The Fourier drawer

A chain of turning circles — each a pure sine wave — adds up to a square wave. The more circles you allow, the sharper the corners, but the little ear of overshoot at each cliff never goes away.

The maths: each circle turns at an odd multiple of the base frequency, with radius 4/(πn) for the n-th odd harmonic. Their tips sum to the wave. Read Why the Fourier drawer starts with a square wave for the why.