Wildfire spread - 2D top-down fire front

Rules of the automaton

Time advances in ticks of 0.12 s. A burning cell loses fuel at rate dF = 0.018 (1 + w)(1 - 0.65 m) per tick, where w is wind (0 to 1) and m is fuel moisture (0 to 1). Its flame intensity b grows by 0.015 per tick until the fuel falls below 0.1, then decays by 0.09 per tick; at F ≤ 0 the cell becomes ash. Each tick a burning cell ignites each unburned neighbour with probability p = 0.022 · d · (1 - m) · b, where the direction weight is d = 1 + 2w for the east neighbour (downwind) and d = 0.7 for the others. Crews randomly cut a burning cell's intensity by 45% with probability 0.012 · r per tick.

Why it behaves like a real fire

Spread is a branching process: if each burning cell ignites on average more than one neighbour before it burns out, the fire grows (supercritical); otherwise it dies. Wetter fuel and more bare ground push the process below that threshold, which is the percolation transition seen in real firebreak design. The downwind weight makes the front elongate along the wind.

Honest simplifications: a square grid with four neighbours, no slope, no spotting by embers, no crown fires, no fuel types, no time-varying weather and a wind that always blows west to east. The km2 and km/h figures reuse the 3D page's scale and are illustrative, not calibrated to a real fire. The rule is the 3D page's rule with one correction: in the 3D scene a cell that has run out of fuel keeps its flame value because of a bookkeeping quirk, so fires there never fully die out; here a burnt-out cell turns to ash and stops burning, so the 2D burned-area numbers can be lower than the 3D ones.

• Start with Hot dry gale and watch the front stretch eastward; then switch to Damp forest and watch it stall.
• Click cells ahead of the fire to paint a firebreak two cells thick and see whether it holds.
• Lower forest cover to 60% and see where the fire stops by itself.
• Enlarge the grid to 60 x 60 for a smoother front shape.