Practical Problem 5: Forrest Fires

This problem is related to the explorable “Critically Inflammatory” that simulates the phenomenon of self-organized criticality in the context of forrest fires.

Write a patch based simulation in which patches can either be

1. empty (e.g. black)
2. occupied with a tree (e.g. green)
3. occupied by a burning tree

Now about the dynamics

1. If a burning tree is neighboring a healthy tree, it can set fire to it with probability \(\alpha\)
2. A healthy tree can reproduce by seeding a new tree in a neighboring empty patch with probability \(\beta\)
3. With a very tiny probability \(\gamma\) lightning strikes anywhere in the world, if it hits a tree, it sets it on fire
4. A patch on fire can burn out with a probability \(\delta\)

Add slider variables for the three parameters.

Add a toggle-switch that replaces rule 2. by a new rule in which a tree doesn't seed a new tree at a neighboring empty patch but rather a random empty patch anywhere in the world.