Sierpinski carpet of using a L-system of six iterations. 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.
A three-dimensional version of the Sierpinski carpet is the Menger
sponge, invented by Karl Menger and sometimes mistakenly called a
Sierpinski sponge.
For an HTML approach of approximating a Sierpinski carpet, see dive into mark
.
See also
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