speice.io/posts/2023/06/flam3/2a-variations.ts

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export type Variation = (
x: number,
y: number,
transformCoefs: Coefs
) => [number, number];
export type Coefs = {
a: number;
b: number;
c: number;
d: number;
e: number;
f: number;
};
function r(x: number, y: number) {
return Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));
}
function theta(x: number, y: number) {
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return Math.atan2(y, x);
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}
function omega(): number {
return Math.random() > 0.5 ? Math.PI : 0;
}
export const linear: Variation = (x, y) => [x, y];
export const julia: Variation = (x, y) => {
const sqrtR = Math.sqrt(r(x, y));
return [
sqrtR * Math.cos(theta(x, y) / 2 + omega()),
sqrtR * Math.sin(theta(x, y) / 2 + omega()),
];
};
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),
];
};
export class Transform {
constructor(
public readonly coefs: Coefs,
public readonly variations: [number, Variation][]
) {}
apply(x: number, y: number) {
const xformX = this.coefs.a * x + this.coefs.b * y + this.coefs.c;
const xformY = this.coefs.d * x + this.coefs.e * y + this.coefs.f;
var [curX, curY] = [0, 0];
this.variations.forEach(([blend, variation]) => {
const [varX, varY] = variation(xformX, xformY, this.coefs);
curX += blend * varX;
curY += blend * varY;
});
return [curX, curY];
}
}
export function weightedChoice<T>(choices: [number, T][]) {
const weightSum = choices.reduce(
(current, [weight, _t]) => 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 t;
}
choice -= weight;
}
throw "unreachable";
}
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export class Flame {
x: number = Math.random() * 2 - 1;
y: number = Math.random() * 2 - 1;
constructor(public readonly transforms: [number, Transform][]) {}
step() {
const transform = weightedChoice(this.transforms);
[this.x, this.y] = transform.apply(this.x, this.y);
}
}
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export function plot(x: number, y: number, image: ImageData) {
const pixelX = Math.floor(((x + 2) * image.width) / 4);
const pixelY = Math.floor(((y + 2) * image.height) / 4);
if (
pixelX < 0 ||
pixelX > image.width ||
pixelY < 0 ||
pixelY > image.height
) {
return;
}
const index = pixelY * (image.width * 4) + pixelX * 4;
image.data[index + 0] = 0;
image.data[index + 1] = 0;
image.data[index + 2] = 0;
image.data[index + 3] = 0xff;
}
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export function render(flame: Flame, quality: number, image: ImageData) {
const iterations = quality * image.width * image.height;
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for (var i = 0; i < iterations; i++) {
flame.step();
if (i > 20) {
plot(flame.x, flame.y, image);
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}
}
}
export const transform1Weight = 0.56453495;
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export const transform1 = new Transform(
{
a: -1.381068,
b: -1.381068,
c: 0,
d: 1.381068,
e: -1.381068,
f: 0,
},
[[1, julia]]
);
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export const transform2Weight = 0.013135;
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export const transform2 = new Transform(
{
a: 0.031393,
b: 0.031367,
c: 0,
d: -0.031367,
e: 0.031393,
f: 0,
},
[
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[1, linear],
[1, popcorn],
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]
);
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export const transform3Weight = 0.42233;
export const transform3Pdj = [1.09358, 2.13048, 2.54127, 2.37267] as const;
export const transform3 = new Transform(
{
a: 1.51523,
b: -3.048677,
c: 0.724135,
d: 0.740356,
e: -1.455964,
f: -0.362059,
},
[[1, pdj(...transform3Pdj)]]
);
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export function renderBaseline(image: ImageData) {
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const flame = new Flame([
[transform1Weight, transform1],
[transform2Weight, transform2],
[transform3Weight, transform3],
]);
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render(flame, 1, image);
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}