Mandelbulb

Splashery stretches a drumhead over this Splash's outline, twelve inches across, and finds the ways it can ring. Its lowest is 312.9 Hz, 90 cents flat of E4, the nearest tine on the comb. The next fifteen are its overtones, and each one draws its own figure: sand gathers on the lines that stay still.

Tap to turn the discs. Hands-on: drag round a disc to turn it like a lock's dial.

The Mandelbulb is a 3D fractal, a cousin of the famous flat Mandelbrot set. It is made by repeating one short formula over and over for each point in space and keeping only the points that never fly away. The mathematical fractal has detail on many scales; this splash has a fixed, finite set of points. It was found in 2009 by Daniel White and Paul Nylander.

Tap it and its seven slices turn like the dials of a combination lock, neighbors in opposite directions, then back again. Each turns one seventh of a turn, because the bulb looks the same after a seventh of a turn, so it lands on the same picture. Pick the power (power n has n − 1 lobes) or a Julia bulb, which turns whole, in the Splash tab.

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.