Wildfire Spread (2D)

A stochastic cellular fire

The forest is a 30 x 30 grid of 1.72 m cells (the same grid and terrain as the 3D page). A burning cell tries to ignite each of its eight unburned neighbours once per step of length Δt = 0.22 model units (1 unit = 18 s). The ignition probability is

with F_wind = max(0.22, 1 + U cosθ / 17), F_slope = exp(2.8 tanφ), F_diag = 0.58 for diagonal neighbours, F_moist = max(0.08, 1 − 2.25 m). Here U is wind speed in km/h, θ the angle between the wind and the direction to the neighbour, tanφ the slope along that direction and m the fuel moisture fraction. The base rate r₀ is 0.29 (pine), 0.36 (chaparral) or 0.47 (grass).

Burn-out and spotting

A cell burns until its accumulated burn exceeds the fuel burn time, accumulating at rate (1.15 − m): t_burn = T/(1.15 − m). Above 22 km/h each flaming cell can launch an ember a few cells downwind with probability 0.00075 U Δt.

Why a head fire, flank fire and back fire

The wind factor makes the head of the fire up to several times faster than the back, so a point ignition grows into an egg-shaped ellipse. Slope does the same as wind: fire runs uphill because flames preheat the fuel above them.

Honest simplifications

• This is a teaching cellular automaton with Rothermel-style factors, not an operational fire-behaviour model (no fuel-load maps, no crown fire, no live fuel moisture dynamics).
• One rate constant per fuel type; the 1 unit = 18 s clock and the m/min readout are calibrated for display only.
• Wind is uniform and steady; there is no fire-atmosphere feedback.
• Cells with too little fuel (bare ground) never burn, so real fire breaks are represented only by that random patchiness.

• Load Calm morning: the burnt area is almost a circle. Then Red-flag wind: it stretches into an ellipse and spots ahead of the front.
• Raise fuel moisture from 8 % to 30 %: the spread factor collapses and the fire may die on its own.
• Click the map to place ignitions on a slope: fire climbs the ridge much faster than it descends.
• Switch the fuel to grass: fast but short-lived; chaparral burns slower but longer.