Fractal to Euclidean crossover and scaling for random walkers on percolation clusters

Simulations of random walkers on two-dimensional (square lattice) percolation clusters were performed for a range of occupation probabilities from critical to unity. The number of distinct sites visited, over 2×105 steps, shows the conjectured scaling, crossover and superuniversaility (ds=4/3, within 1%) behavior over a wide range of site occupation probabilities. Possible deviations from superuniversality and/or scaling are discussed.