Percolation Theory
This is site percolation on a square lattice. Each cell is a tree with probability p or empty.
The percolation threshold p_c ≈ 0.5927 marks a sharp phase transition: below it, fire burns only small local clusters; above it, fire spans the whole forest (infinite cluster appears).
At p_c exactly, cluster sizes follow a power law with fractal dimension d_f = 91/48 ≈ 1.896, and the system has no characteristic length scale.
This models epidemic spreading, electrical conductance in random networks, and geological flow.