## Menger Sponge

A Fractal which is the 3-D analog of the Sierpinski Carpet. Let be the number of filled boxes, the length of a side of a hole, and the fractional Volume after the th iteration.

 (1) (2) (3)

The Capacity Dimension is therefore
 (4)

J. Mosely is leading an effort to construct a large Menger sponge out of old business cards.

Dickau, R. M. Menger (Sierpinski) Sponge.'' http://forum.swarthmore.edu/advanced/robertd/sponge.html.
Mosely, J. Menger's Sponge (Depth 3).'' http://world.std.com/~j9/sponge/.