Mandeltorus

Splashery stretches a drumhead over this Splash's outline, twelve inches across, and finds the ways it can ring. Its lowest is 381.1 Hz, 49 cents flat of G4. The next fifteen are its overtones, and each one draws its own figure: sand gathers on the lines that stay still.

Tap it to spin its rings opposite ways.

The mandeltorus is a fractal: a shape whose small parts repeat the pattern of the whole, over and over, smaller and smaller. It is a piece of math art, made by a computer from a formula related to the Mandelbrot set and bent into a ring, or torus.

Tap it and its rings turn opposite ways in bands with a cyan glow, then lock back into place. The mathematician Benoit Mandelbrot made up the word "fractal" in 1975; fractal patterns turn up in nature too, in ferns, coastlines and snowflakes.

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