The post's PDE, solved live: heat spreads and drifts with the wind, fuel burns at an Arrhenius rate. Each cell is a patch of forest (green) or a gap with nothing to burn (black: rock, water, an old burn). Tap the forest to strike lightning.
Share of the fuel a fire from the west edge burns, solved once in Python on 128 × 128 forests (4 per point, no wind). Solid line: the threshold with no wind; dashed: with a tailwind of 0.5. The yellow dot is the forest you are burning.
Model (dimensionless): ut = D Δu − w·∇u + Q·(fuel burnt per unit time) − g u, with fuel burning at the rate exp(b(1 − 1/u)). D = 0.2, g = 0.2, b = 4, time step 0.1; the fuel of a patch is burnt exactly, f ← f e−r Δt. Moving the fuel slider keeps the same forest and adds or removes patches, so the threshold can be watched as you cross it. Pure percolation, where fire passes only between touching patches, stops at p = 0.5927; the heat of this PDE reaches further, and further still downwind.