diff --git a/public/mandelbrot.html b/public/mandelbrot.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: #000;
+    overflow: hidden;
+    height: 100%;
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
+  }
+  #canvas {
+    display: block;
+    cursor: grab;
+  }
+  #canvas:active {
+    cursor: grabbing;
+  }
+  #hud {
+    position: fixed;
+    top: 10px;
+    left: 10px;
+    color: #eee;
+    background: rgba(0, 0, 0, 0.55);
+    padding: 8px 12px;
+    border-radius: 8px;
+    font-size: 12px;
+    line-height: 1.5;
+    pointer-events: none;
+    max-width: 320px;
+  }
+  #controls {
+    position: fixed;
+    top: 10px;
+    right: 10px;
+    display: flex;
+    gap: 8px;
+  }
+  button {
+    background: #222;
+    color: #eee;
+    border: 1px solid #555;
+    border-radius: 6px;
+    padding: 6px 12px;
+    font-size: 13px;
+    cursor: pointer;
+  }
+  button:hover {
+    background: #333;
+  }
+  #loading {
+    position: fixed;
+    bottom: 10px;
+    left: 10px;
+    color: #888;
+    font-size: 11px;
+  }
+</style>
+</head>
+<body>
+<canvas id="canvas"></canvas>
+<div id="hud">
+  <div><strong>Mandelbrot Set</strong></div>
+  <div>Center: <span id="hud-center">-0.5, 0</span></div>
+  <div>Zoom: <span id="hud-zoom">1x</span></div>
+  <div>Iterations: <span id="hud-iter">100</span></div>
+  <div style="margin-top:4px;color:#aaa;">Scroll to zoom &middot; drag to pan</div>
+</div>
+<div id="controls">
+  <button id="reset-btn">Reset</button>
+</div>
+<div id="loading"></div>
+
+<script>
+(function () {
+  "use strict";
+
+  const canvas = document.getElementById("canvas");
+  const ctx = canvas.getContext("2d");
+  const hudCenter = document.getElementById("hud-center");
+  const hudZoom = document.getElementById("hud-zoom");
+  const hudIter = document.getElementById("hud-iter");
+  const resetBtn = document.getElementById("reset-btn");
+  const loadingEl = document.getElementById("loading");
+
+  // View state: center point in the complex plane and vertical span it covers.
+  const DEFAULT_VIEW = { centerX: -0.5, centerY: 0, scale: 3.0 };
+  let view = Object.assign({}, DEFAULT_VIEW);
+
+  let width = 0;
+  let height = 0;
+  let dpr = Math.max(1, window.devicePixelRatio || 1);
+  let imageData = null;
+  let renderToken = 0;
+
+  function resize() {
+    width = window.innerWidth;
+    height = window.innerHeight;
+    canvas.width = Math.floor(width * dpr);
+    canvas.height = Math.floor(height * dpr);
+    canvas.style.width = width + "px";
+    canvas.style.height = height + "px";
+    imageData = ctx.createImageData(canvas.width, canvas.height);
+    render();
+  }
+
+  function maxIterationsForScale(scale) {
+    // Increase iteration count as we zoom in for more detail.
+    const zoomFactor = DEFAULT_VIEW.scale / scale;
+    const base = 100;
+    const extra = Math.max(0, Math.log2(Math.max(1, zoomFactor))) * 40;
+    return Math.min(2000, Math.round(base + extra));
+  }
+
+  // Smooth HSV -> RGB colouring based on escape-time + fractional smoothing.
+  function paletteColor(t, out, offset) {
+    // t is in [0, 1)
+    const hue = 360 * t;
+    const s = 0.8;
+    const v = 1.0;
+    const c = v * s;
+    const hh = hue / 60;
+    const x = c * (1 - Math.abs((hh % 2) - 1));
+    let r = 0, g = 0, b = 0;
+    if (hh >= 0 && hh < 1) { r = c; g = x; b = 0; }
+    else if (hh < 2) { r = x; g = c; b = 0; }
+    else if (hh < 3) { r = 0; g = c; b = x; }
+    else if (hh < 4) { r = 0; g = x; b = c; }
+    else if (hh < 5) { r = x; g = 0; b = c; }
+    else { r = c; g = 0; b = x; }
+    const m = v - c;
+    out[offset] = Math.round((r + m) * 255);
+    out[offset + 1] = Math.round((g + m) * 255);
+    out[offset + 2] = Math.round((b + m) * 255);
+    out[offset + 3] = 255;
+  }
+
+  function render() {
+    if (!imageData) return;
+    const token = ++renderToken;
+    const pw = canvas.width;
+    const ph = canvas.height;
+    const data = imageData.data;
+
+    const maxIter = maxIterationsForScale(view.scale);
+    hudIter.textContent = String(maxIter);
+    hudZoom.textContent = (DEFAULT_VIEW.scale / view.scale).toFixed(1) + "x";
+    hudCenter.textContent = view.centerX.toFixed(6) + ", " + view.centerY.toFixed(6);
+
+    const scaleY = view.scale;
+    const scaleX = (scaleY * pw) / ph;
+    const xMin = view.centerX - scaleX / 2;
+    const yMin = view.centerY - scaleY / 2;
+
+    loadingEl.textContent = "Rendering...";
+
+    // Render in horizontal chunks so the UI can update the loading indicator.
+    const chunkHeight = 48;
+    let rowStart = 0;
+
+    function renderChunk() {
+      if (token !== renderToken) return; // A newer render superseded this one.
+
+      const rowEnd = Math.min(ph, rowStart + chunkHeight);
+      for (let py = rowStart; py < rowEnd; py++) {
+        const y0 = yMin + (py / ph) * scaleY;
+        for (let px = 0; px < pw; px++) {
+          const x0 = xMin + (px / pw) * scaleX;
+
+          let x = 0, y = 0, x2 = 0, y2 = 0;
+          let iter = 0;
+
+          // Quick check: main cardioid and period-2 bulb membership test.
+          const q = (x0 - 0.25) * (x0 - 0.25) + y0 * y0;
+          if (q * (q + (x0 - 0.25)) < 0.25 * y0 * y0 ||
+              (x0 + 1) * (x0 + 1) + y0 * y0 < 0.0625) {
+            iter = maxIter;
+          } else {
+            while (x2 + y2 <= 4 && iter < maxIter) {
+              y = 2 * x * y + y0;
+              x = x2 - y2 + x0;
+              x2 = x * x;
+              y2 = y * y;
+              iter++;
+            }
+          }
+
+          const offset = (py * pw + px) * 4;
+          if (iter >= maxIter) {
+            data[offset] = 0;
+            data[offset + 1] = 0;
+            data[offset + 2] = 0;
+            data[offset + 3] = 255;
+          } else {
+            // Smooth coloring using the renormalized escape count.
+            const logZn = Math.log(x2 + y2) / 2;
+            const nu = Math.log(logZn / Math.LN2) / Math.LN2;
+            const smoothIter = iter + 1 - nu;
+            const t = (smoothIter % 64) / 64;
+            paletteColor(t, data, offset);
+          }
+        }
+      }
+
+      rowStart = rowEnd;
+      if (rowStart < ph) {
+        setTimeout(renderChunk, 0);
+      } else {
+        ctx.putImageData(imageData, 0, 0);
+        loadingEl.textContent = "";
+      }
+    }
+
+    renderChunk();
+  }
+
+  // --- Interaction: zoom with wheel, pan with drag ---
+
+  canvas.addEventListener("wheel", function (e) {
+    e.preventDefault();
+    const rect = canvas.getBoundingClientRect();
+    const px = (e.clientX - rect.left) / rect.width;
+    const py = (e.clientY - rect.top) / rect.height;
+
+    const scaleY = view.scale;
+    const scaleX = (scaleY * canvas.width) / canvas.height;
+    const xMin = view.centerX - scaleX / 2;
+    const yMin = view.centerY - scaleY / 2;
+    const mouseX = xMin + px * scaleX;
+    const mouseY = yMin + py * scaleY;
+
+    const zoomIntensity = 0.0015;
+    const factor = Math.exp(e.deltaY * zoomIntensity);
+    const newScale = Math.min(4, Math.max(1e-13, view.scale * factor));
+
+    // Zoom centered on the cursor position.
+    view.centerX = mouseX - (mouseX - view.centerX) * (newScale / view.scale);
+    view.centerY = mouseY - (mouseY - view.centerY) * (newScale / view.scale);
+    view.scale = newScale;
+
+    render();
+  }, { passive: false });
+
+  let dragging = false;
+  let lastX = 0, lastY = 0;
+
+  canvas.addEventListener("mousedown", function (e) {
+    dragging = true;
+    lastX = e.clientX;
+    lastY = e.clientY;
+  });
+
+  window.addEventListener("mousemove", function (e) {
+    if (!dragging) return;
+    const dx = e.clientX - lastX;
+    const dy = e.clientY - lastY;
+    lastX = e.clientX;
+    lastY = e.clientY;
+
+    const scaleY = view.scale;
+    const scaleX = (scaleY * canvas.width) / canvas.height;
+    view.centerX -= (dx / canvas.width) * scaleX;
+    view.centerY -= (dy / canvas.height) * scaleY;
+    render();
+  });
+
+  window.addEventListener("mouseup", function () {
+    dragging = false;
+  });
+
+  // Touch support (single-finger pan, pinch zoom).
+  let touchStartDist = null;
+  let touchStartScale = null;
+
+  canvas.addEventListener("touchstart", function (e) {
+    if (e.touches.length === 1) {
+      dragging = true;
+      lastX = e.touches[0].clientX;
+      lastY = e.touches[0].clientY;
+    } else if (e.touches.length === 2) {
+      dragging = false;
+      const dx = e.touches[0].clientX - e.touches[1].clientX;
+      const dy = e.touches[0].clientY - e.touches[1].clientY;
+      touchStartDist = Math.hypot(dx, dy);
+      touchStartScale = view.scale;
+    }
+  }, { passive: true });
+
+  canvas.addEventListener("touchmove", function (e) {
+    if (e.touches.length === 1 && dragging) {
+      const dx = e.touches[0].clientX - lastX;
+      const dy = e.touches[0].clientY - lastY;
+      lastX = e.touches[0].clientX;
+      lastY = e.touches[0].clientY;
+      const scaleY = view.scale;
+      const scaleX = (scaleY * canvas.width) / canvas.height;
+      view.centerX -= (dx / canvas.width) * scaleX;
+      view.centerY -= (dy / canvas.height) * scaleY;
+      render();
+    } else if (e.touches.length === 2 && touchStartDist) {
+      const dx = e.touches[0].clientX - e.touches[1].clientX;
+      const dy = e.touches[0].clientY - e.touches[1].clientY;
+      const dist = Math.hypot(dx, dy);
+      view.scale = Math.min(4, Math.max(1e-13, touchStartScale * (touchStartDist / dist)));
+      render();
+    }
+  }, { passive: true });
+
+  canvas.addEventListener("touchend", function (e) {
+    if (e.touches.length === 0) {
+      dragging = false;
+      touchStartDist = null;
+    }
+  });
+
+  resetBtn.addEventListener("click", function () {
+    view = Object.assign({}, DEFAULT_VIEW);
+    render();
+  });
+
+  window.addEventListener("resize", resize);
+  resize();
+})();
+</script>
+</body>
+</html>