Fourier Earth

How it works

Any closed curve can be rebuilt by adding up circles that spin at whole-number speeds, each one riding on the tip of the last. This piece does that for the whole planet.

The coastlines come from Natural Earth’s 1:110m land data, projected with Equal Earth. Seventy-six landmasses are chained into a single loop: the path enters each one at its nearest point, follows the coast all the way round, then jumps to the next. Those jumps are part of the curve too, so the pen just lifts while they are drawn.

The loop is sampled at 4,096 points and run through a discrete Fourier transform, and the 1,500 largest terms are kept, biggest first. Use the slider to step from 2 terms to 1,500 and watch the error fall: thousands of kilometres with 5 terms, a few hundred with 150, about 30 with all of them. Converge mode plays through the same steps.