#Wildfire Analysis

#Preset Dynamics

The active-fire lifecycle is deterministic: Blaze → Fire → Ember → Char.
All $3$ active-fire states count equally as burning neighbors. Vegetation resistance determines both whether ignition occurs and its initial intensity:

Grass, Bush, Tree, and Char otherwise remain unchanged.

#Derived Metrics

Initial fuel is the first recorded Grass + Bush + Tree population. Total burn fraction is:

Vegetation-specific burn fractions use the same formula separately for Grass, Bush, and Tree. Active fire is simply Ember + Fire + Blaze.

• Fire duration: final active-fire generation minus first recorded generation.
• Peak active fire: largest active-fire count divided by initial fuel.
• Time to peak: peak generation minus first recorded generation.
• Maximum burn rate: largest positive $1$-generation loss of Grass, Bush, and Tree, divided by initial fuel.
• Cumulative burn fraction: fuel lost up to each generation, divided by initial fuel.

#Outcome Distribution

At low and intermediate densities, the seeded fire usually remains local. Median burn fraction is $0.0110\%$ at $50\%$ density and $0.0819\%$ at $80\%$. At $100\%$, the median is $87.469\%$; even a fully occupied grid does not imply total consumption because resistant Tree clusters can remain after the fire front disappears.

The detailed sweep shows a sharp crossover around $90\%$:

The IQR peaks at $90\%$, where identical density settings produce both rapid fadeouts and large burns. It then collapses at $91\%$ as large connected burns become the dominant outcome.

Rare fadeouts still persist above the central crossover. At $91\%$, $3$ of $30$ runs burn less than $1\%$, while $26$ burn more than $50\%$. At $93\%$, $1$ run burns $1.234\%$ and the other $29$ exceed $50\%$.

#Vegetation Type

Median loss follows Grass > Bush > Tree at every sampled density, matching the preset's ordered ignition thresholds.

These are fractions of each vegetation type's own initial population, not shares of all burned cells.

#Fire Dynamics

Duration is longest and most variable around the crossover. Median duration rises from $332$ generations at $89\%$ to $855.5$ at $90\%$, then falls to $738.5$ at $91\%$, $592.5$ at $92\%$, and $383$ at $100\%$. The longest individual run lasts $1\,470$ generations at $89\%$.

At the same time, intensity rises with density. Median peak active-fire fraction is $0.0480\%$ at $89\%$, $0.1038\%$ at $90\%$, $0.2399\%$ at $91\%$, and $0.8482\%$ at $100\%$. Median maximum burn rate rises from $0.0347\%$ of initial fuel per generation at $89\%$ to $0.5274\%$ at $100\%$.

Together, these results distinguish $2$ effects: near the crossover, uncertain connectivity produces long, variable exploration of the fuel network; above it, broader fronts consume fuel more intensely and finish sooner.

#Trajectories And Representative Runs

Individual cumulative-burn trajectories separate into distinct fadeout and sustained-spread outcomes near $90\%$. The transition figure selects $90\%$ runs nearest the $10^{\text{th}}$, $50^{\text{th}}$, and $90^{\text{th}}$ burn-fraction percentiles:

#Transition Runs In Motion

The $3$ recordings below use the same $90\%$ density and correspond to the representative runs in the table and figure above. Together they show how randomized initial vegetation layouts produce rapid fadeout, intermediate spread, or a large burn even though the subsequent Wildfire evolution is deterministic.

#Typical Runs Across Regimes

The $50\%$ run is intentionally brief: its $4$-generation fadeout is representative of a regime in which fire cannot find a connected path through the fuel. The $100\%$ run shows the contrasting broad fire front and the survival of some resistant vegetation.

#Long-Lived Near-Transition Fire

The longest Wildfire run in the dataset occurs at $89\%$ density. Run $5$ burns $27.875\%$ of its initial fuel over $1\,470$ generations, illustrating the slow exploration of marginally connected fuel paths near the crossover.