Let a random n×n (0, 1)-matrix have entries which are 1 (with probability p) or 0 (with probability q = 1 - p) and numbers are assigned to the edges of a grid. A b-cluster is an isolated group of b adjacent (i.e., horizontally or vertically connected) 1s. Let C_n be the total number of "bond" clusters, then K_B(p) congruent lim_(n->∞) (〈C_n 〉)/n^2 exists. The analytic value is known for p = 1/2, K_B(1/2) = 3/2 sqrt(3) - 41/16 = 0.0355762... (OEIS A086269; Ziff et al. 1997).

bond percolation | connected component | percolation theory | s-cluster | Truchet tiling