Bond Percolation on Square Lattice

Each bond open with probability p; critical threshold p_c = 0.5 (exact, Kesten 1980)

p_c reference: 0.5000 Largest cluster: 0 nodes Largest / total: 0.00 Percolates: No
About: Bond percolation on the square lattice: each edge is independently open with probability p. Kesten (1980) proved p_c = 1/2 exactly. Below p_c only finite clusters exist; above p_c an infinite spanning cluster emerges. Cluster sizes near p_c follow a power-law distribution — a signature of self-organized criticality.