Menger (Sierpinski) Sponge

The Menger sponge (or Sierpinski sponge) is a three-dimensional fractal generated beginning with a cube; at each stage, punch a square hole in the middle ninth of each face through to the other side. It’s essentially the Sierpinski carpet process in three dimensions.

The following figure shows the first four stages of the process:

Menger sponge graphics

Code available (in Mathematica 2.2 notebook form) from MathSource [dead link].

Here are the complements of the previous figures, if you’re interested.

Menger sponge complement graphics

While you’re at it, you might enjoy the Jerusalem cube or diagonal slices through the Menger cube or both.

Designed and rendered using Mathematica 2.2 for the Apple Macintosh and (much, much later) 7.0 for Microsoft Windows.

© 1995–2024 Robert Dickau

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