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:
“Odors from decaying food wafting through the air when the door is opened, colorful mold growing between a wet gym uniform and the damp carpet underneath, and the complete supply of bath towels scattered throughout the bedroom can become wonderful opportunities to help your teenager learn once again that the art of living in a community requires compromise, negotiation, and consensus.”
—Barbara Coloroso (20th century)