Sierpinski carpet

The Sierpinski carpet, named after Waclaw Sierpinski, is a fractal derived from a square by cutting it into 9 equal squares with a 3-by-3 grid, removing the central piece and then applying the same procedure ad infinitum to the remaining 8 squares. The Hausdorff dimension of the Carpet is ln 8/ln 3 = 1.8928... It is one generalization of the Cantor set to two dimensions (the other is Cantor Dust); higher-dimensional generalizations are possible, contained inside a cube or N-cube.

Image:sierpinski.png
Sierpinski carpet of six iterations

For an HTML approach of approximating a Sierpinski carpet, see dive into mark.

See also:

• Sierpinski triangle
• A C program that draws the triangle and carpet