Fourier Circles

Splashery stretches a drumhead over this Splash's outline, twelve inches across, and finds the ways it can ring. Its lowest is 255.1 Hz, 44 cents flat of C4. The next fifteen are its overtones, and each one draws its own figure: sand gathers on the lines that stay still.

Tap to spin the circles. Type a word or a curve in the Splash tab.

Circles turning on circles can draw almost any closed shape, given enough of them. Each circle spins a whole number of times per loop while riding on the rim of the one before, and the tip of the last one traces the drawing. This is a Fourier series, named after Joseph Fourier, who showed in the early 1800s that repeating patterns can be built by adding up simple waves.

Tap to spin them and watch the shape drawn again. Few circles draw a wobbly shape and many draw a crisp one: set how many in the Splash tab, pick a heart, a star or a square wave, stack them in 3D, or type words (up to 40 letters) and each letter gets its own chain of circles, five letters at a time.

Made in Splashery. Its code is MIT.

This link opens it in the Playground. To put it on your own page, add the element and one script tag. Every option.