The Sierpinski carpet is a plane fractal first described by Wacław Sierpiński in 1916. The carpet is a generalization of the Cantor set to two dimensions (another is Cantor dust). Sierpiński demonstrated that this fractal is a universal curve, in that any possible one-dimensional graph, projected onto the two-dimensional plane, is homeomorphic to a subset of the Sierpinski carpet. For curves that cannot be drawn on a 2D surface without self-intersections, the corresponding universal curve is the Menger sponge, a higher-dimensional generalization.
The technique can be applied to repetitive tiling arrangement; triangle, square, hexagon being the simplest. It would seem impossible to apply it to other than rep-tile arrangements.
Read more about Sierpinski Carpet: Construction, Brownian Motion On The Sierpinski Carpet
Famous quotes containing the word carpet:
“A wind has started a little whirlpool
of sand where the carpet ought to be,
and shells lie
by the preposterous feet
of that woman who frets me, annihilates me,
O she will kill me yet.”
—Hilda Doolittle (1886–1961)