Mandelbrot explorer · grok-4.20
Render the Mandelbrot set with a smooth color gradient on a full-screen canvas, with click-and-drag to pan and mouse-wheel to zoom.
transcript · 11 messages
Render the Mandelbrot set with a smooth color gradient on a full-screen canvas, with click-and-drag to pan and mouse-wheel to zoom.
thinking
The task is to build a single-page web app that renders the Mandelbrot set with a smooth color gradient on a full-screen canvas. It should support click-and-drag to pan and mouse-wheel to zoom. Everyt...The task is to create a single-page web app in one index.html file that renders the Mandelbrot set with smooth coloring on a full-screen canvas, with click-and-drag panning and mouse-wheel zooming. No external resources, CSS in <style>, JS in <script>.
I need to implement:
- Full-screen 2D canvas.
- Mandelbrot rendering with smooth color gradient based on escape time.
- Pan: click and drag.
- Zoom: mouse wheel.
- Probably reset button or double-click to reset view.
- Keep it self-contained.
Recall Mandelbrot: for c = x + yi, iterate z = z 2 + c, z0=0, if |z| > 2 after max_iter, escapes.
For smooth: use fractional iteration count.
Standard smooth coloring: mu = n + 1 - log(log(|z|))/log(2), where n is integer iter when |z|>2.
Then color 0 to 255 based on mu mod 1 or use hue = mu * factor.
For gradient, use HSL with hue based on mu.
In JS, for each pixel, compute iter and smooth, then set pixel color.
For efficiency: use ImageData, loop over pixels, compute.
Initial view: center around 0,0 with scale to show -2 to 1 on x, -1.5 to 1.5 on y.
Variables: centerX, centerY, zoomFactor (where higher zoom means smaller range).
Scale = pixels per complex unit.
Let's define:
- centerX, centerY: complex center 0+0i
- scale: complex units per pixel (initial ~0.01 or so)
Better: zoom = units per pixel, initial 0.005 for full view.
For full screen say 1920x1080, to cover x range 3.5 units, scale = 3. 5 / 1920 ~0.0018 units/pixel.
But to make initial fixed, use fixed range and adjust center and range.
Let's go with:
let centerX = -0.75;
let centerY = 0;
let zoom = 1; // zoom=1 initial, zoom >1 zoomed in
Then viewWidth = 3 / zoom; // adjust to cover
For standard, viewWidth = 3.5 / zoom; to have range 3.5 when zoom=1.
For y, same but aspect adjusted.
For wheel: zoom *= 1.2 or 0.8 depending on direction (wheel up zoom in).
For direction: wheel deltaY positive down, but usually wheel up zooms in.
For pan: on drag, deltaX * (viewWidth / w) to update centerX -= deltaX * scaleX
Yes.
For color: use a function to map smooth iter 0 to max to color.
Let's use HSV: hue = (smooth * 0.1) % 1 , saturation 1, value 1 or something.
Then rgb = hsv2rgb(hue,1,1)
I need to implement hsv to rgb.
Yes, standard function.
For black 0 when not escaped.
If iter >= maxIter, color black.
Set maxIter = 100 or 200.
For full screen, to avoid slow, but for task ok.
Also add event listeners: mousedown, mousemove, mouseup, wheel, resize.
For resize, redraw.
Reset: double click 0,0 zoom1.
Let's start writing the code in mind.
HTML:
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>Mandelbrot Explorer</title>
<style>
body { margin: 0; overflow: hidden; background: black; }
canvas { display : block; }
#controls {
position: absolute;
top: 10px;
left: 10px;
color: white;
font-family: Arial;
z-index: 10;
}
</style>
</head>
<body>
<canvas id="canvas"></canvas>
<div id=" controls">
<button id="reset">Reset</button>
<span id="info">Drag to pan, scroll to zoom</span>
</div>
<script>
// JS code here
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
const resetBtn = document.getElementBy id('reset');
let w, h;
let centerX = -0.75;
let centerY = 0;
let zoom = 1;
const MAX_ITER = 200;
const VIEW_WIDTH = 3.5;
let dragging = false;
let startX, startY;
let startCenterX, startCenterY;
function resize() {
w = canvas.width = window.innerWidth;
h = canvas.height = window.innerHeight;
draw();
}
function draw() {
const imageData = ctx.createImageData(w, h);
const data = imageData.data;
const viewWidth = VIEW_WIDTH / zoom;
const viewHeight = viewWidth * h / w;
const minX = centerX - viewWidth / 2;
const maxX = centerX + viewWidth / 2;
const minY = centerY - viewHeight / 2;
const maxY = centerY + viewHeight / 2;
const dx = viewWidth / w;
const dy = viewHeight / h;
for (let px = 0; px < w; px++) {
for (let py = 0; py < h; py++) {
const x0 = minX + px * dx;
const y0 = maxY - py * dy; // top maxY
let zx = 0, zy = 0;
let iter = 0;
while (zx*zx + zy*zy <= 4 && iter < MAX_ITER) {
const tx = zx*zx - zy*zy + x0;
zy = 2 * zx * zy + y0;
zx = tx;
iter++;
}
let r, g, b;
if (iter >= MAX_ITER) {
r = g = b = 0;
} else {
// smooth
const z = Math.sqrt(zx*zx + zy*zy);
const smooth = iter + 1 - Math.log(Math.log(z)) / Math.log(2);
// hue = smooth * 10 % 360
const hue = (smooth * 10) % 360;
// use hsv to rgb with s=0.8, v=0.8
const rgb = hsvToRgb(hue, 0.8, 0.8);
r = rgb.r;
g = rgb.g;
b = rgb.b;
}
const idx = (py * w + px) * 4;
data[idx] = r;
data[idx+1] = g;
data[idx+2] = b;
data[idx+3] = 255;
}
}
ctx.putImageData(imageData, 0, 0);
}
function hsvToRgb(h, s, v) {
h = h % 360;
const c = v * s;
const x = c * (1 - Math.abs((h / 60) % 2 - 1));
const m = v - c;
let r1, g1, b1;
if (h < 60) {
r1 = c; g1 = x; b1 = 0;
} else if (h < 120) {
r1 = x; g1 = c; b1 = 0;
} else if (h < 180) {
r1 = 0; g1 = c; b1 = x;
} else if (h < 240) {
r1 = 0; g1 = x; b1 = c;
} else if (h < 300) {
r1 = x; g1 = 0; b1 = c;
} else {
r1 = c; g1 = 0; b1 = x;
}
return {
r: Math.round((r1 + m) * 255 ),
g: Math.round((g1 + m) * 255),
b: Math.round((b1 + m) * 255)
};
}
function updateInfo() {
// update if needed
}
function panStart(e) {
dragging = true;
startX = e.clientX ;
startY = e.clientY;
startCenterX = centerX;
startCenterY = centerY;
canvas.style.cursor = 'grabbing';
}
function panMove(e) {
if (!dragging) return;
const dx = e.index.html (16458 bytes)Successfully wrote 16458 bytes to index.html
thinking
The task is to build a single-page web app for rendering the Mandelbrot set with smooth color gradient on a full-screen canvas, with click-and-drag to pan and mouse-wheel to zoom. All in one index.htm...
{"path":"index.html","edits":[{"oldText":" @import url('https://fonts.googleapis.com/css2?family=Press+Start+2P&display=swap');\n Found 2 occurrences of edits[1] in index.html. Each oldText must be unique. Please provide more context to make it unique.
thinking
The edit failed because the oldText appeared twice. I need to make the oldText unique by including more context.
{"path":"index.html","offset":1,"limit":100}<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title>Mandelbrot Explorer</title> <style> @import url('https://fonts.googleapis.com/css2?family=Press+Start+2P&display=swap'); body { margin: 0; overflow: hidden; background: #000; color: #0ff; font-family: 'Press Start 2P', system-ui; } canvas { display: block; cursor: grab; } canvas:active { cursor: grabbing; } #overlay { position: absolute; top: 20px; left: 20px; background: rgba(0, 0, 20, 0.85); padding: 20px; border: 3px solid #0ff; box-shadow: 0 0 20px #0ff; max-width: 280px; pointer-events: none; z-index: 10; } h1 { margin: 0 0 15px 0; font-size: 18px; text-shadow: 0 0 10px #0ff; color: #0ff; } .instructions { font-size: 11px; line-height: 1.5; color: #0cc; } #info { position: absolute; top: 20px; right: 20px; background: rgba(0, 0, 20, 0.85); padding: 12px 18px; border: 2px solid #0f0; font-size: 13px; font-family: monospace; box-shadow: 0 0 15px #0f0; z-index: 10; min-width: 180px; } #controls { position: absolute; bottom: 30px; left: 50%; transform: translateX(-50%); display: flex; gap: 12px; z-index: 10; } button { background: #001122; color: #0ff; border: 2px solid #0ff; padding: 10px 20px; font-family: 'Press Start 2P', system-ui; font-size: 11px; cursor: pointer; box-shadow: 0 0 10px #0ff; transition: all 0.1s; } button:hover { background: #003355; box-shadow: 0 0 20px #0ff; } .scanline { position: absolute; top: 0; left: 0; width: 100%; height: 100%; background: linear-gradient( [398 more lines in file. Use offset=101 to continue.]
{"path":"index.html","edits":[{"oldText":" @import url('https://fonts.googleapis.com/css2?family=Press+Start+2P&display=swap');\n {"path":"index.html","edits":[{"oldText":" button {\n background: #001122;\n color: #0ff;\n border: Successfully replaced 1 block(s) in index.html.
Successfully replaced 1 block(s) in index.html.
thinking
The app is now complete: a single self-contained index.html with a full-screen canvas rendering the Mandelbrot set using smooth coloring (via the mu formula for fractional iterations). It supports:
The file `index.html` has been created in the current directory. Open it in a web browser to explore the Mandelbrot set (full-screen canvas, smooth coloring, pan via drag, zoom via mouse wheel, etc.).
TAKE IT TO CODE
A single self-contained HTML file — copy it and open in any browser, or reuse the prompt with your own pi-agent run.
RUN
EVALUATION
Smooth-colored Mandelbrot renders correctly; drag pans and wheel zooms work, click/keyboard have no effect as expected.
Vision grade · anthropic/claude-sonnet-5
MEASUREMENTS
Raw readings from the capture, not a verdict — the grade above is the only judgement. Percentages are how much of the screen changed; the measure under-reports sparse motion on a dark background.