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Get full post/final xform working
This commit is contained in:
@ -1,142 +0,0 @@
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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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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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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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function render(transforms: Transform[], image: ImageData) {
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const weightSum = transforms.reduce((val, xform) => val + xform.weight, 0);
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var x = Math.random() * 2 - 1;
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var y = Math.random() * 2 - 1;
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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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var f = Math.random() * weightSum;
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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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// Play the chaos game
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[x, y] = transform.apply(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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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),
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[1, 0, 0, -0.934]
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),
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new Transform(
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0.5,
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new Coefs(0.966511, -0.256624, 0.050305, 0.256624, 0.966511, -0.235518),
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[0, 0.156, 0.778, 0]
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),
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],
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image
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);
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}
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189
posts/2023/06/flam3/2a-variations.ts
Normal file
189
posts/2023/06/flam3/2a-variations.ts
Normal file
@ -0,0 +1,189 @@
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export type Variation = (
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x: number,
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y: number,
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transformCoefs: Coefs
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) => [number, number];
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export type Coefs = {
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a: number;
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b: number;
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c: number;
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d: number;
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e: number;
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f: number;
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};
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function 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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function theta(x: number, y: number) {
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return Math.atan2(x, y);
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}
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function omega(): number {
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return Math.random() > 0.5 ? Math.PI : 0;
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}
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export const linear: Variation = (x, y) => [x, y];
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export const julia: Variation = (x, y) => {
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const sqrtR = Math.sqrt(r(x, y));
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return [
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sqrtR * Math.cos(theta(x, y) / 2 + omega()),
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sqrtR * Math.sin(theta(x, y) / 2 + omega()),
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];
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};
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export const popcorn: Variation = (x, y, transformCoefs) => {
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return [
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x + transformCoefs.c * Math.sin(Math.tan(3 * y)),
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y + transformCoefs.f * Math.sin(Math.tan(3 * x)),
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];
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};
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export const pdj: (
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pdjA: number,
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pdjB: number,
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pdjC: number,
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pdjD: number
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) => Variation = (pdjA, pdjB, pdjC, pdjD) => {
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return (x, y) => [
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Math.sin(pdjA * y) - Math.cos(pdjB * x),
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Math.sin(pdjC * x) - Math.cos(pdjD * y),
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];
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};
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export class Transform {
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constructor(
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public readonly coefs: Coefs,
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public readonly variations: [number, Variation][]
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) {}
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apply(x: number, y: number) {
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const xformX = this.coefs.a * x + this.coefs.b * y + this.coefs.c;
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const xformY = this.coefs.d * x + this.coefs.e * y + this.coefs.f;
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var [curX, curY] = [0, 0];
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this.variations.forEach(([blend, variation]) => {
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const [varX, varY] = variation(xformX, xformY, this.coefs);
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curX += blend * varX;
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curY += blend * varY;
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});
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return [curX, curY];
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}
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}
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export function weightedChoice<T>(choices: [number, T][]) {
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const weightSum = choices.reduce(
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(current, [weight, _t]) => current + weight,
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0
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);
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var choice = Math.random() * weightSum;
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for (var i = 0; i < choices.length; i++) {
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const [weight, t] = choices[i];
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if (choice < weight) {
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return t;
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}
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choice -= weight;
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}
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throw "unreachable";
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}
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export 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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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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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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export class Flame {
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constructor(public readonly transforms: [number, Transform][]) {}
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render(quality: number, image: ImageData) {
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var x = Math.random() * 2 - 1;
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var y = Math.random() * 2 - 1;
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const iter = quality * (image.width * image.height);
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for (var i = 0; i < iter; i++) {
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const transform = weightedChoice(this.transforms);
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// Play the chaos game
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[x, y] = transform.apply(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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}
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export const transform1Coefs: Coefs = {
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a: -1.381068,
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b: -1.381068,
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c: 0,
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d: 1.381068,
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e: -1.381068,
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f: 0,
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};
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export const transform1Weight = 0.56453495;
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export const transform2Coefs: Coefs = {
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a: 0.031393,
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b: 0.031367,
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c: 0,
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d: -0.031367,
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e: 0.031393,
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f: 0,
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};
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export const transform2Weight = 0.013135;
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export const transform3Coefs: Coefs = {
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a: 1.51523,
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b: -3.048677,
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c: 0.724135,
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d: 0.740356,
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e: -1.455964,
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f: -0.362059,
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};
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export const transform3Pdj = [1.09358, 2.13048, 2.54127, 2.37267];
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export const transform3Weight = 0.42233;
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export function renderBaseline(image: ImageData) {
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const transform1 = new Transform(transform1Coefs, [[1, julia]]);
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const transform2 = new Transform(transform2Coefs, [
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[1, linear],
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[1, popcorn],
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]);
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const [pdjA, pdjB, pdjC, pdjD] = transform3Pdj;
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const transform3 = new Transform(transform3Coefs, [
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[1, pdj(pdjA, pdjB, pdjC, pdjD)],
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]);
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|
||||
const flame = new Flame([
|
||||
[transform1Weight, transform1],
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[transform2Weight, transform2],
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[transform3Weight, transform3],
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]);
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||||
flame.render(1, image);
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}
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79
posts/2023/06/flam3/2b-post.ts
Normal file
79
posts/2023/06/flam3/2b-post.ts
Normal file
@ -0,0 +1,79 @@
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import {
|
||||
Coefs,
|
||||
Variation,
|
||||
Flame,
|
||||
Transform,
|
||||
linear,
|
||||
julia,
|
||||
popcorn,
|
||||
pdj,
|
||||
transform1Coefs,
|
||||
transform1Weight,
|
||||
transform2Coefs,
|
||||
transform2Weight,
|
||||
transform3Coefs,
|
||||
transform3Pdj,
|
||||
transform3Weight,
|
||||
} from "./2a-variations";
|
||||
|
||||
export class TransformPost extends Transform {
|
||||
constructor(
|
||||
coefs: Coefs,
|
||||
variations: [number, Variation][],
|
||||
public readonly post: Coefs
|
||||
) {
|
||||
super(coefs, variations);
|
||||
}
|
||||
|
||||
apply(x: number, y: number): [number, number] {
|
||||
const [transformX, transformY] = super.apply(x, y);
|
||||
return [
|
||||
transformX * this.post.a + transformY * this.post.b + this.post.c,
|
||||
transformX * this.post.d + transformY * this.post.e + this.post.f,
|
||||
];
|
||||
}
|
||||
}
|
||||
|
||||
export function variationPost(coefs: Coefs, variation: Variation): Variation {
|
||||
return (x, y, transformCoefs) => {
|
||||
const [varX, varY] = variation(x, y, transformCoefs);
|
||||
return [
|
||||
varX * coefs.a + varY * coefs.b + coefs.c,
|
||||
varX * coefs.d + varY * coefs.e + coefs.f,
|
||||
];
|
||||
};
|
||||
}
|
||||
|
||||
export const transform2Post: Coefs = {
|
||||
a: 1,
|
||||
b: 0,
|
||||
c: 0.241352,
|
||||
d: 0,
|
||||
e: 1,
|
||||
f: 0.271521,
|
||||
};
|
||||
|
||||
export function renderPost(image: ImageData) {
|
||||
const transform1 = new Transform(transform1Coefs, [[1, julia]]);
|
||||
|
||||
const transform2 = new TransformPost(
|
||||
transform2Coefs,
|
||||
[
|
||||
[1, linear],
|
||||
[1, popcorn],
|
||||
],
|
||||
transform2Post
|
||||
);
|
||||
|
||||
const [pdjA, pdjB, pdjC, pdjD] = transform3Pdj;
|
||||
const transform3 = new Transform(transform3Coefs, [
|
||||
[1, pdj(pdjA, pdjB, pdjC, pdjD)],
|
||||
]);
|
||||
|
||||
const flame = new Flame([
|
||||
[transform1Weight, transform1],
|
||||
[transform2Weight, transform2],
|
||||
[transform3Weight, transform3],
|
||||
]);
|
||||
flame.render(1, image);
|
||||
}
|
||||
86
posts/2023/06/flam3/2c-final.ts
Normal file
86
posts/2023/06/flam3/2c-final.ts
Normal file
@ -0,0 +1,86 @@
|
||||
import {
|
||||
Coefs,
|
||||
Flame,
|
||||
Transform,
|
||||
linear,
|
||||
julia,
|
||||
popcorn,
|
||||
pdj,
|
||||
transform1Coefs,
|
||||
transform1Weight,
|
||||
transform2Coefs,
|
||||
transform2Weight,
|
||||
transform3Coefs,
|
||||
transform3Pdj,
|
||||
transform3Weight,
|
||||
weightedChoice,
|
||||
plot,
|
||||
} from "./2a-variations";
|
||||
import { TransformPost, transform2Post } from "./2b-post";
|
||||
|
||||
export class FlameFinal extends Flame {
|
||||
constructor(
|
||||
transforms: [number, Transform][],
|
||||
public readonly final: Transform
|
||||
) {
|
||||
super(transforms);
|
||||
}
|
||||
|
||||
render(quality: number, image: ImageData) {
|
||||
var x = Math.random() * 2 - 1;
|
||||
var y = Math.random() * 2 - 1;
|
||||
|
||||
const iter = quality * (image.width * image.height);
|
||||
for (var i = 0; i < iter; i++) {
|
||||
const transform = weightedChoice(this.transforms);
|
||||
[x, y] = transform.apply(x, y);
|
||||
|
||||
// This line is the only thing that changes:
|
||||
[x, y] = this.final.apply(x, y);
|
||||
|
||||
if (i > 20) {
|
||||
plot(x, y, image);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
export const finalCoefs: Coefs = {
|
||||
a: 2,
|
||||
b: 0,
|
||||
c: 0,
|
||||
d: 0,
|
||||
e: 2,
|
||||
f: 0,
|
||||
};
|
||||
|
||||
export function renderFinal(image: ImageData) {
|
||||
const transform1 = new Transform(transform1Coefs, [[1, julia]]);
|
||||
|
||||
const transform2 = new TransformPost(
|
||||
transform2Coefs,
|
||||
[
|
||||
[1, linear],
|
||||
[1, popcorn],
|
||||
],
|
||||
transform2Post
|
||||
);
|
||||
|
||||
const [pdjA, pdjB, pdjC, pdjD] = transform3Pdj;
|
||||
const transform3 = new Transform(transform3Coefs, [
|
||||
[1, pdj(pdjA, pdjB, pdjC, pdjD)],
|
||||
]);
|
||||
|
||||
const transformFinal = new Transform(finalCoefs, [[1, julia]]);
|
||||
|
||||
const flame = new FlameFinal(
|
||||
[
|
||||
[transform1Weight, transform1],
|
||||
[transform2Weight, transform2],
|
||||
[transform3Weight, transform3],
|
||||
],
|
||||
transformFinal
|
||||
);
|
||||
|
||||
flame.render(1, image);
|
||||
}
|
||||
@ -1,9 +1,10 @@
|
||||
import React from "react";
|
||||
import Blog from "../../../LayoutBlog";
|
||||
|
||||
import { Canvas } from "./0-utility";
|
||||
import { gasket } from "./1-gasket";
|
||||
import { renderBaseline } from "./2-variations";
|
||||
import { renderBaseline } from "./2a-variations";
|
||||
import { renderPost } from "./2b-post";
|
||||
import { renderFinal } from "./2c-final";
|
||||
|
||||
export default function () {
|
||||
const Layout = Blog({
|
||||
@ -15,6 +16,8 @@ export default function () {
|
||||
<Layout>
|
||||
<Canvas f={gasket} />
|
||||
<Canvas f={renderBaseline} />
|
||||
<Canvas f={renderPost} />
|
||||
<Canvas f={renderFinal} />
|
||||
</Layout>
|
||||
);
|
||||
}
|
||||
|
||||
@ -81,6 +81,7 @@
|
||||
<xform weight="0.422330042096567" color="0" pdj="1" coefs="1.51523 0.740356 -3.048677 -1.455964 0.724135 -0.362059" pdj_a="1.09358" pdj_b="2.13048" pdj_c="2.54127" pdj_d="2.37267" />
|
||||
<xform weight="0.564534951145298" color="0" julia="1" coefs="-1.381068 1.381068 -1.381068 -1.381068 0 0" />
|
||||
<xform weight="0.0131350067581356" color="0" linear="1" popcorn="1" coefs="0.031393 -0.031367 0.031367 0.031393 0 0" post="1 0 0 1 0.241352 0.271521" />
|
||||
<finalxform color="0" symmetry="1" julia="1" coefs="2 0 0 2 0 0" />
|
||||
<palette count="256" format="RGB">
|
||||
3A78875998AA5E9DAC78B1C2599BAB36798A2252601B3438
|
||||
1823270D1215080705010101000000000002080A090A0809
|
||||
@ -116,5 +117,4 @@
|
||||
6C303A56213D3033381C343619343B15383E193A431A4E5C
|
||||
</palette>
|
||||
</flame>
|
||||
|
||||
</Flames>
|
||||
|
||||
@ -1,43 +1,4 @@
|
||||
<Flames name="variations">
|
||||
<flame name="baseline" version="Apophysis 2.08 beta" size="600 600" center="0 0" scale="150" oversample="1" filter="0.2" quality="1" background="0 0 0" brightness="4" gamma="4" >
|
||||
<xform weight="0.422330042096567" color="0" pdj="1" coefs="1.51523 0.740356 -3.048677 -1.455964 0.724135 -0.362059" pdj_a="1.09358" pdj_b="2.13048" pdj_c="2.54127" pdj_d="2.37267" />
|
||||
<xform weight="0.564534951145298" color="0" julia="1" coefs="-1.381068 1.381068 -1.381068 -1.381068 0 0" />
|
||||
<xform weight="0.0131350067581356" color="0" linear="1" popcorn="1" coefs="0.031393 -0.031367 0.031367 0.031393 0 0" />
|
||||
<palette count="256" format="RGB">
|
||||
3A78875998AA5E9DAC78B1C2599BAB36798A2252601B3438
|
||||
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|
||||
0C070D0B090A030406010101000000000000000000000000
|
||||
0A00000B0A080E1213101B1F21202830243A6737357A3C31
|
||||
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|
||||
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|
||||
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|
||||
0A0F2F101E37172E40294C5A3B6B7549798758879975A9BE
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
467E92356C81194A6B1A373F132C310E1C1F050409020205
|
||||
0000020000000101010800000B0000170A000D0D0D0D1110
|
||||
0F0E14100F141F11082619082F1904210F05111717101919
|
||||
0F1B1B101F22182C2B252E2B282D311B2E321A2E2F162E30
|
||||
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|
||||
6C303A56213D3033381C343619343B15383E193A431A4E5C
|
||||
</palette>
|
||||
</flame>
|
||||
<flame name="post xform" version="Apophysis 2.08 beta" size="600 600" center="0 0" scale="150" oversample="1" filter="0.2" quality="1" background="0 0 0" brightness="4" gamma="4" >
|
||||
<xform weight="0.422330042096567" color="0" pdj="1" coefs="1.51523 0.740356 -3.048677 -1.455964 0.724135 -0.362059" pdj_a="1.09358" pdj_b="2.13048" pdj_c="2.54127" pdj_d="2.37267" />
|
||||
<xform weight="0.564534951145298" color="0" julia="1" coefs="-1.381068 1.381068 -1.381068 -1.381068 0 0" />
|
||||
@ -117,4 +78,43 @@
|
||||
6C303A56213D3033381C343619343B15383E193A431A4E5C
|
||||
</palette>
|
||||
</flame>
|
||||
<flame name="baseline" version="Apophysis 2.08 beta" size="600 600" center="0 0" scale="150" oversample="1" filter="0.2" quality="1" background="0 0 0" brightness="4" gamma="4" >
|
||||
<xform weight="0.422330042096567" color="0" pdj="1" coefs="1.51523 0.740356 -3.048677 -1.455964 0.724135 -0.362059" pdj_a="1.09358" pdj_b="2.13048" pdj_c="2.54127" pdj_d="2.37267" />
|
||||
<xform weight="0.564534951145298" color="0.13" julia="1" coefs="-1.381068 1.381068 -1.381068 -1.381068 0 0" />
|
||||
<xform weight="0.0131350067581356" color="0.844" linear="1" popcorn="1" coefs="0.031393 -0.031367 0.031367 0.031393 0 0" />
|
||||
<palette count="256" format="RGB">
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
</palette>
|
||||
</flame>
|
||||
</Flames>
|
||||
|
||||
Reference in New Issue
Block a user