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Refactor, fix julia bug, implement binary/linear/logarithmic membership

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This commit is contained in:
Bradlee Speice
2023-07-02 23:34:34 +00:00
parent e8ec0e0521
commit 671b97b7a0
8 changed files with 249 additions and 59 deletions
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65
posts/2023/06/flam3/2a-variations.ts
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@ -1,3 +1,5 @@
import { randomBiUnit, weightedChoice } from "./0-utility";
export type Variation = (
x: number,
y: number,
@ -17,7 +19,7 @@ function r(x: number, y: number) {
}
function theta(x: number, y: number) {
return Math.atan2(y, x);
return Math.atan2(x, y);
}
function omega(): number {
@ -28,10 +30,8 @@ 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()),
];
const thetaVal = theta(x, y) / 2 + omega();
return [sqrtR * Math.cos(thetaVal), sqrtR * Math.sin(thetaVal)];
};
export const popcorn: Variation = (x, y, transformCoefs) => {
@ -74,28 +74,9 @@ export class Transform {
}
}
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";
}
export class Flame {
x: number = Math.random() * 2 - 1;
y: number = Math.random() * 2 - 1;
protected x: number = randomBiUnit();
protected y: number = randomBiUnit();
constructor(public readonly transforms: [number, Transform][]) {}
@ -103,17 +84,35 @@ export class Flame {
const transform = weightedChoice(this.transforms);
[this.x, this.y] = transform.apply(this.x, this.y);
}
current() {
return [this.x, this.y];
}
}
export function camera(x: number, y: number, size: number): [number, number] {
// Assuming both:
// - The origin is the intended center of the output image
// - The output image is square
// ...then map points in the range (-scale, scale) to pixel coordinates.
//
// The way `flam3` actually calculates the "camera" for taking a point
// and determining which pixel to update is fairly involved. The example
// fractal was designed in Apophysis (which shows points in the range
// [-2, 2] by default) so we use that assumption to simplify the math here.
return [Math.floor(((x + 2) * size) / 4), Math.floor(((y + 2) * size) / 4)];
}
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);
// "Zoom out" the camera by a factor of 2 to match the default Apophysis scaling
// (plot all points in the range [-2, 2])
const [pixelX, pixelY] = camera(x, y, image.width);
if (
pixelX < 0 ||
pixelX > image.width ||
pixelX >= image.width ||
pixelY < 0 ||
pixelY > image.height
pixelY >= image.height
) {
return;
}
@ -132,7 +131,8 @@ export function render(flame: Flame, quality: number, image: ImageData) {
for (var i = 0; i < iterations; i++) {
flame.step();
if (i > 20) {
plot(flame.x, flame.y, image);
const [flameX, flameY] = flame.current();
plot(flameX, flameY, image);
}
}
}
@ -167,7 +167,6 @@ export const transform2 = new Transform(
);
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,
@ -177,7 +176,7 @@ export const transform3 = new Transform(
e: -1.455964,
f: -0.362059,
},
[[1, pdj(...transform3Pdj)]]
[[1, pdj(1.09358, 2.13048, 2.54127, 2.37267)]]
);
export function renderBaseline(image: ImageData) {