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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.

Sierpinski carpet of six iterations

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