Sierpinski Carpet
A Fractal which is constructed analogously to the Sierpinski Sieve, but usingsquares instead of triangles. Let 
be the number of black boxes, 
the length of a side of a white box, and 
the fractional Area of black boxes after the 
th iteration. Then
 |  |  | (1) |
 | |  | (2) |
 | |  | (3) |
The Capacity Dimension is therefore
 | |  | |
|  | (4) |
See also Menger Sponge, Sierpinski Sieve
References
Dickau, R. M. ``The Sierpinski Carpet.''http://forum.swarthmore.edu/advanced/robertd/carpet.html. Peitgen, H.-O.; Jürgens, H.; and Saupe, D. Chaos and Fractals: New Frontiers of Science. New York: Springer-Verlag, pp. 112-121, 1992.
Weisstein, E. W. ``Fractals.'' Mathematica notebook Fractal.m.
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