Monorepo for Aesthetic.Computer
aesthetic.computer
add halley piece — Halley's method fractal for z³ + 7
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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system/public/aesthetic.computer/disks/halley.mjs
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system/public/aesthetic.computer/disks/halley.mjs
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// Halley, 2026.3.02
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// Halley's method fractal for f(z) = z³ + 7.
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/* 📝 Engineering Notes
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Each pixel maps to a point z₀ in the complex plane.
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Halley's iteration: z ← z - z(z³+7) / (2z³-7)
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Color by which cube root of -7 the orbit converges to.
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Drag to pan. Use the on-screen buttons to zoom and reset.
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*/
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const { floor, min, cos, sin, PI } = Math;
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// View parameters
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let cx = 0, cy = 0, zoom = 2.5;
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let maxIter = 24;
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let dirty = true;
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// Drag state
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let dragging = false, dragX = 0, dragY = 0, dragCx = 0, dragCy = 0;
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// UI buttons
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let zoomInBtn, zoomOutBtn, resetBtn;
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// The three cube roots of -7: 7^(1/3) · e^(i(π+2πk)/3), k=0,1,2
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const cbrt7 = Math.cbrt(7);
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const roots = [
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[cbrt7 * cos(PI / 3), cbrt7 * sin(PI / 3)],
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[-cbrt7, 0],
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[cbrt7 * cos(5 * PI / 3), cbrt7 * sin(5 * PI / 3)],
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];
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// Root colors — three distinct hues
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const palette = [
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[60, 180, 255], // blue
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[255, 80, 120], // rose
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[80, 255, 160], // mint
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];
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function boot({ ui, screen }) {
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zoomInBtn = new ui.TextButton("zoom +", { bottom: 8, right: 8, screen });
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zoomOutBtn = new ui.TextButton("zoom -", { bottom: 8, right: 80, screen });
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resetBtn = new ui.TextButton("reset", { top: 8, right: 8, screen });
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}
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function paint({ screen, ink }) {
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const { width: w, height: h, pixels } = screen;
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if (dirty) {
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dirty = false;
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const scale = zoom / min(w, h);
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for (let py = 0; py < h; py++) {
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for (let px = 0; px < w; px++) {
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let zr = (px - w / 2) * scale * 2 + cx;
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let zi = (py - h / 2) * scale * 2 + cy;
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let iter = 0;
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let converged = -1;
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for (; iter < maxIter; iter++) {
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const r2 = zr * zr, i2 = zi * zi;
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if (r2 + i2 < 1e-12) break;
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const z2r = r2 - i2;
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const z2i = 2 * zr * zi;
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const z3r = z2r * zr - z2i * zi;
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const z3i = z2r * zi + z2i * zr;
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const fr = z3r + 7;
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const fi = z3i;
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const gr = 2 * z3r - 7;
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const gi = 2 * z3i;
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const nr = zr * fr - zi * fi;
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const ni = zr * fi + zi * fr;
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const denom = gr * gr + gi * gi;
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if (denom < 1e-14) break;
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zr -= (nr * gr + ni * gi) / denom;
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zi -= (ni * gr - nr * gi) / denom;
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for (let k = 0; k < 3; k++) {
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const dr = zr - roots[k][0];
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const di = zi - roots[k][1];
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if (dr * dr + di * di < 1e-6) {
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converged = k;
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break;
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}
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}
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if (converged >= 0) break;
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}
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const idx = (py * w + px) * 4;
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if (converged >= 0) {
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const t = 1 - iter / maxIter;
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const bright = 0.3 + 0.7 * t * t;
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const c = palette[converged];
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pixels[idx] = floor(c[0] * bright);
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pixels[idx + 1] = floor(c[1] * bright);
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pixels[idx + 2] = floor(c[2] * bright);
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} else {
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pixels[idx] = 8;
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pixels[idx + 1] = 6;
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pixels[idx + 2] = 12;
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}
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pixels[idx + 3] = 255;
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}
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}
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}
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// Draw buttons over the fractal
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zoomInBtn.reposition({ bottom: 8, right: 8, screen }, "zoom +");
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zoomOutBtn.reposition({ bottom: 8, right: 80, screen }, "zoom -");
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resetBtn.reposition({ top: 8, right: 8, screen }, "reset");
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const normal = ["white", "black", "black", "white"];
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const hover = ["yellow", "black", "black", "yellow"];
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zoomInBtn.paint({ ink }, normal, hover);
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zoomOutBtn.paint({ ink }, normal, hover);
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resetBtn.paint({ ink }, normal, hover);
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}
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function act({ event: e, screen, pens }) {
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const zoomFactor = 1.3;
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zoomInBtn.act(e, {
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down: () => { zoom /= zoomFactor; dirty = true; },
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}, pens?.());
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zoomOutBtn.act(e, {
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down: () => { zoom *= zoomFactor; dirty = true; },
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}, pens?.());
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resetBtn.act(e, {
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down: () => { cx = 0; cy = 0; zoom = 2.5; dirty = true; },
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}, pens?.());
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// Drag to pan
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if (e.is("touch")) {
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dragging = true;
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dragX = e.x; dragY = e.y;
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dragCx = cx; dragCy = cy;
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}
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if (e.is("draw") && dragging) {
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const scale = (zoom * 2) / min(screen.width, screen.height);
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cx = dragCx - (e.x - dragX) * scale;
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cy = dragCy - (e.y - dragY) * scale;
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dirty = true;
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}
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if (e.is("lift")) {
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dragging = false;
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}
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}
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export { boot, paint, act };
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export const noBios = true;