Forest Fire — Site Percolation Cluster Growth

Spontaneous ignition spreads through the spanning cluster near the percolation threshold

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Statistics

Grid size 80 × 80
Tree count
Burned 0
Spanning cluster
p_c (theory) ≈ 0.5927

Physics

p_c ≈ 0.5927 (site, square)

Each site is occupied (tree) with probability p. At the critical percolation threshold p_c, an infinite spanning cluster first appears. The forest fire reveals this cluster: igniting the left edge, fire spreads only through connected trees. Below p_c, fire dies out. Above p_c, it crosses the lattice.