A fractal, named after Waclaw Sierpinski,
that is derived from a square by cutting it into nine equal squares with
a 3 × 3 grid, removing the central piece, and then applying the same
procedure ad infinitum to the remaining eight squares. It is one of two
generalizations of the Cantor set to two dimensions; the other is the Cantor
Dust. The Carpet's Hausdorff
dimension is log 8/log 3 = 1.8928...
AND PATHOLOGICAL CURVES