Mandelbrot explorer · step-3.5-flash
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 · 6 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 user wants me to create a single-page web application that renders the Mandelbrot set with: - Full-screen canvas - Smooth color gradient - Click-and-drag to pan - Mouse-wheel to zoom This is a classic fractal visualization task. I need to write a complete HTML file with inline CSS and JavaScript. The file should be purely client-side with no external dependencies. Let me think about the implementation: 1. Canvas setup to fill the screen 2. Mandelbrot set calculation (escape time algorithm) 3. Smooth coloring using continuous iteration count or similar technique 4. Pan: update center coordinates based on drag delta 5. Zoom: update scale based on mouse wheel, zoom toward cursor position Key considerations: - Performance: Mandelbrot set calculation can be heavy. I should use Web Workers or optimize with array operations? Actually, for simplicity, I'll just do it on the main thread but with reasonable resolution. Could also use progressive rendering. - Smooth coloring: Usually we use the formula: iteration - log2(log2(|z|)) + 4 - Coordinate mapping: map screen pixels to complex plane - Pan: track mouse down/up/move - Zoom: track wheel, adjust scale, and adjust center to zoom toward mouse position Let me implement this step by step in a single HTML file.
I'll create a full-screen Mandelbrot set viewer with smooth gradients, pan, and zoom capabilities. This will be a single HTML file with all code inline.
/tmp/ws/index.html (9225 bytes)Successfully wrote 9225 bytes to /tmp/ws/index.html
thinking
The file has been written successfully. Let me verify it was created correctly by reading it back.
{"path":"/tmp/ws/index.html"}<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title>Mandelbrot Set Explorer</title> <style> * { margin: 0; padding: 0; box-sizing: border-box; } body { overflow: hidden; background: #000; font-family: 'Courier New', monospace; } canvas { display: block; width: 100vw; height: 100vh; cursor: crosshair; } #info { position: fixed; top: 10px; left: 10px; color: rgba(255, 255, 255, 0.8); background: rgba(0, 0, 0, 0.5); padding: 10px; border-radius: 4px; font-size: 12px; line-height: 1.5; z-index: 100; pointer-events: none; } #loading { position: fixed; top: 50%; left: 50%; transform: translate(-50%, -50%); color: white; font-size: 24px; text-align: center; pointer-events: none; opacity: 0; transition: opacity 0.3s; } #loading.show { opacity: 1; } </style> </head> <body> <div id="info"> <div>Center: <span id="center">0, 0</span></div> <div>Zoom: <span id="zoom">1.0</span>x</div> <div>Iterations: <span id="iters">100</span></div> <div>Drag to pan • Scroll to zoom</div> </div> <div id="loading">Rendering...</div> <canvas id="canvas"></canvas> <script> const canvas = document.getElementById('canvas'); const ctx = canvas.getContext('2d'); const infoCenter = document.getElementById('center'); const infoZoom = document.getElementById('zoom'); const infoIters = document.getElementById('iters'); const loading = document.getElementById('loading'); // View parameters let centerX = -0.5; let centerY = 0; let scale = 3.0; // complex plane width at height 1 let maxIterations = 100; let imageData = null; // Interaction state let isDragging = false; let dragStartX = 0, dragStartY = 0; let dragStartCenterX = 0, dragStartCenterY = 0; // Resize canvas to fill window function resize() { canvas.width = window.innerWidth; canvas.height = window.innerHeight; requestRender(); } // Color palette (smooth gradient) const paletteSize = 256; let palette = new Uint8ClampedArray(paletteSize * 4); function buildPalette() { for (let i = 0; i < paletteSize; i++) { const t = i / paletteSize; // Smooth gradient using cosine waves for nice transitions 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); palette[i * 4] = r; palette[i * 4 + 1] = g; palette[i * 4 + 2] = b; palette[i * 4 + 3] = 255; } } // Mandelbrot iteration with smooth coloring function mandelbrot(cx, cy) { let x = 0, y = 0; let x2 = 0, y2 = 0; let iter = 0; let escapeRadius = 16; // 4^2 while (x2 + y2 < escapeRadius && iter < maxIterations) { y = 2 * x * y + cy; x = x2 - y2 + cx; x2 = x * x; y2 = y * y; iter++; } if (iter === maxIterations) return 0; // Smooth iteration count using log2(log2(|z|)) formula const smooth = iter - Math.log2(Math.log2(x2 + y2) / 2); return smooth; } // Render the Mandelbrot set let renderRequested = false; function requestRender() { if (renderRequested) return; renderRequested = true; loading.classList.add('show'); setTimeout(() => { render(); renderRequested = false; loading.classList.remove('show'); }, 0); } function render() { const width = canvas.width; const height = canvas.height; if (!imageData || imageData.width !== width || imageData.height !== height) { imageData = ctx.createImageData(width, height); } const data = imageData.data; const aspect = width / height; const planeWidth = scale; const planeHeight = scale / aspect; const xMin = centerX - planeWidth / 2; const yMin = centerY - planeHeight / 2; const dx = planeWidth / width; const dy = planeHeight / height; for (let py = 0; py < height; py++) { for (let px = 0; px < width; px++) { const cx = xMin + px * dx; const cy = yMin + py * dy; const smooth = mandelbrot(cx, cy); if (smooth === 0) { // Inside the set - black const idx = (py * width + px) * 4; data[idx] = 0; data[idx + 1] = 0; data[idx + 2] = 0; data[idx + 3] = 255; } else { // Map smooth value to palette index const t = (smooth / maxIterations) * paletteSize; const idx = (py * width + px) * 4; const palIdx = (t | 0) % paletteSize; data[idx] = palette[palIdx * 4]; data[idx + 1] = palette[palIdx * 4 + 1]; data[idx + 2] = palette[palIdx * 4 + 2]; data[idx + 3] = 255; } } } ctx.putImageData(imageData, 0, 0); updateInfo(); } // UI updates function updateInfo() { infoCenter.textContent = `${centerX.toFixed(6)}, ${centerY.toFixed(6)}`; infoZoom.textContent = (3.0 / scale).toExponential(2); infoIters.textContent = maxIterations; } // Mouse interaction canvas.addEventListener('mousedown', (e) => { isDragging = true; dragStartX = e.clientX; dragStartY = e.clientY; dragStartCenterX = centerX; dragStartCenterY = centerY; }); window.addEventListener('mouseup', () => { isDragging = false; }); canvas.addEventListener('mousemove', (e) => { if (!isDragging) return; const dx = e.clientX - dragStartX; const dy = e.clientY - dragStartY; const aspect = canvas.width / canvas.height; const planeWidth = scale; const planeHeight = scale / aspect; centerX = dragStartCenterX - (dx / canvas.width) * planeWidth; centerY = dragStartCenterY + (dy / canvas.height) * planeHeight; requestRender(); }); canvas.addEventListener('wheel', (e) => { e.preventDefault(); const zoomFactor = e.deltaY > 0 ? 1.1 : 0.9; const oldScale = scale; // Get mouse position in canvas coordinates (normalized 0-1) const rect = canvas.getBoundingClientRect(); const mouseX = e.clientX - rect.left; const mouseY = e.clientY - rect.top; // Mouse position in complex plane before zoom const aspect = canvas.width / canvas.height; const planeWidth = scale; const planeHeight = scale / aspect; const xMin = centerX - planeWidth / 2; const yMin = centerY - planeHeight / 2; const mousePlaneX = xMin + (mouseX / canvas.width) * planeWidth; const mousePlaneY = yMin + (mouseY / canvas.height) * planeHeight; // Apply zoom scale *= zoomFactor; // Adjust center to keep mouse position fixed const newPlaneWidth = scale; const newPlaneHeight = scale / aspect; const newXMin = mousePlaneX - (mouseX / canvas.width) * newPlaneWidth; const newYMin = mousePlaneY - (mouseY / canvas.height) * newPlaneHeight; centerX = newXMin + newPlaneWidth / 2; centerY = newYMin + newPlaneHeight / 2; // Increase iterations as we zoom for detail maxIterations = Math.min(500, Math.floor(50 + (3.0 / scale) * 100)); requestRender(); }, { passive: false }); // Handle window resize window.addEventListener('resize', resize); // Initialize buildPalette(); resize(); </script> </body> </html>
thinking
The file is complete and contains: - A full-screen canvas that renders the Mandelbrot set - Smooth color gradient using a custom palette with a polynomial color ramp - Click-and-drag to pan around - Mouse wheel to zoom (with zoom-to-cursor functionality) - Displays current center coordinates, zoom level, and iteration count - Responsive design that handles window resizing - Dynamic iteration count adjustment as you zoom in for more detail Everything is self-contained in one HTML file with inline CSS and JavaScript. No external resources are used. The code should work immediately when opened in any modern browser.
I've created a complete Mandelbrot set explorer in a single HTML file. The features include: **Visualization:** - Full-screen canvas rendering - Smooth color gradient palette (custom polynomial color ramp) - The classic Mandelbrot set in black with smooth color transitions - Real-time performance with debounced rendering **Interactions:** - **Click & drag**: Pan around the complex plane - **Mouse wheel**: Zoom in/out (zooms toward cursor position) - **Dynamic iterations**: Automatically increases from 100 to 500 as you zoom in for more detail **UI Elements:** - Info panel showing current center coordinates, zoom level, and iteration count - Loading indicator during render - Crosshair cursor for precise targeting The implementation uses a smooth iteration count formula (`iter - log2(log2(|z|)/2)`) to eliminate banding and create a continuous gradient. The color palette uses polynomial functions to create a smooth rainbow-like transition. Open `index.html` in any browser to start exploring the infinite complexity of the Mandelbrot set!
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
Mandelbrot renders with smooth gradient coloring; drag pans and wheel zooms correctly, click/keys do nothing (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.