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Fourier Epicycles (2D) — Drawing with Rotating Circles

2D canvas Fourier-epicycle drawer: pick a preset shape or sketch your own closed loop, and watch a chain of rotating circles derived from the Discrete Fourier Transform redraw it.

Mathematics2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

This 2D companion computes the exact same complex Discrete Fourier Transform as the 3D version, but draws the rotating-circle chain directly on a flat canvas: pick a preset shape or sketch a closed loop with the mouse or a finger, drag the epicycle-count slider to add or remove terms, and watch the traced curve converge on the original path as more circles join the chain.

⚙ Under the hood

Canvas2D Fourier-epicycle drawer: DFT of a sampled closed path, rendered as a chain of rotating circles with a live traced curve and reconstruction slider.

fourier seriesepicyclesdiscrete fourier transformcomplex numberssignal processing

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install