mean cluster count per site | mean cluster density

Let a random n×n (0, 1)-matrix have entries which are 1 (with probability p) or 0 (with probability q = 1 - p). An s-cluster is an isolated group of s adjacent (i.e., horizontally or vertically connected) 1s. The counts of s-clusters of various sizes are summarized in the following table for small n×n (0, 1)-matrices (OEIS A086266). n | number of s-clusters for s = 0, 1, ... 1 | 1, 1 2 | 1, 13, 2 3 | 1, 218, 208, 78, 6, 1 4 | 1, 11506, 21172, 20262, 9560, 2593, 408, 32, 2

b-cluster | connected component | percolation theory | site percolation | s-run | Truchet tiling