Mandelbrot explorer · gemma-4-31b-it
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 a single-page web app (`index.html`) that renders the Mandelbrot set.
Key requirements:
- Smooth color gradient.
- Full-screen canvas.
- Click-and-drag to pan.
- Mouse-wheel to zoom.
- All-in-one file (CSS, JS inline).
- No external resources/CDNs.
Plan:
1. HTML structure: A `<canvas>` element covering the whole viewport.
2. CSS: Reset margins/padding, make canvas fill the screen, prevent overflow/scrolling.
3. JS:
- Handle canvas resizing.
- Implement Mandelbrot calculation.
- Use "smooth coloring" algorithm (based on the iteration count and the magnitude of the complex number at the escape).
- Implement interaction logic:
- `mousedown`, `mousemove`, `mouseup` for panning.
- `wheel` for zooming (zooming into the mouse cursor).
- Efficient rendering: Since JavaScript is single-threaded, I should probably use `requestAnimationFrame` and possibly render in chunks or just optimize the inner loop. Given it's a single file, a standard loop should work, but I'll make it as efficient as possible.
Smooth Coloring Formula:
$\nu = n + 1 - \log_2(\log_2(|z|))$
where $n$ is the iteration count and $|z|$ is the magnitude of the complex number when it escapes.
Coloring strategy:
I'll use a HSL-based gradient for smooth transitions.
Implementation details:
- `centerX`, `centerY`: Center of the view in complex plane.
- `zoom`: Zoom level.
- `maxIter`: Maximum iterations to determine if a point escapes.
- `canvas.width`, `canvas.height`: Viewport size.
- Conversion between pixel coordinates and complex coordinates.
Let's write the code.{"content":"<!DOCTYPE html>\n<html lang=\"en\">\n<head>\n <meta charset=\"UTF-8\">\n <meta name=\"viewport\" content=\"width=device-wiValidation failed for tool "write": - path: must have required properties path Received arguments: { "content": "<!DOCTYPE html>\n<html lang=\"en\">\n<head>\n <meta charset=\"UTF-8\">\n <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n <title>Smooth Mandelbrot Set</title>\n <style>\n body, html {\n margin: 0;\n padding: 0;\n width: 100%;\n height: 100%;\n overflow: hidden;\n background-color: #000;\n }\n canvas {\n display: block;\n cursor: crosshair;\n }\n #ui {\n position: absolute;\n top: 10px;\n left: 10px;\n color: white;\n font-family: monospace;\n background: rgba(0, 0, 0, 0.5);\n padding: 10px;\n pointer-events: none;\n border-radius: 5px;\n }\n </style>\n</head>\n<body>\n <div id=\"ui\">\n Drag to Pan | Scroll to Zoom<br>\n <span id=\"coords\">Center: 0, 0 | Zoom: 1x</span>\n </div>\n <canvas id=\"mandelbrotCanvas\"></canvas>\n\n <script>\n const canvas = document.getElementById('mandelbrotCanvas');\n const ctx = canvas.getContext('2d');\n const coordsDisplay = document.getElementById('coords');\n\n let width, height;\n let centerX = -0.5;\n let centerY = 0;\n let zoom = 1;\n let maxIter = 256;\n\n let isDragging = false;\n let lastMouseX, lastMouseY;\n\n function resize() {\n width = window.innerWidth;\n height = window.innerHeight;\n canvas.width = width;\n canvas.height = height;\n render();\n }\n\n function render() {\n const imageData = ctx.createImageData(width, height);\n const data = imageData.data;\n\n // Aspect ratio correction\n const ratio = width / height;\n const viewWidth = 4 / zoom;\n const viewHeight = (4 / ratio) / zoom;\n\n const xMin = centerX - viewWidth / 2;\n const yMin = centerY - viewHeight / 2;\n\n for (let py = 0; py < height; py++) {\n for (let px = 0; px < width; px++) {\n // Map pixel to complex plane\n const x0 = xMin + (px / width) * viewWidth;\n const y0 = yMin + (py / height) * viewHeight;\n\n let x = 0;\n let y = 0;\n let iteration = 0;\n\n // Mandelbrot iteration: z = z^2 + c\n while (x * x + y * y <= 4 && iteration < maxIter) {\n const xTemp = x * x - y * y + x0;\n y = 2 * x * y + y0;\n x = xTemp;\n iteration++;\n }\n\n let color = 0;\n if (iteration < maxIter) {\n // Smooth coloring algorithm\n // nu = n + 1 - log2(log2(|z|))\n const mag = Math.sqrt(x * x + y * y);\n const smoothIter = iteration + 1 - Math.log2(Math.log2(mag));\n \n // Convert smooth iteration to a color\n // Use HSL for a smooth gradient\n const hue = (200 + smoothIter * 2) % 360;\n const saturation = 70;\n const lightness = 50 * (1 - Math.exp(-smoothIter / 10));\n \n const rgb = hslToRgb(hue / 360, saturation / 100, lightness / 100);\n color = (rgb[0] << 16) | (rgb[1] << 8) | rgb[2];\n } else {\n color = 0; // Inside the set is black\n }\n\n const pixIdx = (py * width + px) * 4;\n data[pixIdx] = (color >> 16) & 0xFF;\n data[pixIdx + 1] = (color >> 8) & 0xFF;\n data[pixIdx + 2] = color & 0xFF;\n data[pixIdx + 3] = 255;\n }\n }\n\n ctx.putImageData(imageData, 0, 0);\n coordsDisplay.innerText = `Center: ${centerX.toFixed(6)}, ${centerY.toFixed(6)} | Zoom: ${zoom.toExponential(2)}x`;\n }\n\n function hslToRgb(h, s, l) {\n let r, g, b;\n if (s === 0) {\n r = g = b = l;\n } else {\n const hue2rgb = (p, q, t) => {\n if (t < 0) t += 1;\n if (t > 1) t -= 1;\n if (t < 1 / 6) return p + (q - p) * 6 * t;\n if (t < 1 / 2) return q;\n if (t < 2 / 3) return p + (q - p) * (2 / 3 - t) * 6;\n return p;\n };\n const q = l < 0.5 ? l * (1 + s) : l + s - l * s;\n const p = 2 * l - q;\n r = hue2rgb(p, q, h + 1 / 3);\n g = hue2rgb(p, q, h);\n b = hue2rgb(p, q, h - 1 / 3);\n }\n return [Math.round(r * 255), Math.round(g * 255), Math.round(b * 255)];\n }\n\n // Interaction handlers\n canvas.addEventListener('mousedown', (e) => {\n isDragging = true;\n lastMouseX = e.clientX;\n lastMouseY = e.clientY;\n });\n\n window.addEventListener('mouseup', () => {\n isDragging = false;\n });\n\n window.addEventListener('mousemove', (e) => {\n if (!isDragging) return;\n\n const dx = e.clientX - lastMouseX;\n const dy = e.clientY - lastMouseY;\n \n const ratio = width / height;\n const viewWidth = 4 / zoom;\n const viewHeight = (4 / ratio) / zoom;\n\n centerX -= (dx / width) * viewWidth;\n centerY -= (dy / height) * viewHeight;\n\n lastMouseX = e.clientX;\n lastMouseY = e.clientY;\n \n render();\n });\n\n canvas.addEventListener('wheel', (e) => {\n e.preventDefault();\n\n const zoomFactor = e.deltaY > 0 ? 0.9 : 1.1;\n \n // Zoom towards the mouse cursor\n const ratio = width / height;\n const viewWidth = 4 / zoom;\n const viewHeight = (4 / ratio) / zoom;\n \n const mouseXPercent = (e.clientX / width) - 0.5;\n const mouseYPercent = (e.clientY / height) - 0.5;\n \n const worldX = centerX + mouseXPercent * viewWidth;\n const worldY = centerY + mouseYPercent * viewHeight;\n \n zoom *= zoomFactor;\n \n const newViewWidth = 4 / zoom;\n const newViewHeight = (4 / ratio) / zoom;\n \n centerX = worldX - mouseXPercent * newViewWidth;\n centerY = worldY - mouseYPercent * newViewHeight;\n\n // Adjust maxIter for deeper zooms to keep edges sharp\n maxIter = Math.floor(256 + Math.log10(zoom) * 100);\n\n render();\n }, { passive: false });\n\n window.addEventListener('resize', resize);\n resize();\n </script>\n</body>\n</html>\n" }
thinking
I forgot to include the `path` parameter in the `write` call. I must specify `path: 'index.html'`.
index.html (6674 bytes)Successfully wrote 6674 bytes to index.html
thinking
The user requested a Mandelbrot set renderer with smooth coloring, full-screen, pan, and zoom. I have implemented this in `index.html`. I optimized the inner loop slightly and used a smooth coloring algorithm.
I have created a self-contained `index.html` file that renders the Mandelbrot set. ### Features included: - **Smooth Coloring**: Uses the renormalized iteration count algorithm to eliminate "bands" and create a smooth gradient. - **Full-Screen Rendering**: The canvas automatically resizes to fill the window. - **Interactive Navigation**: - **Pan**: Click and drag the mouse to move around the complex plane. - **Zoom**: Use the mouse wheel to zoom in and out. The zoom is centered on the mouse cursor's current position for intuitive exploration. - **Dynamic Detail**: The maximum iteration count increases as you zoom deeper, ensuring the edges of the set remain sharp. - **Self-Contained**: No external libraries, CSS files, or JS files are used; everything is inline. The file `index.html` is now present in the current directory.
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 well, click/keys unaffected 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.