Mandelbrot explorer · mercury-3
Output generated Cost / run $0.0137 Runtime 66.9s
Prompt for this run
Build an interactive Mandelbrot-set explorer on a full-screen canvas. Use HTML, CSS, and JavaScript as needed. Write it to `index.html` in the current working directory using your file tools. Inline your own CSS and JavaScript. Do not use external assets, CDNs, or network requests. No third-party libraries are provided. Required behavior: - Compute the Mandelbrot set from complex coordinates and use a smooth escape-time color gradient, with a distinct color for points treated as inside the set. - Initially show the complete main cardioid and surrounding lobes. Dragging pans the image with the pointer. Mouse-wheel zoom is centered on the complex point under the cursor. - Recompute the fractal after navigation rather than scaling a static image. Use sufficient iterations to reveal new detail as the user zooms, and keep controls responsive during rendering. - Provide Reset view to restore the initial bounds. Prevent wheel navigation from scrolling the surrounding page. - Use Canvas 2D or WebGL and procedural colors; do not load a fractal image. Verify: Zoom into a recognizable boundary point and check that it stays near the cursor while additional detail is rendered. Pan the view, then use Reset view and compare with the initial framing.
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
METRICS
Transcript · 33 messages
Build an interactive Mandelbrot-set explorer on a full-screen canvas. Use HTML, CSS, and JavaScript as needed. Write it to `index.html` in the current working directory using your file tools. Inline your own CSS and JavaScript. Do not use external assets, CDNs, or network requests. No third-party libraries are provided. Required behavior: - Compute the Mandelbrot set from complex coordinates and use a smooth escape-time color gradient, with a distinct color for points treated as inside the set. - Initially show the complete main cardioid and surrounding lobes. Dragging pans the image with the pointer. Mouse-wheel zoom is centered on the complex point under the cursor. - Recompute the fractal after navigation rather than scaling a static image. Use sufficient iterations to reveal new detail as the user zooms, and keep controls responsive during rendering. - Provide Reset view to restore the initial bounds. Prevent wheel navigation from scrolling the surrounding page. - Use Canvas 2D or WebGL and procedural colors; do not load a fractal image. Verify: Zoom into a recognizable boundary point and check that it stays near the cursor while additional detail is rendered. Pan the view, then use Reset view and compare with the initial framing.
I'll build the Mandelbrot explorer as a single self-contained `index.html`. Let me start by writing the file.
index.html (11605 bytes)Successfully wrote to index.html
Now let me run the app in the browser and inspect the initial output.
{"action":"reload"}{"console":[],"dom":"ZOOM\n0.93×\nITERATIONS\n135\nCENTER\n-0.7500 0.0000i\nReset view\nDrag pan · Wheel zoom","images":"model does not support images"}
{"action":"screenshot"}{"console":[],"dom":"ZOOM\n0.93×\nITERATIONS\n135\nCENTER\n-0.7500 0.0000i\nReset view\nDrag pan · Wheel zoom","images":"model does not support images"}
{"action":"drag","x":600,"y":400,"toX":700,"toY":450}{"console":[],"dom":"ZOOM\n0.93×\nITERATIONS\n135\nCENTER\n-1.0625 -0.1562i\nReset view\nDrag pan · Wheel zoom","images":"model does not support images"}
{"action":"scroll","x":800,"y":600,"delta":100}{"console":[],"dom":"ZOOM\n0.80×\nITERATIONS\n123\nCENTER\n-1.1167 -0.1834i\nReset view\nDrag pan · Wheel zoom","images":"model does not support images"}
{"action":"scroll","x":600,"y":400,"delta":-100}{"console":[],"dom":"ZOOM\n0.93×\nITERATIONS\n135\nCENTER\n-1.0625 -0.1562i\nReset view\nDrag pan · Wheel zoom","images":"model does not support images"}
{"action":"click","x":90,"y":150}{"console":[],"dom":"ZOOM\n0.93×\nITERATIONS\n135\nCENTER\n-1.0625 -0.1562i\nReset view\nDrag pan · Wheel zoom","images":"model does not support images"}
{"action":"click","x":120,"y":105}{"console":[],"dom":"ZOOM\n0.93×\nITERATIONS\n135\nCENTER\n-0.7500 0.0000i\nReset view\nDrag pan · Wheel zoom","images":"model does not support images"}
{"action":"scroll","x":704,"y":452,"delta":-100}{"console":[],"dom":"ZOOM\n1.10×\nITERATIONS\n147\nCENTER\n-0.9718 -0.1363i\nReset view\nDrag pan · Wheel zoom","images":"model does not support images"}
{"action":"scroll","x":704,"y":452,"delta":-100}{"console":[],"dom":"ZOOM\n1.29×\nITERATIONS\n159\nCENTER\n-1.1608 -0.2525i\nReset view\nDrag pan · Wheel zoom","images":"model does not support images"}
{"action":"scroll","x":704,"y":452,"delta":-100}{"console":[],"dom":"ZOOM\n1.51×\nITERATIONS\n170\nCENTER\n-1.3218 -0.3514i\nReset view\nDrag pan · Wheel zoom","images":"model does not support images"}
{"action":"scroll","x":704,"y":452,"delta":-100}{"console":[],"dom":"ZOOM\n1.77×\nITERATIONS\n182\nCENTER\n-1.4591 -0.4358i\nReset view\nDrag pan · Wheel zoom","images":"model does not support images"}
{"action":"click","x":120,"y":105}{"console":[],"dom":"ZOOM\n0.93×\nITERATIONS\n135\nCENTER\n-0.7500 0.0000i\nReset view\nDrag pan · Wheel zoom","images":"model does not support images"}
{"command":"grep -nE \"https?://|cdn|<link|<script[^>]+src\" index.html; echo \"---\"; wc -l index.html; echo \"---\"; tail -3 index.html"}--- 352 index.html --- </script> </body> </html>
{"command":"node -e '\nconst REF=3.5, MIN=1e-12, MAX=20, aspect=1.5;\nlet st={cx:-0.75, cy:0, spanX:Math.min(2.5*aspect,MAX)};\nconst b=()=>anchor before: [ -0.4248750000000001, 0.16249999999999987 ] after: [ -0.4248750000000001, 0.16249999999999987 ] maxDrift: 0 final zoom: 2.44x, iterations: 206
Built `index.html` in `/tmp/job-x4mJHp` — a self-contained, single-file Mandelbrot explorer (inline CSS/JS, no external resources). **Implementation highlights** - Full-screen canvas (`Canvas 2D`), sized to device pixel ratio (capped at 2×), square pixels via aspect-true bounds. - Procedural computation: per-pixel escape-time with **smooth iteration count** (`n + 1 − log₂(log₂|z|)`) mapped through a cyclic cosine gradient; inside points get a distinct pure-black color. - Initial framing: complete cardioid + lobes (Im ∈ [−1.25, 1.25], center −0.75 + 0i). - Pointer drag pans; wheel zoom anchors the complex point under the cursor (analytic fixed-point transform), capped zoom range, and `preventDefault` on the wheel plus `overflow:hidden` so the page never scrolls. - Recompute-on-navigation: every pan/zoom/resize reruns the fractal — coarse preview pass for instant feedback, then full-resolution refinement, both time-budgeted (yields every ~12ms) and cancellable via a render token, so the UI stays responsive mid-render. - Iterations scale with zoom (`140 + 170·log₁₀(3.5/span)`, capped at 3000) to reveal new detail. - Reset button restores the exact initial bounds. **What I actually verified (browser tool + numeric checks)** - Console clean on load and through all interactions (no JS errors). - Initial render shows full set: zoom 0.93×, center −0.7500+0i, 135 iters. - Pan: drag R/D moved center to −1.0625−0.1562i (matches hand-computed expected pan). - Zoom: wheel events recompute — iterations rose 135→147→159→170→182 as zoom went 0.93×→1.77×; anchor invariant confirmed numerically: complex coordinate under cursor stays fixed with **0 drift** across 6 consecutive zooms. - Reset: after pan + multiple zooms, returns to exactly the initial framing (0.93×, −0.7500+0i, 135 iters). - No external network/CDN references in the file; page-scroll prevention in place. - Node re-simulation of the zoom math validated cursor anchoring and iteration scaling. **Not verified** - Visual gradient/colors (the browser tool here can't return images, so pixel-level appearance wasn't eyeballed). - Deep-zoom behavior beyond ~1.8× (iteration cap path) and live window-resize reflow in an actual browser.