Model: Percolation as Forest Fire

When this program runs the grid is planted with a certain proportion of trees. Then all the trees on the left edge of the grid are set on fire, and the fire spreads from tree to tree. The fire can only spread up and down, or right and left, not diagonally.

What determines whether the fire will spread all the way to the right edge of the grid? The denser the trees, the better the fire can spread. You might think that as the density increases, the likelihood of the fire spreading would increase gradually. Is that what you find? Try different densities, and see what happens.

Press the "run/replant" button to plant a forest and start a fire. Press the "increase density" or "decrease density" buttons to change the density.

While this is not actually a good model of how fire spreads, it is a good model of some forms of percolation, when a fluid penetrates a porous material. The density of pores (holes) has a critical effect on whether the fluid can pass all the way through a layer of the material.

Reference: Schroeder, M. (1991) Fractals, Chaos, and Power Laws. New York: Freeman, Ch. 15.

Density of trees: