# 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

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

See also: