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36
posts/2023/06/flam3/0-utility.tsx
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36
posts/2023/06/flam3/0-utility.tsx
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import React, { useEffect, useRef } from "react";
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export type renderFn = (image: ImageData) => void;
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export const Canvas: React.FC<{ f: renderFn }> = ({ f }) => {
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const canvasRef = useRef<HTMLCanvasElement | null>(null);
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let image: ImageData | null = null;
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useEffect(() => {
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if (canvasRef.current) {
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const canvas = canvasRef.current;
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const ctx = canvas.getContext("2d");
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if (!ctx) {
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return;
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}
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if (
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!image ||
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image.width !== canvas.width ||
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image.height !== canvas.height
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) {
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image = ctx.createImageData(canvas.width, canvas.height);
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}
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f(image);
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ctx.putImageData(image, 0, 0);
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}
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});
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return <canvas ref={canvasRef} width={600} height={600} />;
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};
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export function randomInteger(min: number, max: number) {
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return Math.floor(Math.random() * (max - min)) + min;
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}
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61
posts/2023/06/flam3/1-gasket.ts
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61
posts/2023/06/flam3/1-gasket.ts
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import { randomInteger, renderFn } from "./0-utility";
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const ITER = 100_000;
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function plot(x: number, y: number, image: ImageData) {
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// A trivial `plot` implementation would take the range [-1, 1],
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// shift it to [0, 2], then scale by the width or height
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// as appropriate:
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// pixelX = Math.floor((x + 1) * image.width / 2)
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// pixelY = Math.floor((y + 1) * image.height / 2)
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//
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// However, that produces a mirror image (across both X and Y)
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// from the paper. We'll invert X and Y to compensate.
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// Second, because the gasket solution only contains points in
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// the range [0, 1), the naive plot above would waste 75% of
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// the pixels available. We'll keep the shift by 1 (to compensate
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// for mirroring X and Y), but scale by the full image width or
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// height so we'll plot the specific quadrant we care about.
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var pixelX = Math.floor((-x + 1) * image.width);
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var pixelY = Math.floor((-y + 1) * image.height);
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// Now translate the (x, y) pixel coordinates to a buffer index
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// and paint it black:
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const index = pixelY * (image.width * 4) + pixelX * 4;
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image.data[index + 0] = 0;
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image.data[index + 1] = 0;
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image.data[index + 2] = 0;
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image.data[index + 3] = 0xff;
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}
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type Xform = (x: number, y: number) => [number, number];
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export const gasket: renderFn = (image) => {
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const F: Xform[] = [
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(x, y) => {
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return [x / 2, y / 2];
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},
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(x, y) => {
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return [(x + 1) / 2, y / 2];
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},
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(x, y) => {
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return [x / 2, (y + 1) / 2];
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},
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];
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let x = Math.random() * 2 - 1;
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let y = Math.random() * 2 - 1;
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// Heuristic for iteration count
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const iter = image.height * image.width;
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for (var i = 0; i < iter; i++) {
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const Fi = randomInteger(0, F.length);
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[x, y] = F[Fi](x, y);
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|
if (i >= 20) {
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plot(x, y, image);
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}
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}
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};
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142
posts/2023/06/flam3/2-variations.ts
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142
posts/2023/06/flam3/2-variations.ts
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@ -0,0 +1,142 @@
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import { randomInteger } from "./0-utility";
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type Variation = (x: number, y: number) => [number, number];
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const r = (x: number, y: number) => {
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return Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));
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};
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const theta = (x: number, y: number) => {
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return Math.atan2(x, y);
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};
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const linear: Variation = (x, y) => {
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return [x, y];
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};
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const swirl: Variation = (x, y) => {
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const r2 = Math.pow(r(x, y), 2);
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const sinR2 = Math.sin(r2);
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const cosR2 = Math.cos(r2);
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return [x * sinR2 - y * cosR2, x * cosR2 + y * sinR2];
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};
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const polar: Variation = (x, y) => {
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return [theta(x, y) / Math.PI, r(x, y) - 1];
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};
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const disc: Variation = (x, y) => {
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const thetaOverPi = theta(x, y) / Math.PI;
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const piR = Math.PI * r(x, y);
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return [thetaOverPi * Math.sin(piR), thetaOverPi * Math.cos(piR)];
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};
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const variations = [linear, swirl, polar, disc];
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class Coefs {
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constructor(
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public readonly a: number,
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public readonly b: number,
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public readonly c: number,
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public readonly d: number,
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public readonly e: number,
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public readonly f: number
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) {}
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|
}
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|
class Transform {
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|
constructor(
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public readonly weight: number,
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public readonly coefs: Coefs,
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// Assumes that we have a blend for each variation
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public readonly blend: number[]
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) {}
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apply(x: number, y: number) {
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const variationX = this.coefs.a * x + this.coefs.b * y + this.coefs.c;
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const variationY = this.coefs.d * x + this.coefs.e * y + this.coefs.f;
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var transformX = 0;
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var transformY = 0;
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this.blend.forEach((blend, i) => {
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const [perVarX, perVarY] = variations[i](variationX, variationY);
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transformX += blend * perVarX;
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transformY += blend * perVarY;
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});
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return [transformX, transformY];
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}
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}
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|
function plot(x: number, y: number, image: ImageData) {
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|
const pixelX = Math.floor(((x + 2) * image.width) / 4);
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|
const pixelY = Math.floor(((y + 2) * image.height) / 4);
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|
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|
if (
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|
pixelX < 0 ||
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pixelX > image.width ||
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pixelY < 0 ||
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|
pixelY > image.height
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|
) {
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|
return;
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|
}
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|
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|
const index = pixelY * (image.width * 4) + pixelX * 4;
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|
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|
image.data[index + 0] = 0;
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|
image.data[index + 1] = 0;
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|
image.data[index + 2] = 0;
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|
image.data[index + 3] = 0xff;
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|
}
|
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|
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|
function render(transforms: Transform[], image: ImageData) {
|
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|
const weightSum = transforms.reduce((val, xform) => val + xform.weight, 0);
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|
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|
var x = Math.random() * 2 - 1;
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|
var y = Math.random() * 2 - 1;
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|
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|
const iter = 100_000;
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|
for (var i = 0; i < iter; i++) {
|
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|
// Find the tranform we're operating on
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|
|
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|
/*
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|
var f = Math.random() * weightSum;
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|
|
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|
var transform = transforms[0];
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|
transforms.forEach((xform, j) => {
|
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|
if (f > 0 && f < xform.weight) {
|
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|
console.log(`xform=${j}`);
|
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|
transform = xform;
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|
f -= xform.weight;
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|
}
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|
});
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|
*/
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// HACK: Currently assuming weights are equal
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|
const transform = transforms[randomInteger(0, transforms.length)];
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|
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|
// Play the chaos game
|
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|
[x, y] = transform.apply(x, y);
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|
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|
if (i > 20) {
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|
plot(x, y, image);
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|
}
|
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|
}
|
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|
}
|
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|
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|
export function renderBaseline(image: ImageData) {
|
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|
return render(
|
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|
[
|
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|
new Transform(
|
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|
0.5,
|
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|
new Coefs(0.982996, 0, -0.219512, 0, 0.982996, -0.1875),
|
||||||
|
[1, 0, 0, -0.934]
|
||||||
|
),
|
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|
new Transform(
|
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|
0.5,
|
||||||
|
new Coefs(0.966511, -0.256624, 0.050305, 0.256624, 0.966511, -0.235518),
|
||||||
|
[0, 0.156, 0.778, 0]
|
||||||
|
),
|
||||||
|
],
|
||||||
|
image
|
||||||
|
);
|
||||||
|
}
|
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230
posts/2023/06/flam3/baseline.bak
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230
posts/2023/06/flam3/baseline.bak
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@ -0,0 +1,230 @@
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|
<Flames name="baseline">
|
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|
<flame name="dependent" version="Apophysis 2.08 beta" size="555 428" center="0 0" scale="138.75" oversample="1" filter="0.2" quality="1" background="0 0 0" brightness="4" gamma="4" >
|
||||||
|
<xform weight="0.5" color="0" linear="1" disc="-0.934" coefs="0.982996 0 0 0.982996 -0.219512 -0.1875" />
|
||||||
|
<xform weight="0.5" color="0" swirl="0.156" polar="0.778" coefs="0.966511 0.256624 -0.256624 0.966511 0.050305 -0.235518" />
|
||||||
|
<palette count="256" format="RGB">
|
||||||
|
7886955967864652763240672432611E2D5D192757172255
|
||||||
|
11224F0D1D410F1A39101E350F202C0F1F23101B1E0C161C
|
||||||
|
08151A060E14040A12040D13050D12060C11050D12050D11
|
||||||
|
050B0F05080F05080D04080C04080E050912040A18030C25
|
||||||
|
0410350616450A1E560F2362122768172B63192B5D162959
|
||||||
|
13234F1020420B1E3C0B1B380D19300E1A280D18200C191E
|
||||||
|
0D1C200F1C1E0D1A1D0A171E0B171C0B1119070A15040611
|
||||||
|
03050E01050C00060C01060C03090D061213081516071012
|
||||||
|
0813160B1420081022060C24050926040728020528010429
|
||||||
|
00042F060B3B0C124717255A22396D3B4E815564955D6F9B
|
||||||
|
667AA28593AC7A8799707B875F6A784F59694751643F4A60
|
||||||
|
2633602534622536651D3162162D60162B5D16295B15275E
|
||||||
|
182B6324386D3F517F5A6B927686A992A1C1A5B1CAB8C2D4
|
||||||
|
E4EAF3EEF3F8F9FCFDFBFCFDFEFCFDFEFCFDFEFDFDFCFDFF
|
||||||
|
F5F7FBE1E6EED2D6E2C3C7D6B9BFD5AFB8D5B2B8D3B6B9D2
|
||||||
|
CCD1E6DADEEAE8EBEEE3EAEFDFEAF1D8E3EBD1DDE6BACAD8
|
||||||
|
9DB0D28199BF7790B56E87AC6C84A66B82A05C72934A5B7B
|
||||||
|
2935531F2D451626381525351524321625341727371A2B44
|
||||||
|
2536563B4D8955689E6F84B37A90BF869DCCA3B6D7B9C6DF
|
||||||
|
CAD6E7C5CDDDC0C4D3BCC1CDB9BFC7B1B6C0ACB3BFB2BBC1
|
||||||
|
BCC2C6D8DEE1E2E7EBECF0F5EDF1F6EFF3F8E9EFF7DDE3EF
|
||||||
|
BAC0D8ABB1D19CA3CA98A1CA949FCB8E9BD097A2D5A9B3E2
|
||||||
|
BBC6EADFE4F4E3EAF7E8F1FBE8F3FADEE9EECAD8E4B3C3D9
|
||||||
|
8D9AAB808DA474809E737D9A737B977178925F6D9A4E5E95
|
||||||
|
4552841B2D611524540F1C47091236080F2A080D22070C20
|
||||||
|
11162D151E3A1A26482332532C3E5E42567557688B71839F
|
||||||
|
8C9AB0BDC6C9BEC7C9C0C9CAC9C9C6C7CAC4B4BFB9A9AEA9
|
||||||
|
9499A09198A08E97A1929C9D939FA08F9CA5899397767F82
|
||||||
|
586873343A51272F491B2542141B360E142C0A0F250B0D20
|
||||||
|
0B12270E152E1119351721461D2A5622316127387126397C
|
||||||
|
22367C253581222F7E1D2C7722317E333B824A5289636FA2
|
||||||
|
ACB3D0BAC1DAC8D0E4D5E1E7D8E3E2D0DBDBB7C8C69AA8AC
|
||||||
|
</palette>
|
||||||
|
</flame>
|
||||||
|
<flame name="baseline" version="Apophysis 2.08 beta" size="555 428" center="0 0" scale="138.75" oversample="1" filter="0.2" quality="1" background="0 0 0" brightness="4" gamma="4" >
|
||||||
|
<xform weight="0.5" color="0" linear="1" disc="-0.934" coefs="0.982996 0 0 0.982996 -0.219512 -0.1875" />
|
||||||
|
<xform weight="0.5" color="0" swirl="0.156" polar="0.778" coefs="0.966511 0.256624 -0.256624 0.966511 0.050305 -0.235518" />
|
||||||
|
<palette count="256" format="RGB">
|
||||||
|
7886955967864652763240672432611E2D5D192757172255
|
||||||
|
11224F0D1D410F1A39101E350F202C0F1F23101B1E0C161C
|
||||||
|
08151A060E14040A12040D13050D12060C11050D12050D11
|
||||||
|
050B0F05080F05080D04080C04080E050912040A18030C25
|
||||||
|
0410350616450A1E560F2362122768172B63192B5D162959
|
||||||
|
13234F1020420B1E3C0B1B380D19300E1A280D18200C191E
|
||||||
|
0D1C200F1C1E0D1A1D0A171E0B171C0B1119070A15040611
|
||||||
|
03050E01050C00060C01060C03090D061213081516071012
|
||||||
|
0813160B1420081022060C24050926040728020528010429
|
||||||
|
00042F060B3B0C124717255A22396D3B4E815564955D6F9B
|
||||||
|
667AA28593AC7A8799707B875F6A784F59694751643F4A60
|
||||||
|
2633602534622536651D3162162D60162B5D16295B15275E
|
||||||
|
182B6324386D3F517F5A6B927686A992A1C1A5B1CAB8C2D4
|
||||||
|
E4EAF3EEF3F8F9FCFDFBFCFDFEFCFDFEFCFDFEFDFDFCFDFF
|
||||||
|
F5F7FBE1E6EED2D6E2C3C7D6B9BFD5AFB8D5B2B8D3B6B9D2
|
||||||
|
CCD1E6DADEEAE8EBEEE3EAEFDFEAF1D8E3EBD1DDE6BACAD8
|
||||||
|
9DB0D28199BF7790B56E87AC6C84A66B82A05C72934A5B7B
|
||||||
|
2935531F2D451626381525351524321625341727371A2B44
|
||||||
|
2536563B4D8955689E6F84B37A90BF869DCCA3B6D7B9C6DF
|
||||||
|
CAD6E7C5CDDDC0C4D3BCC1CDB9BFC7B1B6C0ACB3BFB2BBC1
|
||||||
|
BCC2C6D8DEE1E2E7EBECF0F5EDF1F6EFF3F8E9EFF7DDE3EF
|
||||||
|
BAC0D8ABB1D19CA3CA98A1CA949FCB8E9BD097A2D5A9B3E2
|
||||||
|
BBC6EADFE4F4E3EAF7E8F1FBE8F3FADEE9EECAD8E4B3C3D9
|
||||||
|
8D9AAB808DA474809E737D9A737B977178925F6D9A4E5E95
|
||||||
|
4552841B2D611524540F1C47091236080F2A080D22070C20
|
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230
posts/2023/06/flam3/baseline.flame
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230
posts/2023/06/flam3/baseline.flame
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@ -0,0 +1,230 @@
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2935531F2D451626381525351524321625341727371A2B44
|
||||||
|
2536563B4D8955689E6F84B37A90BF869DCCA3B6D7B9C6DF
|
||||||
|
CAD6E7C5CDDDC0C4D3BCC1CDB9BFC7B1B6C0ACB3BFB2BBC1
|
||||||
|
BCC2C6D8DEE1E2E7EBECF0F5EDF1F6EFF3F8E9EFF7DDE3EF
|
||||||
|
BAC0D8ABB1D19CA3CA98A1CA949FCB8E9BD097A2D5A9B3E2
|
||||||
|
BBC6EADFE4F4E3EAF7E8F1FBE8F3FADEE9EECAD8E4B3C3D9
|
||||||
|
8D9AAB808DA474809E737D9A737B977178925F6D9A4E5E95
|
||||||
|
4552841B2D611524540F1C47091236080F2A080D22070C20
|
||||||
|
11162D151E3A1A26482332532C3E5E42567557688B71839F
|
||||||
|
8C9AB0BDC6C9BEC7C9C0C9CAC9C9C6C7CAC4B4BFB9A9AEA9
|
||||||
|
9499A09198A08E97A1929C9D939FA08F9CA5899397767F82
|
||||||
|
586873343A51272F491B2542141B360E142C0A0F250B0D20
|
||||||
|
0B12270E152E1119351721461D2A5622316127387126397C
|
||||||
|
22367C253581222F7E1D2C7722317E333B824A5289636FA2
|
||||||
|
ACB3D0BAC1DAC8D0E4D5E1E7D8E3E2D0DBDBB7C8C69AA8AC
|
||||||
|
</palette>
|
||||||
|
</flame>
|
||||||
|
</Flames>
|
||||||
20
posts/2023/06/flam3/index.tsx
Normal file
20
posts/2023/06/flam3/index.tsx
Normal file
@ -0,0 +1,20 @@
|
|||||||
|
import React from "react";
|
||||||
|
import Blog from "../../../LayoutBlog";
|
||||||
|
|
||||||
|
import { Canvas } from "./0-utility";
|
||||||
|
import { gasket } from "./1-gasket";
|
||||||
|
import { renderBaseline } from "./2-variations";
|
||||||
|
|
||||||
|
export default function () {
|
||||||
|
const Layout = Blog({
|
||||||
|
title: "The fractal flame algorithm",
|
||||||
|
description: "Explaining the paper",
|
||||||
|
published: "2023-06-25",
|
||||||
|
});
|
||||||
|
return (
|
||||||
|
<Layout>
|
||||||
|
<Canvas f={gasket} />
|
||||||
|
<Canvas f={renderBaseline} />
|
||||||
|
</Layout>
|
||||||
|
);
|
||||||
|
}
|
||||||
40
posts/2023/06/flam3/renders.flame
Normal file
40
posts/2023/06/flam3/renders.flame
Normal file
@ -0,0 +1,40 @@
|
|||||||
|
<Flames name="renders">
|
||||||
|
<flame name="Apophysis-230625-101" version="Apophysis 2.08 beta" size="640 480" center="0 0" scale="160" oversample="6" filter="0.4" quality="4000" background="0 0 0" brightness="4" gamma="4" >
|
||||||
|
<xform weight="0.5" color="0" linear="1" disc="-0.934" coefs="0.982996 0 0 0.982996 -0.219512 -0.1875" />
|
||||||
|
<xform weight="0.5" color="0" swirl="0.156" polar="0.778" coefs="0.966511 0.256624 -0.256624 0.966511 0.050305 -0.235518" />
|
||||||
|
<palette count="256" format="RGB">
|
||||||
|
7886955967864652763240672432611E2D5D192757172255
|
||||||
|
11224F0D1D410F1A39101E350F202C0F1F23101B1E0C161C
|
||||||
|
08151A060E14040A12040D13050D12060C11050D12050D11
|
||||||
|
050B0F05080F05080D04080C04080E050912040A18030C25
|
||||||
|
0410350616450A1E560F2362122768172B63192B5D162959
|
||||||
|
13234F1020420B1E3C0B1B380D19300E1A280D18200C191E
|
||||||
|
0D1C200F1C1E0D1A1D0A171E0B171C0B1119070A15040611
|
||||||
|
03050E01050C00060C01060C03090D061213081516071012
|
||||||
|
0813160B1420081022060C24050926040728020528010429
|
||||||
|
00042F060B3B0C124717255A22396D3B4E815564955D6F9B
|
||||||
|
667AA28593AC7A8799707B875F6A784F59694751643F4A60
|
||||||
|
2633602534622536651D3162162D60162B5D16295B15275E
|
||||||
|
182B6324386D3F517F5A6B927686A992A1C1A5B1CAB8C2D4
|
||||||
|
E4EAF3EEF3F8F9FCFDFBFCFDFEFCFDFEFCFDFEFDFDFCFDFF
|
||||||
|
F5F7FBE1E6EED2D6E2C3C7D6B9BFD5AFB8D5B2B8D3B6B9D2
|
||||||
|
CCD1E6DADEEAE8EBEEE3EAEFDFEAF1D8E3EBD1DDE6BACAD8
|
||||||
|
9DB0D28199BF7790B56E87AC6C84A66B82A05C72934A5B7B
|
||||||
|
2935531F2D451626381525351524321625341727371A2B44
|
||||||
|
2536563B4D8955689E6F84B37A90BF869DCCA3B6D7B9C6DF
|
||||||
|
CAD6E7C5CDDDC0C4D3BCC1CDB9BFC7B1B6C0ACB3BFB2BBC1
|
||||||
|
BCC2C6D8DEE1E2E7EBECF0F5EDF1F6EFF3F8E9EFF7DDE3EF
|
||||||
|
BAC0D8ABB1D19CA3CA98A1CA949FCB8E9BD097A2D5A9B3E2
|
||||||
|
BBC6EADFE4F4E3EAF7E8F1FBE8F3FADEE9EECAD8E4B3C3D9
|
||||||
|
8D9AAB808DA474809E737D9A737B977178925F6D9A4E5E95
|
||||||
|
4552841B2D611524540F1C47091236080F2A080D22070C20
|
||||||
|
11162D151E3A1A26482332532C3E5E42567557688B71839F
|
||||||
|
8C9AB0BDC6C9BEC7C9C0C9CAC9C9C6C7CAC4B4BFB9A9AEA9
|
||||||
|
9499A09198A08E97A1929C9D939FA08F9CA5899397767F82
|
||||||
|
586873343A51272F491B2542141B360E142C0A0F250B0D20
|
||||||
|
0B12270E152E1119351721461D2A5622316127387126397C
|
||||||
|
22367C253581222F7E1D2C7722317E333B824A5289636FA2
|
||||||
|
ACB3D0BAC1DAC8D0E4D5E1E7D8E3E2D0DBDBB7C8C69AA8AC
|
||||||
|
</palette>
|
||||||
|
</flame>
|
||||||
|
</Flames>
|
||||||
@ -19,6 +19,7 @@ export default defineConfig({
|
|||||||
"/": "/pages/index.tsx",
|
"/": "/pages/index.tsx",
|
||||||
"/about": "/pages/about.mdx",
|
"/about": "/pages/about.mdx",
|
||||||
"/2019/02/the-whole-world": "/posts/2019/02/the-whole-world.mdx",
|
"/2019/02/the-whole-world": "/posts/2019/02/the-whole-world.mdx",
|
||||||
|
"/2023/06/flam3": "/posts/2023/06/flam3/index.tsx",
|
||||||
}),
|
}),
|
||||||
mdx({
|
mdx({
|
||||||
remarkPlugins: [remarkFrontmatter, remarkMath, remarkMdxFrontmatter],
|
remarkPlugins: [remarkFrontmatter, remarkMath, remarkMdxFrontmatter],
|
||||||
|
|||||||
Reference in New Issue
Block a user