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
A three-dimensional version of the Sierpinski carpet is the Menger sponge, invented by Karl Menger and sometimes mistakenly called a Sierpinksi sponge.
For an HTML approach of approximating a Sierpinski carpet, see dive into mark.
See also:
Referenced By
CantorSet | Cantor Dust | Cantor set | Fractal | Fractal geometry | Fractal set | Fractals | Karl Menger | List of mathematical shapes | List of mathematical topics (S-U) | List of real analysis topics | Menger sponge | Serpinski gasket | Sierpinski Triangle | Sierpinski gasket | Waclaw Sierpinski
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