Bernoulli Site Percolation

Phase transition at the critical threshold p_c ≈ 0.5927 (square lattice)

Site Probability p 0.550

Grid Size 60

Action

Set p_c

Open sites: —

Largest cluster: —

Spanning: —

Clusters: —

Each site is independently open (occupied) with probability p. Yellow line marks p_c ≈ 0.5927 (Kesten 1980). Below p_c, only finite clusters form. Above p_c, an infinite spanning cluster appears — a sharp phase transition. Colors show distinct connected components (4-connectivity).