Day 247 · Sep 3

The Mathematics of the Great Fire of London (1666)

The Great Fire burned from 2–6 September 1666. It destroyed 13,200 houses and 87 churches. The fire spread according to a cellular automaton model: a building ignites if wind direction and heat radiation exceed a threshold. Modern fire‑spread models use percolation theory: a grid of cells, each with a probability p of being flammable; if p exceeds a critical threshold, a fire can spread infinitely. For the London fire, narrow streets and wooden houses made p high. Mathematics now guides fire‑safe urban design and wildfire management.

What is the critical percolation threshold on a square grid? (About 0.5927.) If each building has a 60% chance of being combustible, will a fire likely spread across the whole city?

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