Random walks on finitely ramified Sierpinski carpets Original Research Article

A new algorithm is presented that allows an efficient computer simulation of random walks on finitely ramified Sierpinski carpets. Instead of using a bitmap of the nth iteration of the carpet to determine allowed neighbor sites, neighbourhood relations are stored in small lookup tables and a hierarchical coordinate notation is used to give the random walker position. The resulting algorithm has low memory requirements, shows no surface effects even for extremely long walks and is well suited for modern computer architectures.