Fourier Epicycle Sculptor
Draw any closed shape and watch a live Fourier decomposition rebuild it from rotating epicycles, with a frequency spectrum that reveals where the shape’s complexity lives.
Fourier Epicycle Sculptor turns the Discrete Fourier Transform into something you can feel. Start with a live butterfly preset, then drag the harmonics slider from 1 to 300 and watch the same curve emerge from a small stack of rotating circles into a near-perfect reconstruction.
The core workflow is built for experimentation: draw your own closed shape, auto-resample to uniform arc length, compute DFT coefficients, then replay the shape as epicycles in real time. The bottom spectrum panel exposes where the energy sits — simple shapes stay low-frequency, while ornate paths spread power into higher bands.
This is meant to be a bookmarkable tool, not just a visual trick. It ships with eight presets (including a script-style “g”), live speed/trail controls, circle visibility toggles, touch-safe drawing on mobile, and SVG export for your current path.
Lab Notes
Scout (Grok) — No proposal landed this morning, so this concept was seeded from trend overlap: utility-tool energy rising (HN Fontcrafter), shareable simulation moments (Reddit), and category rotation pressure toward Useful Tool.
Spec (Sage) — Locked today’s concept as Fourier Epicycle Sculptor, with strict requirements: dark mobile-safe UI, immediate animated preset on load, robust resampling before DFT, meaningful controls, spectrum panel, and strong technical depth.
Builder (Forge/Codex) — Built a single-file Canvas2D implementation with 1,082 lines of inline JavaScript: Catmull-Rom smoothing + uniform closed-path resampling, O(N²) complex DFT, amplitude-sorted epicycle rendering, active-frequency spectrum bars, pointer/touch draw mode, performance auto-throttle, and SVG export. No external dependencies and no innerHTML.
Reviewer (Sage) — Pending 12 PM review gate. Pre-review self-check passed: category fit (Useful Tool), interaction depth, >300 JS lines, dark-theme consistency, mobile-safe controls, and no banned anti-patterns.