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": { - 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