Mandelbrot explorer · nemotron-3-super-120b-a12b
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 · 14 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
We need to create a single HTML file with CSS and JS that renders the Mandelbrot set with smooth color gradient, full-screen canvas, click-and-drag to pan, mouse-wheel to zoom. We need to write index.html in current directory (/workspace). Let's first check if any file exists. We'll use bash to list files, then write the HTML. Plan: - Create a canvas that fills the window. - Use JavaScript to compute Mandelbrot iteration per pixel, with smooth coloring (using normalized iteration count). - Implement pan: on mouse down, record start position, on mouse move, compute delta and adjust offset; on mouse up, stop. - Implement zoom: on wheel event, adjust scale (zoom factor) based on delta, zoom towards mouse position. - Smooth color gradient: use HSV to RGB conversion, mapping iteration count to hue. We need to ensure no external resources. Use only vanilla JS. We'll write the HTML now. Let's first check current directory.
{"command":"ls -la"}total 4 drwxrwxrwx 2 node node 64 Jul 22 16:46 . drwxr-xr-x 1 root root 4096 Jul 22 16:46 ..
thinking
Directory empty. Now create index.html.
We'll write the content using write tool.
We need to produce the full HTML. Let's craft it.
We'll include:
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>Mandelbrot Set</title>
<style>
body, html { margin:0; padding:0; width:100%; height:100%; overflow:hidden; background:#000; }
canvas { display:block; width:100%; height:100%; }
</style>
</head>
<body>
<canvas id="mandelbrot"></canvas>
<script>
// Code here
</script>
</body>
</html>
Now we need to implement the Mandelbrot rendering.
We'll define variables: canvas, ctx, width, height, offsetX, offsetY, scale, maxIterations.
We'll compute for each pixel: map to complex plane: x = (pixelX - width/2) * scale + offsetX; y = (pixelY - height/2) * scale + offsetY.
Mandelbrot iteration: zx, zy start at 0; iterate zx2 - zy2 + cx, 2*zx*zy + cy; until magnitude^2 > 4 or iterations reached.
Smooth coloring: if escaped, compute normalized iteration count: iter + 1 - log(log2(|z|))/log(2). Actually smooth = iter + 1 - log(log(sqrt(zx*zx+zy*zy)))/log(2). Use Math.log.
Then map to hue: hue = smooth * colorScale % 255; convert HSV to RGB (with saturation and value). Use a nice gradient.
We'll render using ImageData for speed.
We'll have a render() function that computes and draws.
We'll handle mouse events: mousedown, mousemove, mouseup, wheel.
Implementation details:
- Let offsetX, offsetY be the center of the view (complex number). Initially offsetX = -0.5, offsetY = 0 (center of Mandelbrot). scale: initially 3.0 / height? Actually we want to see the whole set: typical view from -2 to 1 on real axis, -1.5 to 1.5 on imaginary. So width 3, height 3. So scale = 3.0 / height (if height <= width?) Better to compute based on aspect ratio.
We'll set scaleX and scaleY separately? Simpler: maintain scale as the size of the view in complex units per pixel? Actually we can have scale factor: the vertical range = scale * height, horizontal range = scale * width. So we set initial scale such that vertical range = 3 (from -1.5 to 1.5). So scale = 3.0 / height.
Then offsetX, offsetY are the center coordinates.
When zooming, we adjust scale: scale *= factor (zoom in reduces scale). For wheel: deltaY negative => zoom in (scale *= 0.9), positive => zoom out (scale *= 1.1). Also adjust offset to keep mouse position fixed.
We need to compute mouse position in complex coordinates before zoom, then after updating scale, adjust offset so that the same complex point stays at same pixel.
Implementation:
function zoom(scaleFactor, mouseX, mouseY) {
// Convert mouse pixel to complex point before zoom
const x = (mouseX - width/2) * scale + offsetX;
const y = (mouseY - height/2) * scale + offsetY;
scale *= scaleFactor;
// New offset so that same complex point maps to same pixel
offsetX = x - (mouseX - width/2) * scale;
offsetY = y - (mouseY - height/2) * scale;
}
Now mouse drag: on mousedown set isDragging = true, startX, startY. On mousemove if dragging: dx = (mouseX - startX) * scale; dy = (mouseY - startY) * scale; offsetX -= dx; offsetY -= dy; startX = mouseX; startY = mouseY; render();
On mouseup set isDragging = false.
Wheel: prevent default, compute scaleFactor = Math.exp(-deltaY * 0.001) maybe. Use factor = deltaY < 0 ? 0.9 : 1.1.
Now we need to render smoothly. We'll requestAnimationFrame loop? We'll just render on change.
We'll also allow double-click to reset? Not required.
Now we need to write the JavaScript.
Let's create the file.
We'll use write to create index.html.
Let's craft the content as a string.
We'll need to escape backticks etc. We'll write as a plain string.
We'll use write tool.
Let's do it.
/workspace/index.html (4439 bytes)Successfully wrote 4439 bytes to /workspace/index.html
thinking
We have created index.html. Now we should verify it works. We can open it in a browser? But we are in a headless environment? We can at least check the file exists and maybe run a quick test using something like puppeteer? Not needed. The task is to render the Mandelbrot set with smooth color gradient, full-screen canvas, click-and-drag to pan, mouse-wheel to zoom. Our code should satisfy. We can optionally test by loading the file in a browser via a simple HTTP server? Not required. The task just says to write the file. Let's double-check the content for any errors: we used Math.LN2 correctly? Actually Math.LN2 is natural log of 2. For log base 2 we can use Math.log(x)/Math.LN2. In smooth color we used Math.log(Math.log(zn) / Math.LN2) / Math.LN2. Let's verify: We want nu = log(log(|z|))/log(2). Using natural log: log2(x) = ln(x)/ln(2). So log(log2(|z|))? Actually formula: smoothed = iter + 1 - log2(log(|z|)). Where log2 is base-2 log. So we need log2(log(|z|)). So compute ln(log(|z|))/ln(2). That's Math.log(Math.log(zn))/Math.LN2. Wait we used Math.log(Math.log(zn) / Math.LN2) / Math.LN2. That's wrong. Let's correct: nu = Math.log(Math.log(zn)) / Math.LN2; Because log base 2 of (ln(zn))? Actually log2(ln(zn)) = ln(ln(zn))/ln(2). So yes. But we must ensure zn > 1? For escaped points, zn > 2, so ln(zn) > 0. Good. Thus smooth = iter + 1 - nu. Let's fix. Also we need to handle case where zn <= 1? Actually if escaped, magnitude > 2, so zn > 2, ln(zn) > ~0.69, ln(ln(zn)) defined (ln(0.69) negative). That's okay. We'll edit the file. We'll use edit tool to replace the smoothColor function. Let's read the file first to see exact content.
{"path":"/workspace/index.html"}<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <title>Mandelbrot Set</title> <style> body, html { margin:0; padding:0; width:100%; height:100%; overflow:hidden; background:#000; } canvas { display:block; width:100%; height:100%; } </style> </head> <body> <canvas id="mandelbrot"></canvas> <script> const canvas = document.getElementById('mandelbrot'); const ctx = canvas.getContext('2d'); let width = window.innerWidth; let height = window.innerHeight; canvas.width = width; canvas.height = height; // View parameters let offsetX = -0.5; // center x (real) let offsetY = 0; // center y (imaginary) let scale = 3.0 / height; // vertical scale (units per pixel) const maxIterations = 1000; // Mouse state let isDragging = false; let startX, startY; // Color palette parameters const colorScale = 0.02; // controls color cycling speed function resize() { width = window.innerWidth; height = window.innerHeight; canvas.width = width; canvas.height = height; // Adjust scale to keep same vertical range? Actually scale defined as units per pixel, // so when height changes, we need to keep same vertical range: scale = verticalRange / height. // We'll keep vertical range constant: verticalRange = scale * height before resize. const verticalRange = scale * height; scale = verticalRange / height; render(); } window.addEventListener('resize', resize); function smoothColor(iter, zx, zy) { if (iter === maxIterations) return [0, 0, 0]; // inside set -> black const zn = Math.sqrt(zx*zx + zy*zy); const nu = Math.log(Math.log(zn) / Math.LN2) / Math.LN2; // smooth fractional part const smooth = iter + 1 - nu; const hue = smooth * colorScale; // Convert HSV to RGB (saturation=0.8, value=0.9) const s = 0.8, v = 0.9; let r, g, b; const i = Math.floor(hue * 6); const f = hue * 6 - i; const p = v * (1 - s); const q = v * (1 - f * s); const t = v * (1 - (1 - f) * s); switch (i % 6) { case 0: r = v; g = t; b = p; break; case 1: r = q; g = v; b = p; break; case 2: r = p; g = v; b = t; break; case 3: r = p; g = q; b = v; break; case 4: r = t; g = p; b = v; break; case 5: r = v; g = p; b = q; break; } return [Math.round(r*255), Math.round(g*255), Math.round(b*255)]; } function render() { const imageData = ctx.createImageData(width, height); const data = imageData.data; for (let py = 0; py < height; py++) { for (let px = 0; px < width; px++) { // Map pixel to complex plane const x0 = (px - width/2) * scale + offsetX; const y0 = (py - height/2) * scale + offsetY; let zx = 0, zy = 0; let iter = 0; let zx2 = 0, zy2 = 0; while (iter < maxIterations && zx2 + zy2 < 4) { zy = 2 * zx * zy + y0; zx = zx2 - zy2 + x0; zx2 = zx * zx; zy2 = zy * zy; iter++; } const color = smoothColor(iter, zx, zy); const idx = (py * width + px) * 4; data[idx] = color[0]; data[idx+1] = color[1]; data[idx+2] = color[2]; data[idx+3] = 255; } } ctx.putImageData(imageData, 0, 0); } // Mouse handlers canvas.addEventListener('mousedown', (e) => { isDragging = true; startX = e.clientX; startY = e.clientY; }); canvas.addEventListener('mousemove', (e) => { if (!isDragging) return; const dx = (e.clientX - startX) * scale; const dy = (e.clientY - startY) * scale; offsetX -= dx; offsetY -= dy; startX = e.clientX; startY = e.clientY; render(); }); canvas.addEventListener('mouseup', () => { isDragging = false; }); canvas.addEventListener('mouseleave', () => { isDragging = false; }); canvas.addEventListener('wheel', (e) => { e.preventDefault(); const scaleFactor = e.deltaY < 0 ? 0.9 : 1.1; // zoom in/out const mouseX = e.clientX; const mouseY = e.clientY; // Convert mouse to complex point before zoom const x0 = (mouseX - width/2) * scale + offsetX; const y0 = (mouseY - height/2) * scale + offsetY; scale *= scaleFactor; // Adjust offset to keep mouse point fixed offsetX = x0 - (mouseX - width/2) * scale; offsetY = y0 - (mouseY - height/2) * scale; render(); }); // Initial render render(); </script> </body> </html>
thinking
Now we need to edit smoothColor function. Replace the lines:
const zn = Math.sqrt(zx*zx + zy*zy);
const nu = Math.log(Math.log(zn) / Math.LN2) / Math.LN2; // smooth fractional part
with:
const zn = Math.sqrt(zx*zx + zy*zy);
const nu = Math.log(Math.log(zn)) / Math.LN2; // smooth fractional part
Also note we need to ensure zn > 1? Actually for escaped points zn > 2, so log(zn) > 0.69, log(log(zn)) defined (may be negative). That's fine.
Let's perform edit.
We'll replace that specific block. We'll also maybe adjust comment.
We'll use edit tool with oldText exactly matching the lines.
Let's extract the exact lines from the file:
function smoothColor(iter, zx, zy) {
if (iter === maxIterations) return [0, 0, 0]; // inside set -> black
const zn = Math.sqrt(zx*zx + zy*zy);
const nu = Math.log(Math.log(zn) / Math.LN2) / Math.LN2; // smooth fractional part
const smooth = iter + 1 - nu;
const hue = smooth * colorScale;
// Convert HSV to RGB (saturation=0.8, value=0.9)
const s = 0.8, v = 0.9;
let r, g, b;
const i = Math.floor(hue * 6);
const f = hue * 6 - i;
const p = v * (1 - s);
const q = v * (1 - f * s);
const t = v * (1 - (1 - f) * s);
switch (i % 6) {
case 0: r = v; g = t; b = p; break;
case 1: r = q; g = v; b = p; break;
case 2: r = p; g = v; b = t; break;
case 3: r = p; g = q; b = v; break;
case 4: r = t; g = p; b = v; break;
case 5: r = v; g = p; b = q; break;
}
return [Math.round(r*255), Math.round(g*255), Math.round(b*255)];
}
We need to replace the two lines after the if statement.
Let's write oldText as:
const zn = Math.sqrt(zx*zx + zy*zy);
const nu = Math.log(Math.log(zn) / Math.LN2) / Math.LN2; // smooth fractional part
newText:
const zn = Math.sqrt(zx*zx + zy*zy);
const nu = Math.log(Math.log(zn)) / Math.LN2; // smooth fractional part
Make sure indentation matches.
Now we call edit.
{"path":"/workspace/index.html","edits":[{"oldText":" const zn = Math.sqrt(zx*zx + zy*zy);\n const nu = Math.log(Math.log(zn) / Math.LSuccessfully replaced 1 block(s) in /workspace/index.html.
thinking
Now we should verify the edit succeeded by reading the function again. Let's read the smoothColor function.
{"path":"/workspace/index.html","offset":1,"limit":5000}<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <title>Mandelbrot Set</title> <style> body, html { margin:0; padding:0; width:100%; height:100%; overflow:hidden; background:#000; } canvas { display:block; width:100%; height:100%; } </style> </head> <body> <canvas id="mandelbrot"></canvas> <script> const canvas = document.getElementById('mandelbrot'); const ctx = canvas.getContext('2d'); let width = window.innerWidth; let height = window.innerHeight; canvas.width = width; canvas.height = height; // View parameters let offsetX = -0.5; // center x (real) let offsetY = 0; // center y (imaginary) let scale = 3.0 / height; // vertical scale (units per pixel) const maxIterations = 1000; // Mouse state let isDragging = false; let startX, startY; // Color palette parameters const colorScale = 0.02; // controls color cycling speed function resize() { width = window.innerWidth; height = window.innerHeight; canvas.width = width; canvas.height = height; // Adjust scale to keep same vertical range? Actually scale defined as units per pixel, // so when height changes, we need to keep same vertical range: scale = verticalRange / height. // We'll keep vertical range constant: verticalRange = scale * height before resize. const verticalRange = scale * height; scale = verticalRange / height; render(); } window.addEventListener('resize', resize); function smoothColor(iter, zx, zy) { if (iter === maxIterations) return [0, 0, 0]; // inside set -> black const zn = Math.sqrt(zx*zx + zy*zy); const nu = Math.log(Math.log(zn)) / Math.LN2; // smooth fractional part const smooth = iter + 1 - nu; const hue = smooth * colorScale; // Convert HSV to RGB (saturation=0.8, value=0.9) const s = 0.8, v = 0.9; let r, g, b; const i = Math.floor(hue * 6); const f = hue * 6 - i; const p = v * (1 - s); const q = v * (1 - f * s); const t = v * (1 - (1 - f) * s); switch (i % 6) { case 0: r = v; g = t; b = p; break; case 1: r = q; g = v; b = p; break; case 2: r = p; g = v; b = t; break; case 3: r = p; g = q; b = v; break; case 4: r = t; g = p; b = v; break; case 5: r = v; g = p; b = q; break; } return [Math.round(r*255), Math.round(g*255), Math.round(b*255)]; } function render() { const imageData = ctx.createImageData(width, height); const data = imageData.data; for (let py = 0; py < height; py++) { for (let px = 0; px < width; px++) { // Map pixel to complex plane const x0 = (px - width/2) * scale + offsetX; const y0 = (py - height/2) * scale + offsetY; let zx = 0, zy = 0; let iter = 0; let zx2 = 0, zy2 = 0; while (iter < maxIterations && zx2 + zy2 < 4) { zy = 2 * zx * zy + y0; zx = zx2 - zy2 + x0; zx2 = zx * zx; zy2 = zy * zy; iter++; } const color = smoothColor(iter, zx, zy); const idx = (py * width + px) * 4; data[idx] = color[0]; data[idx+1] = color[1]; data[idx+2] = color[2]; data[idx+3] = 255; } } ctx.putImageData(imageData, 0, 0); } // Mouse handlers canvas.addEventListener('mousedown', (e) => { isDragging = true; startX = e.clientX; startY = e.clientY; }); canvas.addEventListener('mousemove', (e) => { if (!isDragging) return; const dx = (e.clientX - startX) * scale; const dy = (e.clientY - startY) * scale; offsetX -= dx; offsetY -= dy; startX = e.clientX; startY = e.clientY; render(); }); canvas.addEventListener('mouseup', () => { isDragging = false; }); canvas.addEventListener('mouseleave', () => { isDragging = false; }); canvas.addEventListener('wheel', (e) => { e.preventDefault(); const scaleFactor = e.deltaY < 0 ? 0.9 : 1.1; // zoom in/out const mouseX = e.clientX; const mouseY = e.clientY; // Convert mouse to complex point before zoom const x0 = (mouseX - width/2) * scale + offsetX; const y0 = (mouseY - height/2) * scale + offsetY; scale *= scaleFactor; // Adjust offset to keep mouse point fixed offsetX = x0 - (mouseX - width/2) * scale; offsetY = y0 - (mouseY - height/2) * scale; render(); }); // Initial render render(); </script> </body> </html>
thinking
The edit looks correct. Now the file is ready. We should ensure there are no syntax errors. The code looks fine. Now we can consider the task complete. However, we might want to test quickly by opening in a browser? Not possible in this environment, but we can assume it's correct. We'll output final confirmation. Let's also ensure the file is named index.html in current directory (/workspace). It is. Thus we can finish.
{"command":"ls -l /workspace/index.html"}-rw-r--r-- 1 node node 4428 Jul 22 16:48 /workspace/index.html
thinking
We have the file. Task is done. Now we can send final answer.
The Mandelbrot set visualizer has been created as a single self-contained `index.html` file in the current directory. It features: - Full-screen canvas rendering - Smooth color gradient using normalized iteration count and HSV-to-RGB conversion - Click-and-drag to pan - Mouse-wheel to zoom (zoom towards cursor) - No external resources or network requests The file is ready to be opened in any web browser to explore the Mandelbrot set. ```bash ls -l /workspace/index.html ```
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, click/keys have no effect (not required).
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.