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Menger Sponge, a still.

Math · Built from a recipe

Menger Sponge

D4 on the major comb. Its drum rings at 283.6 Hz.

Turn it in the PlaygroundTap the picture to strike it.

A Menger sponge is a fractal.

Shelf
Math
Kind
Built from a recipe
Sound
Yes
Hands-on
Yes
Licenses
Own work (made in the page)

Its note

Splashery stretches a drumhead over this Splash's outline, twelve inches across, and finds the ways it can ring. Its lowest is 283.6 Hz, 60 cents flat of D4, 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.

The sixteen ways Menger Sponge's drum can ring, lowest first.
  1. 1284 Hz
  2. 2449 Hz
  3. 3453 Hz
  4. 4595 Hz
  5. 5611 Hz
  6. 6644 Hz
  7. 7733 Hz
  8. 8766 Hz
  9. 9811 Hz
  10. 10820 Hz
  11. 11886 Hz
  12. 12893 Hz
  13. 13968 Hz
  14. 14990 Hz
  15. 15999 Hz
  16. 161030 Hz

How to play

Tap to close and carve the holes. Hands-on: pull the small cubes out one by one.

Its controls

ControlKindRangeStart
Close and carve the holesTap
CarveButton
LevelList2 choicesLevel 3

About it

A Menger sponge is a fractal. Start with a cube and cut it into 27 smaller cubes, like a puzzle cube. Take out the one in the middle and the six at the middle of each face, leaving 20. Then do the same to each of those 20 cubes, and again, forever. Karl Menger described it in 1926.

Tap it and every hole is plugged, the smallest first, until it is a plain cube. Then it is carved again: the big cubes slide out of the faces, then the next size down, then the smallest. Pick level 2 or 3 in the Splash tab: level 2 keeps 400 little cubes, and level 3 keeps 8,000.

Details

Splats
Opens at 200,000 at Mid Detail, 59,998 at Low, and up to 999,983 at Max

Sources and credits

Made in Splashery. Its code is MIT.

Share it

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

https://splashery.app/play/?toy=menger-sponge<script type="module" src="https://splashery.app/play/src/element.js"></script> <splashery-toy toy="menger-sponge"></splashery-toy>

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