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