Flame blending example

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}) {
+type Transform = (x: number, y: number) => [number, number];
-    return (
-        <div style={{paddingLeft: '1.5em', paddingRight: '1.5em'}}>
-            {children}
-            <input type={'range'} min={0} max={1} step={.01} style={{width: '100%'}} value={value} onInput={e => setValue(Number(e.currentTarget.value))}/>
-        </div>
-    )
-}
 
 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) => (
+        <>
+            <div className={styles.inputDiv}>
+                <p><TeX>{title}</TeX> weight:<span style={{float: 'right'}}>{weight}</span></p>
+                <input type={'range'} min={0} max={1} step={.01} style={{width: '100%'}} value={weight}
+                    onInput={e => setWeight(Number(e.currentTarget.value))}/>
+            </div>
+        </>
+    )
+
     return (
         <>
             <Canvas width={image.width} height={image.height} painter={game}/>
             <div style={{paddingTop: '1em', display: 'grid', gridTemplateColumns: 'auto auto auto'}}>
-                <WeightInput value={f0Weight} setValue={setF0Weight}>
+                {weightInput("F_0", f0Weight, setF0Weight)}
-                    <p><TeX>F_0</TeX> weight:<span style={{float: 'right'}}>{f0Weight}</span></p>
+                {weightInput("F_1", f1Weight, setF1Weight)}
-                </WeightInput>
+                {weightInput("F_2", f2Weight, setF2Weight)}
-                <WeightInput value={f1Weight} setValue={setF1Weight}>
-                    <p><TeX>F_1</TeX> weight:<span style={{float: 'right'}}>{f1Weight}</span></p>
-                </WeightInput>
-                <WeightInput value={f2Weight} setValue={setF2Weight}>
-                    <p><TeX>F_2</TeX> weight:<span style={{float: 'right'}}>{f2Weight}</span></p>
-                </WeightInput>
             </div>
         </>
     )

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(<Gasket/>)

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;

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 banner from '../banner.png'
-import bannerLight from '../banner-light.png'
 
 <center>
-    <!-- Why are these backwards? -->
+    <img src={banner} style={{filter: isDarkMode() ? '' : 'invert(1)'}}/>
-    <img src={bannerLight} hidden={isDarkMode()}/>
-    <img src={bannerDark} hidden={!isDarkMode()}/>
 </center>
 
 <!-- truncate -->
@@ -204,6 +201,4 @@ import chaosGameWeightedSource from "!!raw-loader!./chaosGameWeighted";
 import BrowserOnly from "@docusaurus/BrowserOnly";
 import GasketWeighted from "./GasketWeighted"
 
-<BrowserOnly>
+<BrowserOnly>{() => <GasketWeighted/>}</BrowserOnly>
-    <GasketWeighted/>
-</BrowserOnly>

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 (
+            <>
+                <p style={{gridColumn: '1/-1'}}>{title}:</p>
+                <div className={styles.inputDiv}>
+                    <p>Linear: {variations.linear}</p>
+                    <input type={'range'} min={0} max={1} step={0.01} style={{width: '100%'}} value={variations.linear}
+                           onInput={e => setVariations({...variations, linear: Number(e.currentTarget.value)})}/>
+                </div>
+                <div className={styles.inputDiv}>
+                    <p>Julia: {variations.julia}</p>
+                    <input type={'range'} min={0} max={1} step={0.01} style={{width: '100%'}} value={variations.julia}
+                           onInput={e => setVariations({...variations, julia: Number(e.currentTarget.value)})}/>
+                </div>
+                <div className={styles.inputDiv}>
+                    <p>Popcorn: {variations.popcorn}</p>
+                    <input type={'range'} min={0} max={1} step={0.01} style={{width: '100%'}} value={variations.popcorn}
+                           onInput={e => setVariations({...variations, popcorn: Number(e.currentTarget.value)})}/>
+                </div>
+                <div className={styles.inputDiv}>
+                    <p>PDJ: {variations.pdj}</p>
+                    <input type={'range'} min={0} max={1} step={0.01} style={{width: '100%'}} value={variations.pdj}
+                           onInput={e => setVariations({...variations, pdj: Number(e.currentTarget.value)})}/>
+                </div>
+            </>
+        )
+    }
+
+    return (
+        <>
+            <Canvas
+                width={image.width}
+                height={image.height}
+                painter={chaosGame()}/>
+            <div style={{paddingTop: '1em', display: 'grid', gridTemplateColumns: 'auto auto auto auto'}}>
+                {variationEditor("Transform 1", xform1Variations, setXform1Variations)}
+                {variationEditor("Transform 2", xform2Variations, setXform2Variations)}
+                {variationEditor("Transform 3", xform3Variations, setXform3Variations)}
+            </div>
+        </>
+    )
+}

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];
+}

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 ($v_j$).
+Each variation receives the same $x$ and $y$ inputs, and we add together each variation's $x$ and $y$ outputs.
-Afterward, sum up the $x$ and $y$ values respectively:
+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";
+
+<FlameBlend/>

blog/2024-11-15-playing-with-fire/src/camera.ts

@@ -0,0 +1,44 @@
+/**
+ * Translate 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;
+}

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)
+    ]
 }

blog/2024-11-15-playing-with-fire/src/css/styles.module.css

@@ -0,0 +1,4 @@
+.inputDiv {
+    padding-left: .5em;
+    padding-right: 1em;
+}

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;
 

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)

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;
+}

blog/2024-11-15-playing-with-fire/src/transform.ts

@@ -1,9 +1 @@
-import { Coefs } from './coefs'
+export type Transform = (x: number, y: number) => [number, number];
-import { Variation } from './variation'
-
-export interface Transform {
-    coefs: Coefs,
-    variations: [number, Variation][],
-    coefsPost: Coefs,
-    color: number
-}