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+# Mandelbrot Set Renderer
+
+A single-file, dependency-free HTML/JavaScript renderer for everyone's
+favorite infinitely-zoomable blob of math: the Mandelbrot set.
+
+![Mandelbrot set screenshot](./screenshot.png)
+
+## Usage
+
+Open `index.html` in a browser. That's it - no `npm install`, no build
+step, no bundler to configure. Just double-click the file and go stare
+into the fractal abyss.
+
+## Controls
+
+- **Click** to zoom in, **Shift+Click** to zoom back out
+- **Drag** to lasso a region and zoom into it
+- **Scroll** to zoom in/out under the cursor
+- **Reset View** when you get lost (you will get lost)
+- **Cycle Palette** to switch up the vibe (classic / fire / grayscale)
+
+Iteration count quietly ramps up the deeper you zoom, so the edges stay
+crisp instead of turning into a blurry mess.
+
+## How it works
+
+Every pixel becomes a point `c` on the complex plane. Starting from
+`z = 0`, we repeatedly compute `z = z^2 + c` and count how many
+iterations it survives before `|z|` blows past 2 and "escapes." Points
+that never escape belong to the set and get colored black; everything
+else gets shaded by how fast it fled. A couple of early-out checks
+(the main cardioid and period-2 bulb formulas) let us skip the math
+entirely for points we already know are staying put, which is the
+closest thing this renderer has to a shortcut.
diff --git a/examples/mandelbrot/index.html b/examples/mandelbrot/index.html
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+<!DOCTYPE html>
+<html lang="en">
+<head>
+<meta charset="UTF-8" />
+<title>Mandelbrot Set Renderer</title>
+<meta name="viewport" content="width=device-width, initial-scale=1" />
+<style>
+  html, body {
+    margin: 0;
+    padding: 0;
+    background: #111;
+    color: #eee;
+    font-family: system-ui, -apple-system, "Segoe UI", Roboto, sans-serif;
+    overflow: hidden;
+    height: 100%;
+  }
+  #container {
+    position: relative;
+    width: 100vw;
+    height: 100vh;
+  }
+  canvas {
+    display: block;
+    width: 100%;
+    height: 100%;
+    cursor: crosshair;
+  }
+  #panel {
+    position: absolute;
+    top: 12px;
+    left: 12px;
+    background: rgba(0, 0, 0, 0.6);
+    border: 1px solid #444;
+    border-radius: 6px;
+    padding: 10px 14px;
+    font-size: 13px;
+    line-height: 1.5;
+    max-width: 280px;
+  }
+  #panel button {
+    background: #333;
+    color: #eee;
+    border: 1px solid #555;
+    border-radius: 4px;
+    padding: 4px 10px;
+    margin: 4px 4px 0 0;
+    cursor: pointer;
+    font-size: 12px;
+  }
+  #panel button:hover {
+    background: #444;
+  }
+  #panel code {
+    color: #9cf;
+  }
+  #status {
+    margin-top: 6px;
+    opacity: 0.8;
+    font-size: 11px;
+  }
+</style>
+</head>
+<body>
+<div id="container">
+  <canvas id="mandelbrot"></canvas>
+  <div id="panel">
+    <strong>Mandelbrot Set</strong><br />
+    Click to zoom in &middot; Shift+Click to zoom out<br />
+    Drag to select a zoom region<br />
+    <button id="resetBtn">Reset View</button>
+    <button id="paletteBtn">Cycle Palette</button>
+    <div id="status">iterations: <span id="iterVal">0</span></div>
+  </div>
+</div>
+
+<script>
+(function () {
+  "use strict";
+
+  const canvas = document.getElementById("mandelbrot");
+  const ctx = canvas.getContext("2d");
+  const iterVal = document.getElementById("iterVal");
+  const resetBtn = document.getElementById("resetBtn");
+  const paletteBtn = document.getElementById("paletteBtn");
+
+  // Viewport in the complex plane.
+  const DEFAULT_VIEW = { centerX: -0.5, centerY: 0, scale: 3.0 };
+  let view = Object.assign({}, DEFAULT_VIEW);
+
+  let maxIterations = 200;
+  let paletteIndex = 0;
+  const palettes = ["classic", "fire", "grayscale"];
+
+  let dragStart = null;
+  let dragCurrent = null;
+
+  function resizeCanvas() {
+    const dpr = window.devicePixelRatio || 1;
+    canvas.width = Math.floor(window.innerWidth * dpr);
+    canvas.height = Math.floor(window.innerHeight * dpr);
+    render();
+  }
+
+  function colorFor(iter, maxIter) {
+    if (iter >= maxIter) {
+      return [0, 0, 0];
+    }
+    const t = iter / maxIter;
+    const palette = palettes[paletteIndex];
+
+    if (palette === "classic") {
+      const r = Math.floor(9 * (1 - t) * t * t * t * 255);
+      const g = Math.floor(15 * (1 - t) * (1 - t) * t * t * 255);
+      const b = Math.floor(8.5 * (1 - t) * (1 - t) * (1 - t) * t * 255);
+      return [r, g, b];
+    } else if (palette === "fire") {
+      const r = Math.floor(Math.min(255, t * 3 * 255));
+      const g = Math.floor(Math.min(255, Math.max(0, (t * 3 - 1)) * 255));
+      const b = Math.floor(Math.min(255, Math.max(0, (t * 3 - 2)) * 255));
+      return [r, g, b];
+    } else {
+      const v = Math.floor(t * 255);
+      return [v, v, v];
+    }
+  }
+
+  // Compute number of iterations for a point c = (cx, cy) using the
+  // escape-time algorithm, with an optional cardioid/bulb early-out check
+  // for performance.
+  function mandelbrotIterations(cx, cy, maxIter) {
+    // Quick rejection using the main cardioid and period-2 bulb formulas.
+    const q = (cx - 0.25) * (cx - 0.25) + cy * cy;
+    if (q * (q + (cx - 0.25)) < 0.25 * cy * cy) {
+      return maxIter;
+    }
+    if ((cx + 1) * (cx + 1) + cy * cy < 0.0625) {
+      return maxIter;
+    }
+
+    let x = 0, y = 0, x2 = 0, y2 = 0;
+    let iter = 0;
+    while (x2 + y2 <= 4 && iter < maxIter) {
+      y = 2 * x * y + cy;
+      x = x2 - y2 + cx;
+      x2 = x * x;
+      y2 = y * y;
+      iter++;
+    }
+    return iter;
+  }
+
+  function render() {
+    const width = canvas.width;
+    const height = canvas.height;
+    if (width === 0 || height === 0) return;
+
+    const imageData = ctx.createImageData(width, height);
+    const data = imageData.data;
+
+    const aspect = width / height;
+    const scaleX = view.scale * aspect;
+    const scaleY = view.scale;
+
+    for (let py = 0; py < height; py++) {
+      const cy = view.centerY + (py / height - 0.5) * scaleY;
+      for (let px = 0; px < width; px++) {
+        const cx = view.centerX + (px / width - 0.5) * scaleX;
+        const iter = mandelbrotIterations(cx, cy, maxIterations);
+        const [r, g, b] = colorFor(iter, maxIterations);
+        const idx = (py * width + px) * 4;
+        data[idx] = r;
+        data[idx + 1] = g;
+        data[idx + 2] = b;
+        data[idx + 3] = 255;
+      }
+    }
+
+    ctx.putImageData(imageData, 0, 0);
+    iterVal.textContent = String(maxIterations);
+  }
+
+  function screenToComplex(screenX, screenY) {
+    const rect = canvas.getBoundingClientRect();
+    const px = ((screenX - rect.left) / rect.width) * canvas.width;
+    const py = ((screenY - rect.top) / rect.height) * canvas.height;
+    const aspect = canvas.width / canvas.height;
+    const scaleX = view.scale * aspect;
+    const scaleY = view.scale;
+    const cx = view.centerX + (px / canvas.width - 0.5) * scaleX;
+    const cy = view.centerY + (py / canvas.height - 0.5) * scaleY;
+    return { cx, cy };
+  }
+
+  function zoomAt(cx, cy, factor) {
+    view.centerX = cx;
+    view.centerY = cy;
+    view.scale *= factor;
+    // Increase iteration count as we zoom in for better detail.
+    maxIterations = Math.min(2000, Math.round(200 + 100 * Math.log2(DEFAULT_VIEW.scale / view.scale + 1)));
+    render();
+  }
+
+  canvas.addEventListener("mousedown", (e) => {
+    dragStart = { x: e.clientX, y: e.clientY };
+  });
+
+  canvas.addEventListener("mousemove", (e) => {
+    if (dragStart) {
+      dragCurrent = { x: e.clientX, y: e.clientY };
+    }
+  });
+
+  canvas.addEventListener("mouseup", (e) => {
+    if (!dragStart) return;
+    const dx = Math.abs(e.clientX - dragStart.x);
+    const dy = Math.abs(e.clientY - dragStart.y);
+
+    if (dx > 5 && dy > 5) {
+      // Drag box zoom: zoom into the midpoint of the dragged rectangle.
+      const midX = (dragStart.x + e.clientX) / 2;
+      const midY = (dragStart.y + e.clientY) / 2;
+      const { cx, cy } = screenToComplex(midX, midY);
+      const rect = canvas.getBoundingClientRect();
+      const factor = Math.max(dx / rect.width, dy / rect.height);
+      zoomAt(cx, cy, Math.max(factor, 0.02));
+    } else {
+      // Simple click: zoom in, or zoom out with shift.
+      const { cx, cy } = screenToComplex(e.clientX, e.clientY);
+      zoomAt(cx, cy, e.shiftKey ? 2 : 0.5);
+    }
+    dragStart = null;
+    dragCurrent = null;
+  });
+
+  canvas.addEventListener("wheel", (e) => {
+    e.preventDefault();
+    const { cx, cy } = screenToComplex(e.clientX, e.clientY);
+    const factor = e.deltaY > 0 ? 1.2 : 1 / 1.2;
+    zoomAt(cx, cy, factor);
+  }, { passive: false });
+
+  resetBtn.addEventListener("click", () => {
+    view = Object.assign({}, DEFAULT_VIEW);
+    maxIterations = 200;
+    render();
+  });
+
+  paletteBtn.addEventListener("click", () => {
+    paletteIndex = (paletteIndex + 1) % palettes.length;
+    render();
+  });
+
+  window.addEventListener("resize", resizeCanvas);
+  resizeCanvas();
+})();
+</script>
+</body>
+</html>
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