Epicycles
Draw any closed shape. A Fourier transform splits it into circles that spin at whole-number speeds, and chained tip to tip, they trace your drawing back. Use fewer circles and the shape blurs into the smooth orbit Ptolemy would have drawn.
Draw here. One continuous stroke works best.
Smoothness decides how many circles a shape needs. The Lemniscate has no corners and is within 0.03% of the original at 12 circles. The Square and Star need about 22 to get under 0.1%, because every corner leaves slow-shrinking terms behind. The Heart is the hardest of the five: the sharp dip at its top still leaves about 0.5% error at 22 circles. Your drawing is sampled at 256 points, so with every circle switched on the curve passes through all of them exactly.