Fire spread is partly chance. Run the same landscape hundreds of times and the pattern of chance becomes a risk map: where wind, slope, dry fuel and gaps in the forest make a place likely to burn.
Green: mean over all runs. Orange: the one fire shown in 3D. Hectares against hours.
Percent of runs that burn at least this many hectares.
The science
Cellular model. The landscape is a 96 x 96 grid of 25 m cells with a fuel type each (forest, grass, rock, cleared strip, water). A burning cell can ignite each of its 8 neighbours. The probability per minute is p = 1 − exp(−r Δt / d) with r = R0(fuel) · ηM · W · S, where d is the distance to the neighbour.
Moisture. The Rothermel damping coefficient ηM = 1 − 2.59ρ + 5.11ρ² − 3.52ρ³, ρ = M / Mx, Mx = 30 %: fire does not spread at the moisture of extinction. Wind W = exp(c V cos φ) (c = 0.111 per km/h, after the exponential wind functions of Canadian fire-behaviour work), φ the angle between wind and spread direction. Slope S = exp(κ tan θ), κ = 3.5, limited to a factor of about 0.3 to 4. These are model values, not calibrated to a particular fire.
Monte Carlo. Each link needs a geometric waiting time (memoryless per minute while the source burns, 30 min in forest, 8 min in grass). One run is solved event by event. Repeating N runs gives the burn probability per cell, the mean area and its 10 to 90 percent range. The statistical error of a probability is about √(p(1−p)/N).
Simplifications. No ember spotting, no crown fire, no fuel-load differences inside a type, constant wind and moisture for the whole fire, no weather change, no suppression, no smoke physics (smoke is decoration drifting with the wind). The terrain is synthetic. Do not use for any real decision; follow local fire authorities. Models built with Blender, scene by Three.js.