Sierpinski Carpet-Square
The Sierpinski carpet is a plane fractal first described by
Wacław Sierpiński in 1916. The carpet is one generalization of
the Cantor set to two dimensions.The technique of subdividing
a shape into smaller copies of itself, removing one or more
copies, and continuing recursively can be extended to other
shapes.
The construction of the Sierpinski carpet begins with a square.
The square is cut into 9 congruent subsquares in a 3-by-3 grid,
and the central subsquare is removed. The same procedure is
then applied recursively to the remaining 8 subsquares, ad
infinitum. It can be realised as the set of points in the unit
square whose coordinates written in base three do not both
have a digit '1' in the same position.The process of recursively
removing squares is an example of a finite subdivision rule.