Percolation theory predicts a sharp threshold: a fire front driven with certainty can cross a random lattice only if the tree density exceeds the site-percolation threshold p_c = 0.5927 (square lattice, nearest neighbours).

Each cell is empty, tree, burning or ash. A burning cell becomes ash next step; a tree next to a burning neighbour ignites with probability p(1 + 3w) on the downwind side and p(1 - 1.1w) upwind, where w is the wind strength. Lightning ignites any tree with a small probability and ash regrows to forest.

With deterministic spread the question is pure site percolation: a fire spans the lattice only when trees form a connected cluster across it, which happens abruptly at p_c = 0.5927 (Stauffer and Aharony). Near p_c the cluster-size distribution is a power law, n(s) ~ s^-2.05, which is why forests tuned just below the threshold show fires of every size (Drossel-Schwabl self-organised criticality).

Simplifications: no fuel moisture, slope or ember spotting; wind is a multiplicative bias on the four neighbours. Educational model, not a fire-danger forecast.