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
See also:
