In my Fall course of Math Models, I have three groups working on projects to finish up the semester. One of the groups have an assignment to explore a model of the spread of a forest fire. The assumptions are that the trees are on a rectangular grid, or a lattice. The time is a discrete variable and at each time step the probability that the fire spreads from one point in the lattice to an adjacent point (up, down, left or right) is given by p. For simplicity, the event that the fire spreads to each point is assumed to be independent of any other point.
Part of their project is to implement a numerical simulation of their forest fire. I couldn’t let them have all the fun, so below is an example of my version of the simulation in MATLAB. I have to hold off on posting the code until after they have handed in their project.
In the graphical representation of my simulation, green represents an unburnt tree, black is burnt and red is currently on fire. The fire lasts for exactly one time step. I also implemented a 3-D version, where a height of 1 is unburnt, 2 is on fire, and 0 is burnt. I’ll confess to having way too much fun with this.
I have used a 200×200 lattice with p = 0.5.