Number of growth sites for diffusion at the percolation threshold

The effective exponent for d=2 describing how the number of growth sites depends on the cluster size is found to depend on the ‘‘ensemble’’ used, i.e., whether the number of visited sites or the number of time steps is kept constant. The constant-site ensemble supports the Leyvraz-Stanley prediction, while the constant-time ensemble supports the Aharony-Stauffer prediction for the growth-site fractal dimension.