Structure and perimeters of percolation clusters

Abstract

Site percolation clusters are simulated at the percolation threshold on the square lattice. An algorithm for walks around each cluster is used to obtain information on its fractal geometry. The fractal dimensionality of the external perimeter is found to depend on the size of adsorbent particles used to measure it: if the vacant perimeter sites have only nearest-neighbour connectivity then the perimeter has dimension D_e=1.37+or-0.03, instead of that of the hull (D_h=1.75). The authors also measured the mass of internal dangling sites (surrounded by the backbone's 'blobs'), singly and doubly connected sites, the number of 'blobs' and the average linear distance between entry into the exit from a 'blob'.