0); - useEffect(() => { - if (sizingRef) { - setWidth(sizingRef.current.offsetWidth); - } - }, [sizingRef]); +export const PaletteBar: React.FC = ({ height, palette, children }) => { + const sizingRef = useRef(null); + const [width, setWidth] = useState(0); + useEffect(() => { + if (sizingRef) { + setWidth(sizingRef.current.offsetWidth); + } + }, [sizingRef]); - const canvasRef = useRef(null); - const paletteImage = useMemo(() => { - if (width === 0) { - return; - } + const canvasRef = useRef(null); + const paletteImage = useMemo(() => { + if (width === 0) { + return; + } - const image = new ImageData(width, height); - for (let x = 0; x < width; x++) { - const colorIndex = x / width; - const [r, g, b] = colorFromPalette(palette, colorIndex); + const image = new ImageData(width, height); + for (let x = 0; x < width; x++) { + const colorIndex = x / width; + const [r, g, b] = colorFromPalette(palette, colorIndex); - for (let y = 0; y < height; y++) { - const pixelIndex = histIndex(x, y, width, 4); - image.data[pixelIndex] = r * 0xff; - image.data[pixelIndex + 1] = g * 0xff; - image.data[pixelIndex + 2] = b * 0xff; - image.data[pixelIndex + 3] = 0xff; - } - } + for (let y = 0; y < height; y++) { + const pixelIndex = histIndex(x, y, width, 4); + image.data[pixelIndex] = r * 0xff; + image.data[pixelIndex + 1] = g * 0xff; + image.data[pixelIndex + 2] = b * 0xff; + image.data[pixelIndex + 3] = 0xff; + } + } - return image; - }, [width, height, palette]); + return image; + }, [width, height, palette]); - useEffect(() => { - if (canvasRef && paletteImage) { - canvasRef.current.getContext("2d").putImageData(paletteImage, 0, 0); - } - }, [canvasRef, paletteImage]); + useEffect(() => { + if (canvasRef && paletteImage) { + canvasRef.current.getContext("2d").putImageData(paletteImage, 0, 0); + } + }, [canvasRef, paletteImage]); - const canvasStyle = {filter: useColorMode().colorMode === 'dark' ? 'invert(1)' : ''}; + const canvasStyle = { filter: useColorMode().colorMode === "dark" ? "invert(1)" : "" }; - return ( - <> -
    - {width > 0 ? : null} -
    - {children} - - ) -} + return ( + <> +
    + {width > 0 ? : null} +
    + {children} + + ); +}; type ColorEditorProps = { - title: string; - palette: number[]; - transformColor: TransformColor; - setTransformColor: (transformColor: TransformColor) => void; - resetTransformColor: () => void; - children?: React.ReactNode; + title: string; + palette: number[]; + transformColor: TransformColor; + setTransformColor: (transformColor: TransformColor) => void; + resetTransformColor: () => void; + children?: React.ReactNode; } -const ColorEditor: React.FC = ({title, palette, transformColor, setTransformColor, resetTransformColor, children}) => { - const resetButton = +const ColorEditor: React.FC = ( + { + title, + palette, + transformColor, + setTransformColor, + resetTransformColor, + children + }) => { + const resetButton = ; - const [r, g, b] = colorFromPalette(palette, transformColor.color); - const colorCss = `rgb(${Math.floor(r * 0xff)},${Math.floor(g * 0xff)},${Math.floor(b * 0xff)})`; + const [r, g, b] = colorFromPalette(palette, transformColor.color); + const colorCss = `rgb(${Math.floor(r * 0xff)},${Math.floor(g * 0xff)},${Math.floor(b * 0xff)})`; - const {colorMode} = useColorMode(); + const { colorMode } = useColorMode(); - return ( - <> -
    -

    {title} {resetButton}

    -
    -

    Color: {transformColor.color}

    - setTransformColor({...transformColor, color: Number(e.currentTarget.value)})}/> -
    -
    -

    Speed: {transformColor.colorSpeed}

    - setTransformColor({...transformColor, colorSpeed: Number(e.currentTarget.value)})}/> -
    -
    -
    - {children} - - ) -} + return ( + <> +
    +

    {title} {resetButton}

    +
    +

    Color: {transformColor.color}

    + setTransformColor({ ...transformColor, color: Number(e.currentTarget.value) })} /> +
    +
    +

    Speed: {transformColor.colorSpeed}

    + setTransformColor({ ...transformColor, colorSpeed: Number(e.currentTarget.value) })} /> +
    +
    +
    + {children} + + ); +}; type Props = { - quality?: number; - children?: React.ReactElement; + children?: React.ReactElement; } -export default function FlameColor({quality, children}: Props) { - const {width, height, setPainter} = useContext(PainterContext); +export default function FlameColor({ children }: Props) { + const { width, height, setPainter } = useContext(PainterContext); - const xform1ColorDefault: TransformColor = {color: params.xform1Color, colorSpeed: 0.5}; - const [xform1Color, setXform1Color] = useState(xform1ColorDefault); - const resetXform1Color = () => setXform1Color(xform1ColorDefault); + const xform1ColorDefault: TransformColor = { color: params.xform1Color, colorSpeed: 0.5 }; + const [xform1Color, setXform1Color] = useState(xform1ColorDefault); + const resetXform1Color = () => setXform1Color(xform1ColorDefault); - const xform2ColorDefault: TransformColor = {color: params.xform2Color, colorSpeed: 0.5}; - const [xform2Color, setXform2Color] = useState(xform2ColorDefault); - const resetXform2Color = () => setXform2Color(xform2ColorDefault); + const xform2ColorDefault: TransformColor = { color: params.xform2Color, colorSpeed: 0.5 }; + const [xform2Color, setXform2Color] = useState(xform2ColorDefault); + const resetXform2Color = () => setXform2Color(xform2ColorDefault); - const xform3ColorDefault: TransformColor = {color: params.xform3Color, colorSpeed: 0.5}; - const [xform3Color, setXform3Color] = useState(xform3ColorDefault); - const resetXform3Color = () => setXform3Color(xform3ColorDefault); + const xform3ColorDefault: TransformColor = { color: params.xform3Color, colorSpeed: 0.5 }; + const [xform3Color, setXform3Color] = useState(xform3ColorDefault); + const resetXform3Color = () => setXform3Color(xform3ColorDefault); - const xformFinalColorDefault: TransformColor = {color: params.xformFinalColor, colorSpeed: 0}; - const [xformFinalColor, setXformFinalColor] = useState(xformFinalColorDefault); - const resetXformFinalColor = () => setXformFinalColor(xformFinalColorDefault); + const xformFinalColorDefault: TransformColor = { color: params.xformFinalColor, colorSpeed: 0 }; + const [xformFinalColor, setXformFinalColor] = useState(xformFinalColorDefault); + const resetXformFinalColor = () => setXformFinalColor(xformFinalColorDefault); - useEffect(() => { - const gameParams: ChaosGameColorProps = { - width, - height, - transforms: params.xforms, - final: params.xformFinal, - palette: params.palette, - colors: [xform1Color, xform2Color, xform3Color], - finalColor: xformFinalColor - } - setPainter(chaosGameColor(gameParams)); - }, [xform1Color, xform2Color, xform3Color, xformFinalColor]); + useEffect(() => { + const gameParams: ChaosGameColorProps = { + width, + height, + transforms: params.xforms, + final: params.xformFinal, + palette: params.palette, + colors: [xform1Color, xform2Color, xform3Color], + finalColor: xformFinalColor + }; + setPainter(chaosGameColor(gameParams)); + }, [xform1Color, xform2Color, xform3Color, xformFinalColor]); - return ( - <> - - - - - - {children} - - ); + return ( + <> + + + + + + {children} + + ); } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx b/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx index 3ac3a86..c7c854c 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/FlameHistogram.tsx @@ -1,25 +1,25 @@ -import React, {useContext, useEffect} from "react"; -import {xforms as transforms, xformFinal as final} from "../src/params"; -import {PainterContext} from "../src/Canvas"; -import {chaosGameHistogram} from "./chaosGameHistogram"; +import React, { useContext, useEffect } from "react"; +import { xformFinal as final, xforms as transforms } from "../src/params"; +import { PainterContext } from "../src/Canvas"; +import { chaosGameHistogram } from "./chaosGameHistogram"; type Props = { - paint: (width: number, height: number, histogram: number[]) => ImageData; - children?: React.ReactElement; + paint: (width: number, height: number, histogram: number[]) => ImageData; + children?: React.ReactElement; } -export default function FlameHistogram({paint, children}: Props) { - const {width, height, setPainter} = useContext(PainterContext); +export default function FlameHistogram({ paint, children }: Props) { + const { width, height, setPainter } = useContext(PainterContext); - useEffect(() => { - const gameParams = { - width, - height, - transforms, - final, - paint - } - setPainter(chaosGameHistogram(gameParams)); - }, [width, height]); + useEffect(() => { + const gameParams = { + width, + height, + transforms, + final, + paint + }; + setPainter(chaosGameHistogram(gameParams)); + }, [width, height]); - return children; + return children; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts index 4b75409..76f6f5c 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameColor.ts @@ -1,64 +1,135 @@ // hidden-start -import {Props as ChaosGameFinalProps} from "../2-transforms/chaosGameFinal"; -import {randomBiUnit} from "../src/randomBiUnit"; -import {randomChoice} from "../src/randomChoice"; -import {camera, histIndex} from "../src/camera"; -import {colorFromPalette} from "./colorFromPalette"; -import {mixColor} from "./mixColor"; -import {paintColor} from "./paintColor"; +import { Props as ChaosGameFinalProps } from "../2-transforms/chaosGameFinal"; +import { randomBiUnit } from "../src/randomBiUnit"; +import { randomChoice } from "../src/randomChoice"; +import { camera, histIndex } from "../src/camera"; +import { colorFromPalette } from "./colorFromPalette"; +import { mixColor } from "./mixColor"; +import { paintColor } from "./paintColor"; const quality = 15; const step = 100_000; // hidden-end export type TransformColor = { - color: number; - colorSpeed: number; + color: number; + colorSpeed: number; } export type Props = ChaosGameFinalProps & { - palette: number[]; - colors: TransformColor[]; - finalColor: TransformColor; + palette: number[]; + colors: TransformColor[]; + finalColor: TransformColor; } -export function* chaosGameColor({width, height, transforms, final, palette, colors, finalColor}: Props) { - const imgRed = Array(width * height).fill(0); - const imgGreen = Array(width * height).fill(0); - const imgBlue = Array(width * height).fill(0); - const imgAlpha = Array(width * height).fill(0); - let [x, y] = [randomBiUnit(), randomBiUnit()]; - let c = Math.random(); +export function* chaosGameColor( + { + width, + height, + transforms, + final, + palette, + colors, + finalColor + }: Props +) { + const pixels = width * height; - const iterations = width * height * quality; - for (let i = 0; i < iterations; i++) { - const [transformIndex, transform] = randomChoice(transforms); - [x, y] = transform(x, y); + // highlight-start + const imgRed = Array(pixels) + .fill(0); + const imgGreen = Array(pixels) + .fill(0); + const imgBlue = Array(pixels) + .fill(0); + const imgAlpha = Array(pixels) + .fill(0); - // highlight-start - const transformColor = colors[transformIndex]; - c = mixColor(c, transformColor.color, transformColor.colorSpeed); - // highlight-end + const plotColor = ( + x: number, + y: number, + c: number + ) => { + const [pixelX, pixelY] = + camera(x, y, width); - const [finalX, finalY] = final(x, y); + if ( + pixelX < 0 || + pixelX >= width || + pixelY < 0 || + pixelY >= width + ) + return; - if (i > 20) { - const [pixelX, pixelY] = camera(finalX, finalY, width); - const pixelIndex = histIndex(pixelX, pixelY, width, 1); + const hIndex = + histIndex(pixelX, pixelY, width, 1); - if (pixelIndex < 0 || pixelIndex >= imgAlpha.length) - continue; + const [r, g, b] = + colorFromPalette(palette, c); - const colorFinal = mixColor(c, finalColor.color, finalColor.colorSpeed); - const [r, g, b] = colorFromPalette(palette, colorFinal); - imgRed[pixelIndex] += r; - imgGreen[pixelIndex] += g; - imgBlue[pixelIndex] += b; - imgAlpha[pixelIndex] += 1; - } + imgRed[hIndex] += r; + imgGreen[hIndex] += g; + imgBlue[hIndex] += b; + imgAlpha[hIndex] += 1; + } + // highlight-end - if (i % step === 0) - yield paintColor(width, height, imgRed, imgGreen, imgBlue, imgAlpha); - } + let [x, y] = [ + randomBiUnit(), + randomBiUnit() + ]; + let c = Math.random(); - yield paintColor(width, height, imgRed, imgGreen, imgBlue, imgAlpha); + const iterations = quality * pixels; + for (let i = 0; i < iterations; i++) { + const [transformIndex, transform] = + randomChoice(transforms); + [x, y] = transform(x, y); + + // highlight-start + const transformColor = + colors[transformIndex]; + + c = mixColor( + c, + transformColor.color, + transformColor.colorSpeed + ); + // highlight-end + + const [finalX, finalY] = final(x, y); + + // highlight-start + const finalC = mixColor( + c, + finalColor.color, + finalColor.colorSpeed + ); + // highlight-end + + if (i > 20) + plotColor( + finalX, + finalY, + finalC + ) + + if (i % step === 0) + yield paintColor( + width, + height, + imgRed, + imgGreen, + imgBlue, + imgAlpha + ); + } + + yield paintColor( + width, + height, + imgRed, + imgGreen, + imgBlue, + imgAlpha + ); } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts index 0f122a4..66253c0 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/chaosGameHistogram.ts @@ -1,45 +1,78 @@ // hidden-start -import {randomBiUnit} from "../src/randomBiUnit"; -import {randomChoice} from "../src/randomChoice"; -import {Props as ChaosGameFinalProps} from "../2-transforms/chaosGameFinal"; -import {camera, histIndex} from "../src/camera"; +import { randomBiUnit } from "../src/randomBiUnit"; +import { randomChoice } from "../src/randomChoice"; +import { Props as ChaosGameFinalProps } from "../2-transforms/chaosGameFinal"; +import { camera, histIndex } from "../src/camera"; const quality = 10; const step = 100_000; // hidden-end -export type Props = ChaosGameFinalProps & { - paint: (width: number, height: number, histogram: number[]) => ImageData; +type Props = ChaosGameFinalProps & { + paint: ( + width: number, + height: number, + histogram: number[] + ) => ImageData; } -export function* chaosGameHistogram({width, height, transforms, final, paint}: Props) { - let iterations = quality * width * height; - // highlight-start - const histogram = Array(width * height).fill(0); - // highlight-end +export function* chaosGameHistogram( + { + width, + height, + transforms, + final, + paint + }: Props +) { + const pixels = width * height; + const iterations = quality * pixels; - let [x, y] = [randomBiUnit(), randomBiUnit()]; + // highlight-start + const hist = Array(pixels) + .fill(0); - for (let i = 0; i < iterations; i++) { - const [_, transform] = randomChoice(transforms); - [x, y] = transform(x, y); - const [finalX, finalY] = final(x, y); + const plotHist = ( + x: number, + y: number + ) => { + const [pixelX, pixelY] = + camera(x, y, width); - if (i > 20) { - // highlight-start - const [pixelX, pixelY] = camera(finalX, finalY, width); - const hIndex = histIndex(pixelX, pixelY, width, 1); + if ( + pixelX < 0 || + pixelX >= width || + pixelY < 0 || + pixelY >= height + ) + return; - if (hIndex < 0 || hIndex >= histogram.length) { - continue; - } + const hIndex = + histIndex(pixelX, pixelY, width, 1); - histogram[hIndex] += 1; - // highlight-end - } + hist[hIndex] += 1; + }; + // highlight-end - if (i % step === 0) - yield paint(width, height, histogram); + let [x, y] = [ + randomBiUnit(), + randomBiUnit() + ]; + + for (let i = 0; i < iterations; i++) { + const [_, transform] = + randomChoice(transforms); + [x, y] = transform(x, y); + const [finalX, finalY] = final(x, y); + + if (i > 20) { + // highlight-start + plotHist(finalX, finalY); + // highlight-end } - yield paint(width, height, histogram); + if (i % step === 0) + yield paint(width, height, hist); + } + + yield paint(width, height, hist); } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/colorFromPalette.ts b/blog/2024-11-15-playing-with-fire/3-log-density/colorFromPalette.ts index a039313..9dc66dc 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/colorFromPalette.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/colorFromPalette.ts @@ -1,4 +1,14 @@ -export function colorFromPalette(palette: number[], colorIndex: number): [number, number, number] { - const paletteIndex = Math.floor(colorIndex * (palette.length / 3)) * 3; - return [palette[paletteIndex], palette[paletteIndex + 1], palette[paletteIndex + 2]]; +export function colorFromPalette( + palette: number[], + colorIndex: number +): [number, number, number] { + const numColors = palette.length / 3; + const paletteIndex = Math.floor( + colorIndex * (numColors) + ) * 3; + return [ + palette[paletteIndex], // red + palette[paletteIndex + 1], // green + palette[paletteIndex + 2] // blue + ]; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index a9356ea..0254a4f 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -165,7 +165,7 @@ import colorFromPaletteSource from "!!raw-loader!./colorFromPalette";
    As an alternative... - ...you could also interpolate between colors in the palette. + ...you could interpolate between colors in the palette. For example, `flam3` uses [linear interpolation](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L483-L486)
    diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/mixColor.ts b/blog/2024-11-15-playing-with-fire/3-log-density/mixColor.ts index f27b175..d065103 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/mixColor.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/mixColor.ts @@ -1,3 +1,8 @@ -export function mixColor(color1: number, color2: number, colorSpeed: number) { - return color1 * (1 - colorSpeed) + color2 * colorSpeed; +export function mixColor( + color1: number, + color2: number, + colorSpeed: number +) { + return color1 * (1 - colorSpeed) + + color2 * colorSpeed; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/paintColor.ts b/blog/2024-11-15-playing-with-fire/3-log-density/paintColor.ts index 33b0470..650057e 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/paintColor.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/paintColor.ts @@ -1,25 +1,34 @@ -// hidden-start -import {colorFromPalette} from "./colorFromPalette"; -// hidden-end export function paintColor( - width: number, - height: number, - red: number[], - green: number[], - blue: number[], - alpha: number[] + width: number, + height: number, + red: number[], + green: number[], + blue: number[], + alpha: number[] ): ImageData { - const image = new ImageData(width, height); + const pixels = width * height; + const img = + new ImageData(width, height); - for (let i = 0; i < width * height; i++) { - const alphaScale = Math.log10(alpha[i]) / (alpha[i] * 1.5); + for (let i = 0; i < pixels; i++) { + const scale = + Math.log10(alpha[i]) / + (alpha[i] * 1.5); - const pixelIndex = i * 4; - image.data[pixelIndex] = red[i] * alphaScale * 0xff; - image.data[pixelIndex + 1] = green[i] * alphaScale * 0xff; - image.data[pixelIndex + 2] = blue[i] * alphaScale * 0xff; - image.data[pixelIndex + 3] = alpha[i] * alphaScale * 0xff; - } + const pixelIndex = i * 4; - return image; + const rVal = red[i] * scale * 0xff; + img.data[pixelIndex] = rVal; + + const gVal = green[i] * scale * 0xff; + img.data[pixelIndex + 1] = gVal; + + const bVal = blue[i] * scale * 0xff; + img.data[pixelIndex + 2] = bVal; + + const aVal = alpha[i] * scale * 0xff; + img.data[pixelIndex + 3] = aVal; + } + + return img; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/paintLinear.ts b/blog/2024-11-15-playing-with-fire/3-log-density/paintLinear.ts index 077b3a6..cd2527b 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/paintLinear.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/paintLinear.ts @@ -1,18 +1,26 @@ -export function paintLinear(width: number, height: number, histogram: number[]): ImageData { - const image = new ImageData(width, height); +export function paintLinear( + width: number, + height: number, + hist: number[] +) { + const img = + new ImageData(width, height); - let valueMax = 0; - for (let value of histogram) { - valueMax = Math.max(valueMax, value); - } + let hMax = 0; + for (let value of hist) { + hMax = Math.max(hMax, value); + } - for (let i = 0; i < histogram.length; i++) { - const pixelIndex = i * 4; - image.data[pixelIndex] = 0; - image.data[pixelIndex + 1] = 0; - image.data[pixelIndex + 2] = 0; - image.data[pixelIndex + 3] = histogram[i] / valueMax * 0xff; - } + for (let i = 0; i < hist.length; i++) { + const pixelIndex = i * 4; - return image; + img.data[pixelIndex] = 0; + img.data[pixelIndex + 1] = 0; + img.data[pixelIndex + 2] = 0; + + const alpha = hist[i] / hMax * 0xff; + img.data[pixelIndex + 3] = alpha; + } + + return img; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/paintLogarithmic.ts b/blog/2024-11-15-playing-with-fire/3-log-density/paintLogarithmic.ts index eacad34..93bf83f 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/paintLogarithmic.ts +++ b/blog/2024-11-15-playing-with-fire/3-log-density/paintLogarithmic.ts @@ -1,21 +1,29 @@ -export function paintLogarithmic(width: number, height: number, histogram: number[]): ImageData { - const image = new ImageData(width, height); +export function paintLogarithmic( + width: number, + height: number, + hist: number[] +) { + const img = + new ImageData(width, height); - const histogramLog: number[] = []; - histogram.forEach(value => histogramLog.push(Math.log(value))); + const histLog = hist.map(Math.log); - let histogramLogMax = -Infinity; - for (let value of histogramLog) { - histogramLogMax = Math.max(histogramLogMax, value); - } + let hLogMax = -Infinity; + for (let value of histLog) { + hLogMax = Math.max(hLogMax, value); + } - for (let i = 0; i < histogram.length; i++) { - const pixelIndex = i * 4; - image.data[pixelIndex] = 0; // red - image.data[pixelIndex + 1] = 0; // green - image.data[pixelIndex + 2] = 0; // blue - image.data[pixelIndex + 3] = histogramLog[i] / histogramLogMax * 0xff; - } + for (let i = 0; i < hist.length; i++) { + const pixelIndex = i * 4; - return image; + img.data[pixelIndex] = 0; // red + img.data[pixelIndex + 1] = 0; // green + img.data[pixelIndex + 2] = 0; // blue + + const alpha = + histLog[i] / hLogMax * 0xff; + img.data[pixelIndex + 3] = alpha; + } + + return img; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/params.flame b/blog/2024-11-15-playing-with-fire/params.flame index 6be89c4..61dac5a 100644 --- a/blog/2024-11-15-playing-with-fire/params.flame +++ b/blog/2024-11-15-playing-with-fire/params.flame @@ -1,8 +1,8 @@ - - + + 3130323635383B3A3D403F424644484B494D504E52565358 5B585D605D626562686B676D706C737571787B767D807B83 @@ -39,9 +39,9 @@ - + 3130323635383B3A3D403F424644484B494D504E52565358 5B585D605D626562686B676D706C737571787B767D807B83 @@ -78,9 +78,9 @@ - + 3130323635383B3A3D403F424644484B494D504E52565358 diff --git a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx index b7ea30c..155b982 100644 --- a/blog/2024-11-15-playing-with-fire/src/Canvas.tsx +++ b/blog/2024-11-15-playing-with-fire/src/Canvas.tsx @@ -11,7 +11,7 @@ export const PainterContext = createContext(null) const downloadImage = (name: string) => (e: MouseEvent) => { const link = document.createElement("a"); - link.download = "flame.png"; + link.download = `${name}.png`; link.href = (e.target as HTMLCanvasElement).toDataURL("image/png"); link.click(); } diff --git a/blog/2024-11-15-playing-with-fire/src/applyTransform.ts b/blog/2024-11-15-playing-with-fire/src/applyTransform.ts index 92b2165..a307d59 100644 --- a/blog/2024-11-15-playing-with-fire/src/applyTransform.ts +++ b/blog/2024-11-15-playing-with-fire/src/applyTransform.ts @@ -1,8 +1,8 @@ -import {Transform, Coefs, applyCoefs} from "./transform"; -import {blend, VariationBlend} from "./blend"; +import { applyCoefs, Coefs, Transform } from "./transform"; +import { blend, Blend } from "./blend"; -export const applyTransform = (coefs: Coefs, variations: VariationBlend): Transform => - (x, y) => blend(...applyCoefs(x, y, coefs), variations); +export const applyTransform = (coefs: Coefs, variations: Blend): Transform => + (x, y) => blend(...applyCoefs(x, y, coefs), variations) export const applyPost = (coefsPost: Coefs, transform: Transform): Transform => - (x, y) => applyCoefs(...transform(x, y), coefsPost); \ No newline at end of file + (x, y) => applyCoefs(...transform(x, y), coefsPost); \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/blend.ts b/blog/2024-11-15-playing-with-fire/src/blend.ts index d47f2cc..13692df 100644 --- a/blog/2024-11-15-playing-with-fire/src/blend.ts +++ b/blog/2024-11-15-playing-with-fire/src/blend.ts @@ -1,19 +1,20 @@ // hidden-start -import {Variation} from "./variation"; +import { Variation } from "./variation"; // hidden-end -export type VariationBlend = [number, Variation][]; +export type Blend = [number, Variation][]; + export function blend( - x: number, - y: number, - variations: VariationBlend + x: number, + y: number, + varFns: Blend ): [number, number] { - let [outX, outY] = [0, 0]; + let [outX, outY] = [0, 0]; - for (const [weight, variation] of variations) { - const [varX, varY] = variation(x, y); - outX += weight * varX; - outY += weight * varY; - } + for (const [weight, varFn] of varFns) { + const [varX, varY] = varFn(x, y); + outX += weight * varX; + outY += weight * varY; + } - return [outX, outY]; + return [outX, outY]; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/julia.ts b/blog/2024-11-15-playing-with-fire/src/julia.ts index cd0ede6..3d2508b 100644 --- a/blog/2024-11-15-playing-with-fire/src/julia.ts +++ b/blog/2024-11-15-playing-with-fire/src/julia.ts @@ -1,16 +1,21 @@ // hidden-start -import { Variation } from './variation' +import { Variation } from "./variation"; // hidden-end -export const julia: Variation = (x, y) => { - const r = Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2)); +const omega = + () => Math.random() > 0.5 ? 0 : Math.PI; + +export const julia: Variation = + (x, y) => { + const x2 = Math.pow(x, 2); + const y2 = Math.pow(y, 2); + const r = Math.sqrt(x2 + y2); const theta = Math.atan2(x, y); - const omega = Math.random() > 0.5 ? 0 : Math.PI; const sqrtR = Math.sqrt(r); - const thetaVal = theta / 2 + omega; + const thetaVal = theta / 2 + omega(); return [ - sqrtR * Math.cos(thetaVal), - sqrtR * Math.sin(thetaVal) - ] -} \ No newline at end of file + sqrtR * Math.cos(thetaVal), + sqrtR * Math.sin(thetaVal) + ]; + }; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/linear.ts b/blog/2024-11-15-playing-with-fire/src/linear.ts index 36b234a..3733d98 100644 --- a/blog/2024-11-15-playing-with-fire/src/linear.ts +++ b/blog/2024-11-15-playing-with-fire/src/linear.ts @@ -1,4 +1,5 @@ // hidden-start import {Variation} from "./variation" //hidden-end -export const linear: Variation = (x, y) => [x, y]; \ No newline at end of file +export const linear: Variation = + (x, y) => [x, y]; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/params.ts b/blog/2024-11-15-playing-with-fire/src/params.ts index 66098af..9f53aef 100644 --- a/blog/2024-11-15-playing-with-fire/src/params.ts +++ b/blog/2024-11-15-playing-with-fire/src/params.ts @@ -3,119 +3,118 @@ * translated into something that's easier to work with. */ -import { Coefs } from './coefs'; -import {VariationBlend} from "./blend"; -import { linear } from './linear' -import { julia } from './julia' -import { popcorn } from './popcorn' -import {pdj, PdjParams} from './pdj' -import {Transform} from "./transform"; -import {applyPost, applyTransform} from "./applyTransform"; +import { Blend } from "./blend"; +import { linear } from "./linear"; +import { julia } from "./julia"; +import { popcorn } from "./popcorn"; +import { pdj, PdjParams } from "./pdj"; +import { Coefs, Transform } from "./transform"; +import { applyPost, applyTransform } from "./applyTransform"; export const identityCoefs: Coefs = { - a: 1, b: 0, c: 0, - d: 0, e: 1, f: 0, -} + a: 1, b: 0, c: 0, + d: 0, e: 1, f: 0 +}; export const pdjParams: PdjParams = { - a: 1.09358, b: 2.13048, c: 2.54127, d: 2.37267 -} + a: 1.09358, b: 2.13048, c: 2.54127, d: 2.37267 +}; export const xform1Weight = 0.56453495; export const xform1Coefs = { - a: -1.381068, b: -1.381068, c: 0, - d: 1.381068, e: -1.381068, f: 0, -} + a: -1.381068, b: -1.381068, c: 0, + d: 1.381068, e: -1.381068, f: 0 +}; export const xform1CoefsPost = identityCoefs; -export const xform1Variations: VariationBlend = [ - [1, julia] -] +export const xform1Variations: Blend = [ + [1, julia] +]; export const xform1Color = 0; export const xform2Weight = 0.013135; export const xform2Coefs = { - a: 0.031393, b: 0.031367, c: 0, - d: -0.031367, e: 0.031393, f: 0, -} + a: 0.031393, b: 0.031367, c: 0, + d: -0.031367, e: 0.031393, f: 0 +}; export const xform2CoefsPost = { - a: 1, b: 0, c: 0.24, - d: 0, e: 1, f: 0.27, -} -export const xform2Variations: VariationBlend = [ - [1, linear], - [1, popcorn(xform2Coefs)] -] + a: 1, b: 0, c: 0.24, + d: 0, e: 1, f: 0.27 +}; +export const xform2Variations: Blend = [ + [1, linear], + [1, popcorn(xform2Coefs)] +]; export const xform2Color = 0.844; export const xform3Weight = 0.42233; export const xform3Coefs = { - a: 1.51523, b: -3.048677, c: 0.724135, - d: 0.740356, e: -1.455964, f: -0.362059, -} + a: 1.51523, b: -3.048677, c: 0.724135, + d: 0.740356, e: -1.455964, f: -0.362059 +}; export const xform3CoefsPost = identityCoefs; -export const xform3Variations: VariationBlend = [ - [1, pdj(pdjParams)] +export const xform3Variations: Blend = [ + [1, pdj(pdjParams)] ]; export const xform3Color = 0.349; export const xformFinalCoefs = { - a: 2, b: 0, c: 0, - d: 0, e: 2, f: 0 -} + a: 2, b: 0, c: 0, + d: 0, e: 2, f: 0 +}; export const xformFinalCoefsPost = identityCoefs; -export const xformFinalVariations: VariationBlend = [ - [1, julia] -] +export const xformFinalVariations: Blend = [ + [1, julia] +]; export const xformFinalColor = 0; export const xforms: [number, Transform][] = [ - [xform1Weight, applyPost(xform1CoefsPost, applyTransform(xform1Coefs, xform1Variations))], - [xform2Weight, applyPost(xform2CoefsPost, applyTransform(xform2Coefs, xform2Variations))], - [xform3Weight, applyPost(xform3CoefsPost, applyTransform(xform3Coefs, xform3Variations))], -] + [xform1Weight, applyPost(xform1CoefsPost, applyTransform(xform1Coefs, xform1Variations))], + [xform2Weight, applyPost(xform2CoefsPost, applyTransform(xform2Coefs, xform2Variations))], + [xform3Weight, applyPost(xform3CoefsPost, applyTransform(xform3Coefs, xform3Variations))] +]; export const xformFinal: Transform = applyPost(xformFinalCoefsPost, applyTransform(xformFinalCoefs, xformFinalVariations)); export const paletteString = - "3130323635383B3A3D403F424644484B494D504E52565358" + - "5B585D605D626562686B676D706C737571787B767D807B83" + - "8580888A858D908A93958F989A949DA099A3A59EA8AAA3AD" + - "AFA8B3B5ADB8BAB2BEBFB7C3C5BCC8CAC1CECFC6D3D4CBD8" + - "DAD0DEDFD5E3DFD2E0DFCEDDE0CBDAE0C8D7E0C4D3E0C1D0" + - "E1BECDE1BBCAE1B7C7E1B4C4E1B1C1E2ADBEE2AABAE2A7B7" + - "E2A3B4E2A0B1E39DAEE399ABE396A8E393A5E490A1E48C9E" + - "E4899BE48698E48295E57F92E57C8FE5788CE57589E57285" + - "E66E82E66B7FE6687CE66479E76176E75E73E75B70E7576C" + - "E75469E85166E84D63E84A60E4495EE0485CDC475BD84659" + - "D44557D04455CB4353C74252C34150BF404EBB3F4CB73E4B" + - "B33D49AF3C47AB3B45A73A43A339429F38409B373E97363C" + - "92353A8E34398A33378632358231337E30327A2F30762E2E" + - "722D2C6E2C2A6A2B29662A276229255E2823592721552620" + - "51251E4D241C49231A4522194121173D20153C1F153A1F14" + - "391E14381E14361D14351C13341C13321B13311B132F1A12" + - "2E19122D19122B18122A1811291711271611261611251510" + - "23151022141021140F1F130F1E120F1C120F1B110E1A110E" + - "18100E170F0E160F0D140E0D130E0D120D0D100C0C0F0C0C" + - "0E0B0C0C0B0C0B0A0B09090B08090B07080B05080A04070A" + - "0606090804090A03088C46728A457087446D85436B824369" + - "8042667D41647B4061793F5F763E5D743D5A713D586F3C56" + - "6C3B536A3A5168394F65384C63374A6037485E36455B3543" + - "59344057333E54323C5231394F31374D30354A2F32482E30" + - "462D2E432C2B412B293E2B273C2A2439292237281F35271D" + - "32261B3025182D25162B241428231126220F25210F24210E" + - "23200E221F0E221E0D211E0D201D0D1F1C0D1E1B0C1D1B0C" + - "1C1A0C1B190B1B180B1A180B19170A18160A17150A161509" + - "1514091413091413081312081211081110081010070F0F07" + - "0E0E070D0D060C0D060C0C060B0B050A0A05090A05080904" + - "070804060704050704050603040503030403020402010302" + - "0608070C0D0D1112121617171B1C1D2121222626272B2B2D" + "3130323635383B3A3D403F424644484B494D504E52565358" + + "5B585D605D626562686B676D706C737571787B767D807B83" + + "8580888A858D908A93958F989A949DA099A3A59EA8AAA3AD" + + "AFA8B3B5ADB8BAB2BEBFB7C3C5BCC8CAC1CECFC6D3D4CBD8" + + "DAD0DEDFD5E3DFD2E0DFCEDDE0CBDAE0C8D7E0C4D3E0C1D0" + + "E1BECDE1BBCAE1B7C7E1B4C4E1B1C1E2ADBEE2AABAE2A7B7" + + "E2A3B4E2A0B1E39DAEE399ABE396A8E393A5E490A1E48C9E" + + "E4899BE48698E48295E57F92E57C8FE5788CE57589E57285" + + "E66E82E66B7FE6687CE66479E76176E75E73E75B70E7576C" + + "E75469E85166E84D63E84A60E4495EE0485CDC475BD84659" + + "D44557D04455CB4353C74252C34150BF404EBB3F4CB73E4B" + + "B33D49AF3C47AB3B45A73A43A339429F38409B373E97363C" + + "92353A8E34398A33378632358231337E30327A2F30762E2E" + + "722D2C6E2C2A6A2B29662A276229255E2823592721552620" + + "51251E4D241C49231A4522194121173D20153C1F153A1F14" + + "391E14381E14361D14351C13341C13321B13311B132F1A12" + + "2E19122D19122B18122A1811291711271611261611251510" + + "23151022141021140F1F130F1E120F1C120F1B110E1A110E" + + "18100E170F0E160F0D140E0D130E0D120D0D100C0C0F0C0C" + + "0E0B0C0C0B0C0B0A0B09090B08090B07080B05080A04070A" + + "0606090804090A03088C46728A457087446D85436B824369" + + "8042667D41647B4061793F5F763E5D743D5A713D586F3C56" + + "6C3B536A3A5168394F65384C63374A6037485E36455B3543" + + "59344057333E54323C5231394F31374D30354A2F32482E30" + + "462D2E432C2B412B293E2B273C2A2439292237281F35271D" + + "32261B3025182D25162B241428231126220F25210F24210E" + + "23200E221F0E221E0D211E0D201D0D1F1C0D1E1B0C1D1B0C" + + "1C1A0C1B190B1B180B1A180B19170A18160A17150A161509" + + "1514091413091413081312081211081110081010070F0F07" + + "0E0E070D0D060C0D060C0C060B0B050A0A05090A05080904" + + "070804060704050704050603040503030403020402010302" + + "0608070C0D0D1112121617171B1C1D2121222626272B2B2D"; function hexToBytes(hex: string) { - let bytes: number[] = []; - for (let i = 0; i < hex.length; i += 2) { - bytes.push(parseInt(hex.substring(i, i + 2), 16)); - } - return bytes; + let bytes: number[] = []; + for (let i = 0; i < hex.length; i += 2) { + bytes.push(parseInt(hex.substring(i, i + 2), 16)); + } + return bytes; } export const palette = hexToBytes(paletteString).map(value => value / 0xff); \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/pdj.ts b/blog/2024-11-15-playing-with-fire/src/pdj.ts index 5afd470..bec8e8d 100644 --- a/blog/2024-11-15-playing-with-fire/src/pdj.ts +++ b/blog/2024-11-15-playing-with-fire/src/pdj.ts @@ -1,10 +1,15 @@ // hidden-start import { Variation } from './variation' //hidden-end -export type PdjParams = {a: number, b: number, c: number, d: number}; -export function pdj({a, b, c, d}: PdjParams): Variation { - return (x, y) => [ +export type PdjParams = { + a: number, + b: number, + c: number, + d: number +}; +export const pdj = + ({a, b, c, d}: PdjParams): Variation => + (x, y) => [ Math.sin(a * y) - Math.cos(b * x), Math.sin(c * x) - Math.cos(d * y) - ] -} \ No newline at end of file + ] \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/plotBinary.ts b/blog/2024-11-15-playing-with-fire/src/plotBinary.ts index fd5b9a8..1beb080 100644 --- a/blog/2024-11-15-playing-with-fire/src/plotBinary.ts +++ b/blog/2024-11-15-playing-with-fire/src/plotBinary.ts @@ -1,14 +1,14 @@ -import { camera, histIndex } from "./camera" +import { camera, histIndex } from "./camera"; export function plotBinary(x: number, y: number, image: ImageData) { - const [pixelX, pixelY] = camera(x, y, image.width); - const pixelIndex = histIndex(pixelX, pixelY, image.width, 4); - if (pixelIndex < 0 || pixelIndex > image.data.length) { - return; - } + const [pixelX, pixelY] = camera(x, y, image.width); + if (pixelX < 0 || pixelX >= image.width || pixelY < 0 || pixelY >= image.height) + return; - image.data[pixelIndex] = 0; - image.data[pixelIndex + 1] = 0; - image.data[pixelIndex + 2] = 0; - image.data[pixelIndex + 3] = 0xff; + const pixelIndex = histIndex(pixelX, pixelY, image.width, 4); + + image.data[pixelIndex] = 0; + image.data[pixelIndex + 1] = 0; + image.data[pixelIndex + 2] = 0; + image.data[pixelIndex + 3] = 0xff; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/popcorn.ts b/blog/2024-11-15-playing-with-fire/src/popcorn.ts index bcb2741..168070f 100644 --- a/blog/2024-11-15-playing-with-fire/src/popcorn.ts +++ b/blog/2024-11-15-playing-with-fire/src/popcorn.ts @@ -1,10 +1,10 @@ // hidden-start -import {Coefs} from './coefs' -import {Variation} from './variation' +import { Coefs } from "./transform"; +import { Variation } from "./variation"; // hidden-end -export function popcorn({c, f}: Coefs): Variation { - return (x, y) => [ - x + c * Math.sin(Math.tan(3 * y)), - y + f * Math.sin(Math.tan(3 * x)) - ]; -} \ No newline at end of file +export const popcorn = + ({ c, f }: Coefs): Variation => + (x, y) => [ + x + c * Math.sin(Math.tan(3 * y)), + y + f * Math.sin(Math.tan(3 * x)) + ]; \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/randomChoice.ts b/blog/2024-11-15-playing-with-fire/src/randomChoice.ts index 58cf17e..9d72fd2 100644 --- a/blog/2024-11-15-playing-with-fire/src/randomChoice.ts +++ b/blog/2024-11-15-playing-with-fire/src/randomChoice.ts @@ -7,7 +7,8 @@ export function randomChoice( ); let choice = Math.random() * weightSum; - for (const [idx, elem] of choices.entries()) { + for (const entry of choices.entries()) { + const [idx, elem] = entry; const [weight, t] = elem; if (choice < weight) { return [idx, t]; diff --git a/blog/2024-11-15-playing-with-fire/src/transform.ts b/blog/2024-11-15-playing-with-fire/src/transform.ts index 9b7e783..ab2c364 100644 --- a/blog/2024-11-15-playing-with-fire/src/transform.ts +++ b/blog/2024-11-15-playing-with-fire/src/transform.ts @@ -1,13 +1,23 @@ -export type Transform = (x: number, y: number) => [number, number]; +export type Transform = + (x: number, y: number) => + [number, number]; export interface Coefs { - a: number, b: number, c: number, - d: number, e: number, f: number + a: number, + b: number, + c: number, + d: number, + e: number, + f: number } -export function applyCoefs(x: number, y: number, coefs: Coefs): [number, number] { - return [ - (x * coefs.a + y * coefs.b + coefs.c), - (x * coefs.d + y * coefs.e + coefs.f) - ] +export function applyCoefs( + x: number, + y: number, + coefs: Coefs +): [number, number] { + return [ + (x * coefs.a + y * coefs.b + coefs.c), + (x * coefs.d + y * coefs.e + coefs.f) + ]; } \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/src/variation.ts b/blog/2024-11-15-playing-with-fire/src/variation.ts index 3b90d18..eec745c 100644 --- a/blog/2024-11-15-playing-with-fire/src/variation.ts +++ b/blog/2024-11-15-playing-with-fire/src/variation.ts @@ -1 +1,4 @@ -export type Variation = (x: number, y: number) => [number, number]; \ No newline at end of file +export type Variation = ( + x: number, + y: number +) => [number, number]; \ No newline at end of file From a6194763d19e22cc8f5c99dddcbc173cf8d1f8ad Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Sun, 15 Dec 2024 21:35:03 -0500 Subject: [PATCH 48/51] Wording tweaks --- .../1-introduction/index.mdx | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index dd9dacc..9489018 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -144,11 +144,11 @@ Or, to put it in English, we might say: > Our solution, $S$, is the union of all sets produced by applying each function, $F_i$, > to points in the solution. -There's just one small problem: to find the solution, we must apply these functions to points -we know are in the solution. But how do we know which points are in the solution to start with? +There's just one small problem: to find the solution, we must already know which points are in the solution. +What? -John E. Hutchinson provides an answer in the [original paper](https://maths-people.anu.edu.au/~john/Assets/Research%20Papers/fractals_self-similarity.pdf) -explaining the mathematics of iterated function systems: +John E. Hutchinson provides an explanation in the [original paper](https://maths-people.anu.edu.au/~john/Assets/Research%20Papers/fractals_self-similarity.pdf) +defining the mathematics of iterated function systems: > Furthermore, $S$ is compact and is the closure of the set of fixed points $s_{i_1...i_p}$ > of finite compositions $F_{i_1...i_p}$ of members of $F$. @@ -159,7 +159,7 @@ I've tweaked the conventions of that paper slightly to match the Fractal Flame p Before your eyes glaze over, let's unpack this: -- **$S$ is [compact](https://en.wikipedia.org/wiki/Compact_space)...**: All points in our solution will be in a finite range +- **Furthermore, $S$ is [compact](https://en.wikipedia.org/wiki/Compact_space)...**: All points in our solution will be in a finite range - **...and is the [closure](https://en.wikipedia.org/wiki/Closure_(mathematics)) of the set of [fixed points](https://en.wikipedia.org/wiki/Fixed_point_(mathematics))**: Applying our functions to points in the solution will give us other points that are in the solution - **...of finite compositions $F_{i_1...i_p}$ of members of $F$**: By composing our functions (that is, @@ -188,7 +188,7 @@ This is still a bit vague, so let's work through an example. ## [Sierpinski's gasket](https://www.britannica.com/biography/Waclaw-Sierpinski) -The Fractal Flame paper gives us three functions to use for our first IFS: +The Fractal Flame paper gives three functions to use for a first IFS: $$ F_0(x, y) = \left({x \over 2}, {y \over 2} \right) \\ @@ -200,8 +200,8 @@ $$ ### The chaos game -Next, how do we find the "fixed points" we mentioned earlier? The paper lays out an algorithm called the "[chaos game](https://en.wikipedia.org/wiki/Chaos_game)" -that gives us points in the solution set: +Next, how do we find the "fixed points" mentioned earlier? The paper lays out an algorithm called the "[chaos game](https://en.wikipedia.org/wiki/Chaos_game)" +that gives us points in the solution: $$ \begin{align*} @@ -218,7 +218,7 @@ $$ The chaos game algorithm is effectively the "finite compositions of $F_{i_1..i_p}$" mentioned earlier. ::: -Now, let's turn this into code, one piece at a time. +Let's turn this into code, one piece at a time. First, we need to generate some random numbers. The "bi-unit square" is the range $[-1, 1]$, so we generate a random point using an existing API: From 37e2992865dbc22ec839ed27d5a0ce243841cd2d Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Mon, 16 Dec 2024 21:29:03 -0500 Subject: [PATCH 49/51] Proofreading --- .../1-introduction/index.mdx | 85 ++++++++---------- .../2-transforms/index.mdx | 60 +++++++------ .../3-log-density/index.mdx | 61 ++++++------- blog/2024-11-15-playing-with-fire/banner.png | Bin 570793 -> 428018 bytes 4 files changed, 99 insertions(+), 107 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index 9489018..6ca0ff9 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -22,15 +22,14 @@ import banner from '../banner.png' -I don't remember exactly when I first learned about fractal flames, but I do remember being entranced by the images they created. +I don't remember when exactly I first learned about fractal flames, but I do remember being entranced by the images they created. I also remember their unique appeal to my young engineering mind; this was an art form I could participate in. -The original [Fractal Flame Algorithm paper](https://flam3.com/flame_draves.pdf) describing their structure was too much +The [Fractal Flame Algorithm paper](https://flam3.com/flame_draves.pdf) describing their structure was too much for me to handle at the time (I was ~12 years old), so I was content to play around and enjoy the pictures. -But the desire to understand it stuck around. Now, with a graduate degree under my belt, I want to revisit it -and try to make some progress. +But the desire to understand it stuck around. Now, with a graduate degree under my belt, I wanted to revisit it. -This guide is my attempt to explain how fractal flames work in a way that younger me — and others interested in the art — +This guide is my attempt to explain how fractal flames work so that younger me — and others interested in the art — can understand without too much prior knowledge. --- @@ -42,7 +41,7 @@ This post covers section 2 of the Fractal Flame Algorithm paper ::: As mentioned, fractal flames are a type of "[iterated function system](https://en.wikipedia.org/wiki/Iterated_function_system)," -or IFS. The formula for an IFS is short, but takes some time to unpack: +or IFS. The formula for an IFS is short, but takes some time to work through: $$ S = \bigcup_{i=0}^{n-1} F_i(S) @@ -52,7 +51,7 @@ $$ First, $S$. $S$ is the set of points in two dimensions (in math terms, $S \in \mathbb{R}^2$) that represent a "solution" of some kind to our equation. -Our goal is to find all points in $S$, plot them, and display that image. +Our goal is to find all the points in $S$, plot them, and display that image. For example, if we say $S = \{(0,0), (1, 1), (2, 2)\}$, there are three points to plot: @@ -67,20 +66,17 @@ export const simpleData = [ -However, this is a pretty boring image. With fractal flames, rather than listing individual points, -we use functions to describe which points are part of the solution. This means there are an infinite -number of points, but if we find _enough_ points to plot, we'll end up with a nice picture. -And if the functions change, the solution also changes, and we get a new picture. +With fractal flames, rather than listing individual points, we use functions to describe the solution. +This means there are an infinite number of points, but if we find _enough_ points to plot, we get a nice picture. +And if the functions change, the solution also changes, and we get something new. ### Transform functions Second, the $F_i(S)$ functions, also known as "transforms." -At their most basic, each $F_i$ takes in a 2-dimensional point and gives back a new point +Each transform takes in a 2-dimensional point and gives a new point back (in math terms, $F_i \in \mathbb{R}^2 \rightarrow \mathbb{R}^2$). -While you could theoretically use any function, we'll start with a specific kind of function -called an "[affine transformation](https://en.wikipedia.org/wiki/Affine_transformation)." - -The general form of an affine transformation is: +While you could theoretically use any function, we'll focus on a specific kind of function +called an "[affine transformation](https://en.wikipedia.org/wiki/Affine_transformation)." Every transform uses the same formula: $$ F_i(a_i x + b_i y + c_i, d_i x + e_i y + f_i) @@ -91,8 +87,8 @@ import CodeBlock from '@theme/CodeBlock' {transformSource} -The parameters ($a_i$, $b_i$, etc.) are values we get to choose. -For example, we can represent a "shift" function like this: +The parameters ($a_i$, $b_i$, etc.) are values we choose. +For example, we can define a "shift" function like this: $$ \begin{align*} @@ -106,7 +102,7 @@ F_{shift}(x, y) &= (1 \cdot x + 0.5, 1 \cdot y + 1.5) \end{align*} $$ -Applying this function to our original points will give us a new set of points: +Applying this transform to the original points gives us a new set of points: import {applyCoefs} from "../src/transform" @@ -139,7 +135,7 @@ $$ S = \bigcup_{i=0}^{n-1} F_i(S) $$ -Or, to put it in English, we might say: +Or, in English, we might say: > Our solution, $S$, is the union of all sets produced by applying each function, $F_i$, > to points in the solution. @@ -153,17 +149,13 @@ defining the mathematics of iterated function systems: > Furthermore, $S$ is compact and is the closure of the set of fixed points $s_{i_1...i_p}$ > of finite compositions $F_{i_1...i_p}$ of members of $F$. -:::note -I've tweaked the conventions of that paper slightly to match the Fractal Flame paper -::: - Before your eyes glaze over, let's unpack this: - **Furthermore, $S$ is [compact](https://en.wikipedia.org/wiki/Compact_space)...**: All points in our solution will be in a finite range - **...and is the [closure](https://en.wikipedia.org/wiki/Closure_(mathematics)) of the set of [fixed points](https://en.wikipedia.org/wiki/Fixed_point_(mathematics))**: Applying our functions to points in the solution will give us other points that are in the solution - **...of finite compositions $F_{i_1...i_p}$ of members of $F$**: By composing our functions (that is, - using the output of one function as input to the next function), we will arrive at the points in the solution + using the output of one function as input to the next), we will arrive at the points in the solution Thus, by applying the functions to fixed points of our system, we will find the other points we care about. @@ -177,11 +169,11 @@ Thus, by applying the functions to fixed points of our system, we will find the algorithm demonstrates, we only need functions to be contractive _on average_. At worst, the system will degenerate and produce a bad image. - Second, we're focused on $\mathbb{R}^2$ because we're generating images, but the Hutchinson paper + Second, we're focused on $\mathbb{R}^2$ because we're generating images, but the math allows for arbitrary dimensions; you could also have 3-dimensional fractal flames. Finally, there's a close relationship between fractal flames and [attractors](https://en.wikipedia.org/wiki/Attractor). - Specifically, the fixed points of $S$ act as attractors for the chaos game (explained in more detail below). + Specifically, the fixed points of $S$ act as attractors for the chaos game (explained below).
    This is still a bit vague, so let's work through an example. @@ -200,7 +192,7 @@ $$ ### The chaos game -Next, how do we find the "fixed points" mentioned earlier? The paper lays out an algorithm called the "[chaos game](https://en.wikipedia.org/wiki/Chaos_game)" +Now, how do we find the "fixed points" mentioned earlier? The paper lays out an algorithm called the "[chaos game](https://en.wikipedia.org/wiki/Chaos_game)" that gives us points in the solution: $$ @@ -220,8 +212,8 @@ The chaos game algorithm is effectively the "finite compositions of $F_{i_1..i_p Let's turn this into code, one piece at a time. -First, we need to generate some random numbers. The "bi-unit square" is the range $[-1, 1]$, -so we generate a random point using an existing API: +To start, we need to generate some random numbers. The "bi-unit square" is the range $[-1, 1]$, +and we can do this using an existing API: import biunitSource from '!!raw-loader!../src/randomBiUnit' @@ -235,14 +227,14 @@ import randintSource from '!!raw-loader!../src/randomInteger' ### Plotting -Finally, implementing the `plot` function. This blog series is designed to be interactive, +Finally, implementing the `plot` function. This blog series is interactive, so everything displays directly in the browser. As an alternative, software like `flam3` and Apophysis can "plot" by saving an image to disk. -To show the results, we'll use the [Canvas API](https://developer.mozilla.org/en-US/docs/Web/API/Canvas_API). -This allows us to manipulate individual pixels in an image and display it on screen. +To see the results, we'll use the [Canvas API](https://developer.mozilla.org/en-US/docs/Web/API/Canvas_API). +This allows us to manipulate individual pixels in an image and show it on screen. -First, we need to convert from Fractal Flame coordinates to pixel coordinates. +First, we need to convert from fractal flame coordinates to pixel coordinates. To simplify things, we'll assume that we're plotting a square image with range $[0, 1]$ for both $x$ and $y$: @@ -251,7 +243,7 @@ import cameraSource from "!!raw-loader!./cameraGasket" {cameraSource} Next, we'll store the pixel data in an [`ImageData` object](https://developer.mozilla.org/en-US/docs/Web/API/ImageData). -Each pixel in the image on screen has a corresponding index in the `data` array. +Each pixel on screen has a corresponding index in the `data` array. To plot a point, we set that pixel to be black: import plotSource from '!!raw-loader!./plot' @@ -277,25 +269,22 @@ import chaosGameSource from '!!raw-loader!./chaosGame' ### Weights -There's one last step before we finish the introduction. So far, each function $F_i$ has -the same chance of being chosen. We can change that by introducing a "weight" ($w_i$) -to each transform in the chaos game: +There's one last step before we finish the introduction. So far, each transform has +the same chance of being picked in the chaos game. +We can change that by giving them a "weight" ($w_i$) instead: import randomChoiceSource from '!!raw-loader!../src/randomChoice' {randomChoiceSource} +If we let the chaos game run forever, these weights wouldn't matter. +But because the iteration count is limited, changing the weights +means we don't plot some parts of the image: + import chaosGameWeightedSource from "!!raw-loader!./chaosGameWeighted"; {chaosGameWeightedSource} -For Sierpinski's Gasket, we start with equal weighting, -but changing the transform weights affects how often -the chaos game "visits" parts of the image. If the chaos -were to run forever, we'd get the same image; -but because the iteration count is limited, -some parts may be missing below. - :::tip Double-click the image if you want to save a copy! ::: @@ -308,7 +297,7 @@ import {SquareCanvas} from "../src/Canvas"; ## Summary Studying the foundations of fractal flames is challenging, -but we now have an understanding of both the mathematics -and implementations of iterated function systems. +but we now have an understanding of the mathematics +and the implementation of iterated function systems. -In the next post, we'll study the first innovation of fractal flames: variations. \ No newline at end of file +In the next post, we'll look at the first innovation of fractal flame algorithm: variations. \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index 8c64c7a..c21fd66 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -6,31 +6,30 @@ authors: [bspeice] tags: [] --- -Now that we have a basic chaos game in place, it's time to spice things up. Variations create the +Now that we've learned about the chaos game, it's time to spice things up. Variations create the shapes and patterns that fractal flames are known for. :::info This post uses [reference parameters](../params.flame) to demonstrate the fractal flame algorithm. -If you're interested in tweaking the parameters, or generating your own art, [Apophysis](https://sourceforge.net/projects/apophysis/) -can load that file to play around with! +If you're interested in tweaking the parameters, or creating your own, [Apophysis](https://sourceforge.net/projects/apophysis/) +can load that file. ::: ## Variations :::note -This post covers section 3 for the Fractal Flame Algorithm paper +This post covers section 3 of the Fractal Flame Algorithm paper ::: import CodeBlock from '@theme/CodeBlock' We previously introduced transforms as the "functions" of an "iterated function system," and showed how -playing the chaos game leads to an image of Sierpinski's Gasket. Even though we used simple functions, -the image it generates is exciting. But it's still not nearly as exciting as the images the Fractal Flame -algorithm is known for. +playing the chaos game gives us an image of Sierpinski's Gasket. Even though we used simple functions, +the image it generates is intriguing. But what would happen if we used something more complex? -This leads us to the first big innovation of the Fractal Flame algorithm: adding non-linear functions +This leads us to the first big innovation of the fractal flame algorithm: adding non-linear functions after the affine transform. These functions are called "variations": $$ @@ -44,14 +43,14 @@ import variationSource from '!!raw-loader!../src/variation' Just like transforms, variations ($V_j$) are functions that take in $(x, y)$ coordinates and give back new $(x, y)$ coordinates. However, the sky is the limit for what happens between input and output. -The Fractal Flame paper lists 49 different variation functions, +The Fractal Flame paper lists 49 variation functions, and the official `flam3` implementation supports [98 different variations](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/variations.c). -To draw our reference image, we'll focus on four variations: +To draw our reference image, we'll focus on just four: ### Linear (variation 0) -This variation is dead simple: just return the $x$ and $y$ coordinates as-is. +This variation is dead simple: return the $x$ and $y$ coordinates as-is. $$ V_0(x,y) = (x,y) @@ -63,12 +62,12 @@ import linearSrc from '!!raw-loader!../src/linear' :::tip In a way, we've already been using this variation! The transforms that define Sierpinski's Gasket -apply the affine coefficients to the input point, and use that as the output point. +apply the affine coefficients to the input point and use that as the output. ::: ### Julia (variation 13) -This variation is a good example of the non-linear functions we can use. It uses both trigonometry +This variation is a good example of a non-linear function. It uses both trigonometry and probability to produce interesting shapes: $$ @@ -93,7 +92,7 @@ import juliaSrc from '!!raw-loader!../src/julia' ### Popcorn (variation 17) Some variations rely on knowing the transform's affine coefficients; they're called "dependent variations." -For the popcorn variation, we use $c$ and $f$: +For this variation, we use $c$ and $f$: $$ V_{17}(x,y) = (x + c\ \text{sin}(\text{tan }3y), y + f\ \text{sin}(\text{tan }3x)) @@ -105,8 +104,8 @@ import popcornSrc from '!!raw-loader!../src/popcorn' ### PDJ (variation 24) -Some variations have extra parameters; they're called "parametric variations." -For the PDJ variation, there are four extra parameters we can choose: +Some variations have extra parameters we can choose; they're called "parametric variations." +For the PDJ variation, there are four extra parameters: $$ p_1 = \text{pdj.a} \hspace{0.1cm} p_2 = \text{pdj.b} \hspace{0.1cm} p_3 = \text{pdj.c} \hspace{0.1cm} p_4 = \text{pdj.d} \\ @@ -133,11 +132,11 @@ import blendSource from "!!raw-loader!../src/blend"; {blendSource} -With that in place, we have enough to render a first fractal flame. We'll use the same -chaos game as before, but our new transforms and variations produce a dramatically different image: +With that in place, we have enough to render a fractal flame. We'll use the same +chaos game as before, but the new transforms and variations produce a dramatically different image: :::tip -Try using the variation weight sliders to figure out which parts of the image each transform controls. +Try using the variation weights to figure out which parts of the image each transform controls. ::: import {SquareCanvas} from "../src/Canvas"; @@ -147,9 +146,9 @@ import FlameBlend from "./FlameBlend"; ## Post transforms -Next, we'll introduce a second affine transform, applied _after_ variation blending. This is called a "post transform." +Next, we'll introduce a second affine transform applied _after_ variation blending. This is called a "post transform." -We'll use some new variables, but the post transform function should look familiar: +We'll use some new variables, but the post transform should look familiar: $$ \begin{align*} @@ -163,7 +162,7 @@ import postSource from '!!raw-loader!./post' {postSource} The image below uses the same transforms/variations as the previous fractal flame, -but allows modifying the post-transform coefficients: +but allows changing the post-transform coefficients:
    If you want to test your understanding... @@ -178,12 +177,12 @@ import FlamePost from "./FlamePost"; ## Final transforms -Our last step is to introduce a "final transform" ($F_{final}$) that is applied -regardless of which transform the chaos game selects. It works just like a normal transform -(composition of affine transform, variation blend, and post transform), -but it doesn't change the chaos game state. +The last step is to introduce a "final transform" ($F_{final}$) that is applied +regardless of which regular transform ($F_i$) the chaos game selects. +It's just like a normal transform (composition of affine transform, variation blend, and post transform), +but it doesn't affect the chaos game state. -With that in place, our chaos game algorithm changes slightly: +After adding the final transform, our chaos game algorithm looks like this: $$ \begin{align*} @@ -201,6 +200,9 @@ import chaosGameFinalSource from "!!raw-loader!./chaosGameFinal" {chaosGameFinalSource} +This image uses the same normal/post transforms as above, but allows modifying +the coefficients and variations of the final transform: + import FlameFinal from "./FlameFinal"; @@ -208,7 +210,7 @@ import FlameFinal from "./FlameFinal"; ## Summary Variations are the fractal flame algorithm's first major innovation. -By blending variation functions, and post/final transforms, we generate unique images. +By blending variation functions and post/final transforms, we generate unique images. -However, the images themselves are grainy and unappealing. In the next post, we'll clean up +However, these images are grainy and unappealing. In the next post, we'll clean up the image quality and add some color. \ No newline at end of file diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index 0254a4f..7faa251 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -6,7 +6,7 @@ authors: [bspeice] tags: [] --- -So far, our `plot()` function has been fairly simple; map a fractal flame coordinate to a specific pixel, +So far, our `plot()` function has been fairly simple: map a fractal flame coordinate to a specific pixel, and color in that pixel. This works well for simple function systems (like Sierpinski's Gasket), but more complex systems (like the reference parameters) produce grainy images. @@ -20,21 +20,20 @@ In this post, we'll refine the image quality and add color to really make things This post covers sections 4 and 5 of the Fractal Flame Algorithm paper ::: -One problem with the existing chaos game is that we waste work -by treating pixels as a binary "on" (opaque) or "off" (transparent). -If the chaos game encounters the same location twice, nothing actually changes. +One problem with the current chaos game algorithm is that we waste work +because pixels are either "on" (opaque) or "off" (transparent). +If the chaos game encounters the same pixel twice, nothing changes. -To demonstrate how much work is wasted, we'll render the reference image again. -However, we'll also count each time the chaos game encounters a pixel. -This gives us a kind of image "histogram": +To demonstrate how much work is wasted, we'll count each time the chaos game +visits a pixel while iterating. This gives us a kind of image "histogram": import chaosGameHistogramSource from "!!raw-loader!./chaosGameHistogram" {chaosGameHistogramSource} -When the chaos game finishes, we find the pixel encountered most frequently. -Finally, we "paint" the image by setting each pixel's alpha value (transparency) -to the ratio of times encountered divided by the maximum: +When the chaos game finishes, we find the pixel encountered most often. +Finally, we "paint" the image by setting each pixel's alpha (transparency) value +to the ratio of times visited divided by the maximum: import CodeBlock from "@theme/CodeBlock"; @@ -50,22 +49,22 @@ import {paintLinear} from "./paintLinear"; ## Tone mapping -While using a histogram reduces the "graininess" of the image, it also leads to some parts vanishing entirely. -In the reference parameters, the outer circle is preserved, but the interior appears to be missing! +While using a histogram reduces the "graining," it also leads to some parts vanishing entirely. +In the reference parameters, the outer circle is still there, but the interior is gone! To fix this, we'll introduce the second major innovation of the fractal flame algorithm: [tone mapping](https://en.wikipedia.org/wiki/Tone_mapping). This is a technique used in computer graphics to compensate for differences in how -computers represent brightness, and how people see brightness. +computers represent brightness, and how people actually see brightness. -As a concrete example, high dynamic range (HDR) photography uses this technique to capture -nice images of scenes with a wide range of brightnesses. To take a picture of something dark, +As a concrete example, high-dynamic-range (HDR) photography uses this technique to capture +scenes with a wide range of brightnesses. To take a picture of something dark, you need a long exposure time. However, long exposures lead to "hot spots" (sections that are pure white). By taking multiple pictures with different exposure times, we can combine them to create a final image where everything is visible. In fractal flames, this "tone map" is accomplished by scaling brightness according to the _logarithm_ of how many times we encounter a pixel. This way, "cold spots" (pixels the chaos game visits infrequently) -will still be visible, and "hot spots" (pixels the chaos game visits frequently) won't wash out. +are still visible, and "hot spots" (pixels the chaos game visits frequently) won't wash out.
    Log-scale vibrancy also explains fractal flames appear to be 3D... @@ -89,7 +88,7 @@ import {paintLogarithmic} from './paintLogarithmic' ## Color -Finally, we'll introduce the last innovation of the fractal flame algorithm: color. +Now we'll introduce the last innovation of the fractal flame algorithm: color. By including a third coordinate ($c$) in the chaos game, we can illustrate the transforms responsible for the image. @@ -100,11 +99,12 @@ Color in a fractal flame is continuous on the range $[0, 1]$. This is important - It helps blend colors together in the final image. Slight changes in the color value lead to slight changes in the actual color - It allows us to swap in new color palettes easily. We're free to choose what actual colors - each color value represents + each value represents We'll give each transform a color value ($c_i$) in the $[0, 1]$ range. +The final transform gets a value too ($c_f$). Then, at each step in the chaos game, we'll set the current color -by blending it with the previous color and the current transform: +by blending it with the previous color: $$ \begin{align*} @@ -123,13 +123,13 @@ $$ ### Color speed :::warning -Color speed as a concept isn't introduced in the Fractal Flame Algorithm paper. +Color speed isn't introduced in the Fractal Flame Algorithm paper. It is included here because [`flam3` implements it](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/variations.c#L2140), and because it's fun to play with. ::: -Next, we'll add a parameter to each transform that controls how much it affects the current color. +Next, we'll add a parameter to each transform that controls how much it changes the current color. This is known as the "color speed" ($s_i$): $$ @@ -155,7 +155,7 @@ There's one small complication: the color coordinate is continuous, but the pale uses discrete colors. How do we handle situations where the color coordinate is "in between" the colors of our palette? -One way is to use a step function. In the code below, we multiply the color coordinate +One way to handle this is a step function. In the code below, we multiply the color coordinate by the number of colors in the palette, then truncate that value. This gives us a discrete index: import colorFromPaletteSource from "!!raw-loader!./colorFromPalette"; @@ -169,7 +169,7 @@ import colorFromPaletteSource from "!!raw-loader!./colorFromPalette"; For example, `flam3` uses [linear interpolation](https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L483-L486)
    -In the diagram below, each color in our palette is plotted on a small vertical strip. +In the diagram below, each color in the palette is plotted on a small vertical strip. Putting the strips side by side shows the full palette used by the reference parameters: import * as params from "../src/params" @@ -179,8 +179,9 @@ import {PaletteBar} from "./FlameColor" ### Plotting -We're now ready to plot our $(x_f,y_f,c_f)$ coordinates. After translating from color coordinate ($c_f$) -to RGB value, add that to the image histogram: +We're now ready to plot our $(x_f,y_f,c_f)$ coordinates. This time, we'll use a histogram +for each color channel (red, green, blue, alpha). After translating from color coordinate ($c_f$) +to RGB value, add that to the histogram: import chaosGameColorSource from "!!raw-loader!./chaosGameColor" @@ -208,14 +209,14 @@ brightness/transparency to reduce the visual "graining" of previous images. Next, introducing a third coordinate to the chaos game makes color images possible, the third major innovation of the fractal flame algorithm. Using a continuous -color scale and color palette adds a splash of color to our transforms. +color scale and color palette adds a splash of excitement to the image. -The Fractal Flame Algorithm paper does go on to describe more techniques -not covered here. For example, Image quality can be improved with density estimation +The Fractal Flame Algorithm paper goes on to describe more techniques +not covered here. For example, image quality can be improved with density estimation and filtering. New parameters can be generated by "mutating" existing fractal flames. And fractal flames can even be animated to produce videos! -That said, I think this is a good place to wrap up. We were able to go from +That said, I think this is a good place to wrap up. We went from an introduction to the mathematics of fractal systems all the way to generating full-color images. 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blog/2024-11-15-playing-with-fire/2-transforms/index.mdx | 2 +- blog/2024-11-15-playing-with-fire/3-log-density/index.mdx | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx index 6ca0ff9..aa77cf9 100644 --- a/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx +++ b/blog/2024-11-15-playing-with-fire/1-introduction/index.mdx @@ -1,7 +1,7 @@ --- slug: 2024/11/playing-with-fire title: "Playing with fire: The fractal flame algorithm" -date: 2024-11-15 12:00:00 +date: 2024-12-16 21:30:00 authors: [bspeice] tags: [] --- diff --git a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx index c21fd66..55fd175 100644 --- a/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx +++ b/blog/2024-11-15-playing-with-fire/2-transforms/index.mdx @@ -1,7 +1,7 @@ --- slug: 2024/11/playing-with-fire-transforms title: "Playing with fire: Transforms and variations" -date: 2024-11-15 13:00:00 +date: 2024-12-16 21:31:00 authors: [bspeice] tags: [] --- diff --git a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx index 7faa251..5abb1d0 100644 --- a/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx +++ b/blog/2024-11-15-playing-with-fire/3-log-density/index.mdx @@ -1,7 +1,7 @@ --- slug: 2024/11/playing-with-fire-log-density title: "Playing with fire: Tone mapping and color" -date: 2024-11-15 14:00:00 +date: 2024-12-16 21:32:00 authors: [bspeice] tags: [] --- From 34cc4bca1c7806f1bdfc742c246ea47d06ff13fd Mon Sep 17 00:00:00 2001 From: Bradlee Speice Date: Mon, 16 Dec 2024 21:32:08 -0500 Subject: [PATCH 51/51] Vendor katex --- static/katex/fonts/KaTeX_AMS-Regular.woff2 | Bin 0 -> 28076 bytes static/katex/fonts/KaTeX_Caligraphic-Bold.woff2 | Bin 0 -> 6912 bytes 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