Fourier Epicycles

Any closed path is a sum of spinning circles.

Draw a closed shape with your mouse, or pick a preset below. The chain of circles redraws it.

How it works

The drawing is a list of points, read as complex numbers z = x + iy. A discrete Fourier transform decomposes them into rotating components — each a circle with its own frequency, radius (amplitude) and starting phase. Sorted by amplitude and chained tip-to-tip, the final pen traces the original curve. Fewer harmonics = a coarse approximation; all of them reproduce the path exactly.

Why it matters

The same decomposition powers JPEG, MP3, MRI reconstruction and signal filtering: complex signals become a few dominant frequencies you can keep, drop or analyse. Watching circles redraw a heart makes the abstract idea of a frequency spectrum tangible.

← Gallery