sierpinski carpet recursive::For curves that cannot be drawn on a 2d surface without selfintersections, the corresponding universal curve is the , a higherdimensional generalization sierpinski carpet recursive

sierpinski carpet recursive

sierpinski carpet recursive

sierpinski carpet recursive::For curves that cannot be drawn on a 2d surface without selfintersections, the corresponding universal curve is the , a higherdimensional 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 arrangements.
The square is cut into 9 subsquares in a 3by3 grid, and the central subsquare is removed.
The same procedure is then applied to the remaining 8 subsquares, ad infinitum.
The sierpinski carpet can also be created by iterating every pixel in a square and using the following algorithm to decide if the pixel is filled.
The following implementation is valid , , and.
Martin barlow and richard bass have shown that a on the sierpinski carpet diffuses at a slower rate than an unrestricted random walk in the plane.
The existence of such an example was an open problem for many years.