Fourier Epicycle Drawing

Draw any shape — watch rotating circles reconstruct it via Fourier series

How It Works

Any closed curve can be represented as a sum of rotating circles (epicycles). The Fourier transform finds the frequencies, amplitudes, and phases of each circle.

f(t) = Σ cₙ · e^(i·2πnt/T)
where cₙ = (1/T)∫f(t)e^(-i2πnt/T)dt

Each rotating arrow is one Fourier term.
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Components used
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Draw a closed shape on the canvas, then press Play to see Fourier epicycles reconstruct it!