Percolation Explorer

Phase transitions in random lattices -- from isolated clusters to spanning paths

Controls

Status

No spanning cluster
Occupied cells--
Clusters--
Largest cluster--
Spanning?--

Phase diagram

-- P(percolation)   | p_c ~ 0.593

Top clusters

About

Each cell is occupied with probability p. Connected occupied cells form clusters. At the critical threshold pc ~ 0.5927 (square lattice, site percolation), a cluster first spans from top to bottom -- a phase transition.

Drag the slider to feel the transition. Near pc, the system is maximally sensitive -- tiny changes in p produce dramatic changes in connectivity. This is the same physics behind critical phenomena in magnets, epidemics, and forest fires.