Epicycle Gallery

Epicycle Gallery is a hands-on studio for Fourier series. Any closed drawing can be rebuilt as a chain of rotating circles — epicycles. Open a sketch and watch the mathematics draw. See the series, not just the formula. Each sketch splits the screen: rotating circles on top, the reconstructed path below. Play, pause, or restart a cycle. Open Epicycle Details to read every harmonic's radius, phase, and speed. A gallery of original mathematics. Simple Shapes covers hearts, roses, Lissajous figures, rolling-circle families, and other classic curves. Complex Shapes pushes the same idea into denser harmonic weaves, nested spirographs, and a constructed nautilus. Every curve in the gallery is original mathematics — no third-party characters or logos. Four labs when you want to invent. • Fourier Lab — retune harmonics, samples, and speed on any gallery curve • Circle Composer — stack circles by hand and invent new patterns • Freehand Fourier — draw a stroke and decompose it • Paste Diagram — paste point lists or a high-contrast line image; contours are extracted on your device Built to teach. Help & About explains what an epicycle is, how the discrete Fourier transform produces the circles, and how to read the screen. Reduce Motion shows the finished reconstruction immediately. Private by design. No account. No ads. No tracking. Drawings, clipboard text, and pasted images never leave your iPhone or iPad. Download Epicycle Gallery and watch rotating circles become a drawing.