Forest Fire

–of the forest has trees now (one fire can cross it all above 59%)

–trees in the biggest fire lately

–of burned trees went in the big fires (over 1% of the forest each)

–trees in a typical (median) fire

tree fire ash firebreak

Every fire

one dot per fire: when it ended and how many trees it burned (log scale)something you did

How often each size sizes on a normal scale (semi-log)

needs a few dozen fires…

Trees

share of the forest with trees59%: one fire can cross it all

Why big fires are rare but never impossible

The "How often each size" chart shows a power law (also called scale-free or heavy-tailed): fires 10× bigger are always about the same factor rarer, here roughly 12×. On a log-log chart that is a straight line. An exponential decline would instead be straight on a semi-log chart (tick the box) and would make giant fires practically impossible: with a typical fire of about 35 trees, a 20,000-tree fire would have a chance of about e⁻⁵⁷⁰. Here it happens every few thousand ticks.

Why: a fire burns exactly one connected patch of trees, so its size is the size of the patch the lightning hits. Slow growth and sudden fires turn the forest into a patchwork of thin and thick areas, always near the point where patches just start joining up. There, patches come in all sizes with no typical size, and lightning hits big patches more often because they have more trees. Too thick, and a huge fire clears it; too thin, and only small fires happen while it regrows. The forest keeps itself at this edge with nobody tuning it: self-organized criticality (Bak, Tang and Wiesenfeld 1987; Drossel and Schwabl 1992). The last points bend down because no fire can be bigger than the forest. Real forest fires (Malamud, Morein and Turcotte, 1998), earthquakes (the Gutenberg–Richter law), avalanches and blackouts follow power laws too.

Run

Speed

ticks

fires so far

burning now

–

trees burned per 1,000 ticks

strikes on bare ground

fires put out at once

One tick: fire moves one tree on, trees grow, lightning may strike. "Lately" means the last 20,000 ticks.

Ranger

Click or drag on the forest with the chosen tool.

Firebreak every Thin by

Firefighters

Firebreaks are strips with no trees, so a fire cannot cross them. Thinning cuts down a share of the trees once. Firefighters put out that share of new fires before they spread. Watch the charts after each.

Forest

Growth Lightning Spreads to Catch chance Size

Growth is the chance per tick that bare ground grows a tree. Lightning is strikes per tick anywhere. These apply at once; Size starts a new forest.

Why it happens

A fire can only spread through trees that touch. In a thin forest the patches are small, so fires stay small, and trees pile up. In a thick forest the patches join into one, and a single strike burns it. The forest swings between the two on its own and settles near 40% trees, just below the point where everything joins. There, fires of every size happen, and the rare giant ones do most of the burning. Earthquakes, avalanches and blackouts behave the same way. And here is the trap: in the long run every tree that grows will burn. Putting out small fires leaves the fuel for a bigger one later. This is what happened in Yellowstone in 1988.