← Builds Toy · Fourier series

Draw anything with circles.

Upload an image, type a word, pick a country or draw your own. Its outline gets broken into up to 2,048 spinning circles, each turning at its own speed. Add enough of them and they redraw the shape.

N = 2approximation error = –
01 · Trace

Find the outline

The picture is reduced to its edges, and the edge points are joined into one long path, always stepping to the nearest point next.

02 · Transform

Split it into circles

A Fourier transform rewrites that path as 2,048 circles. Each spins at a fixed whole-number speed, and each one rides on the tip of the one before.

03 · Add up

Watch it converge

A few big circles give the rough shape, thousands of tiny ones add the detail. The error shows how far the drawing is from the real outline.

The same maths compresses images and music, and it's how engineers read vibration from jet engines. See it catch an engine fault before an inspection would →