Skip to drawing

Fourier Epicycles

Draw any closed shape. A stack of spinning circles reconstructs it as a Fourier series.

z(t) = Σ ck e2πikt
80

0.40×
What’s a Fourier series?

Any closed drawing is a sum of circular motions. The still centre is the average position. Each extra circle spins at an integer frequency and adds a wiggle. The slider chooses how many of those wiggles to keep — crank it up and corners appear.

D draw · Space pause · [ ] harmonics · 1–8 presets

Scribble a closed shape — lift to watch it retrace