A percolation model of critical-cluster scaling is studied. The model allows the generation of configurations of strongly self-similar clusters by stochastic decimation on a tree. Tree traversal is controlled by a probability parameter p. At p=0 or 1, the configuration is deterministic, but, for 0<p<1, it is random. The decimation algorithm uses the Sierpinski carpet and Vicsek snowflake generators, so that the treelike character (connectedness) of the clusters can be changed continuously. Various dimensions of the (fractal) percolation cluster are calculated using boundary conditions that give correct values at the deterministic limits. The usual cluster distribution law, $n_s$∝$s^{\mathrm{-}\tau }$ with τ=d/D+1, is obeyed for stationary p in (0,1), although τ=d/D, the deterministic value at p=0 or 1. Here d is the space dimension, and D the fractal dimension of the percolation cluster. The sensitivity of τ to changes in p near p=0 or 1 allows anomalous cluster scaling, so that τ may be fixed between d/D and d/D+1, without affecting D. Possible applications of the model are discussed.

• Received 28 October 1987

DOI:https://doi.org/10.1103/PhysRevA.38.953