Sierpinski Carpet

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 CarpetConstruction, Brownian Motion On The Sierpinski Carpet

Other articles related to "sierpinski carpet":

Brownian Motion On The Sierpinski Carpet
... The topic of Brownian motion on the Sierpinski carpet has attracted interest in recent years ... have shown that a random walk on the Sierpinski carpet diffuses at a slower rate than an unrestricted random walk in the plane ... after n steps, but the random walk on the discrete Sierpinski carpet reaches only a mean distance proportional to n1/β for some β > 2 ...

Famous quotes containing the word carpet:

    There are lots of things that you can brush under the carpet about yourself until you’re faced with somebody whose needs won’t be put off.
    Angela Carter (1940–1992)