Structure of clusters generated by random walks

The authors study the cluster structure resulting from a nearest-neighbour random walk embedded in a d-dimensional space. Each bond visited by the random walks is regarded as belonging to the cluster. The diffusion exponent and the fracton dimensional of the fractal cluster in d=3 is found to be d _w=3.5+or-0.1 and d=0.57+or-0.02, using a method of exact enumeration of random walks on these fractals.