The Menger sponge (or Sierspinski 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:
Code
available (in Mathematica 2.2 notebook form) from MathSource [dead link].
Designed and rendered using Mathematica 2.2 for the Apple Macintosh and (much, much later) 7.0 for Microsoft Windows.
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