A Computational Approach to Percolation Theory Fun with Forest Fires A Computational Approach to Percolation Theory IA

Percolation Percolation theory is a problem in math and physics concerning the size of connected clusters in a random lattice as the probability of their components increases As the name suggests, part of the motivation is modeling the flow of fluids through porous materials. But it can also model other things.

Percolation One interesting problem in percolation is that of the critical threshold or the percolation threshold which refers to the required probability to create a cluster that has infinite connectivity on an infinite lattice (site percolation). This is dependent on the structure of the lattice. A one-dimensional lattice clearly has a threshold of 1, while a 2d square lattice has a threshold of ~0.59.

Percolation This becomes useful for modeling phase transitions One example is the forest fire model. Some starting assumptions: Forests can be modeled as discrete lattices Lattice sites can be empty, on fire, or containing a tree Trees might appear in empty spots and fire might appear in spots with trees Fires spread to adjacent sites

Percolation This becomes useful for modeling phase transitions One example is the forest fire model. Some starting assumptions: Forests can be modeled as discrete lattices Lattice sites can be empty, on fire, or containing a tree Trees might appear in empty spots and fire might appear in spots with trees Fires spread to adjacent sites

Sources Christensen, Kim. "Percolation theory." Imperial College London, London (2002): 40. Christensen, Kim, Henrik Flyvbjerg, and Zeev Olami. "Self-organized critical forest-fire model: Mean-field theory and simulation results in 1 to 6 dimenisons." Physical review letters 71.17 (1993): 2737.