Fourier EpicyclesChain enough spinning circles together, each riding on the rim of the last, and the tip of the final arm can trace any closed drawing at all. It is the same idea Ptolemy used for the planets and the same maths that powers JPEG and MP3: every shape is a sum of pure rotations. The journey: walk the target curve as a complex-valued signal, run a discrete Fourier transform to get each frequency's amplitude and phase, then draw the strongest few as nested rotating arms and let the pen at the end write the shape back out.