Sierpinski Tetrix

Splashery stretches a drumhead over this Splash's outline, twelve inches across, and finds the ways it can ring. Its lowest is 1302.5 Hz, 21 cents flat of E6. The next fifteen are its overtones, and each one draws its own figure: sand gathers on the lines that stay still.

Tap to explode it. Hands-on: lift the small tetrahedra off and stack them back.

A Sierpinski tetrahedron is a fractal pyramid. It is made of four smaller copies of itself, each half as tall, and each of those is made of four smaller ones, and so on. It is the 3D cousin of the Sierpinski triangle, named after the mathematician Wacław Sierpiński, who described the triangle in 1915.

Tap it to explode it into its pieces; tap again to put it back together. Pick the level in the Splash tab: each level has four times as many little pyramids, so levels 3, 4 and 5 have 64, 256 and 1,024 respectively. With ✋ Hands-on on, lift the four small tetrahedra off one by one and set them down, then stack them back: brought near its place, each settles in.

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.