Analyzing a Cell-Automaton Forest Fire Model
Introduction
Cell-automaton models are probability-based models that use the concept of "neighborhood" to model dynamic systems. The model that I chose to analyze is a Cell-automaton-based forest fire model. The original code I worked from is linked to below.
https://courses.cit.cornell.edu/bionb441/CA/forest.m
In this model, there are four variables:
1. A grid size n (generates an n X n matrix).
2. Probability that lightning will strike a particular grid-square Plightning.
3. Probability that trees will grow at a certain grid-square Pgrowth.
4. Designated time step number t.
By changing these four values, some interesting results can be obtained.
This model uses the following rules(taken from the Cornell page):
Because of limitations in computing speed, I will limit my grid size to no more than n = 200.
Analysis
Cell-automaton models are probability-based models that use the concept of "neighborhood" to model dynamic systems. The model that I chose to analyze is a Cell-automaton-based forest fire model. The original code I worked from is linked to below.
https://courses.cit.cornell.edu/bionb441/CA/forest.m
In this model, there are four variables:
1. A grid size n (generates an n X n matrix).
2. Probability that lightning will strike a particular grid-square Plightning.
3. Probability that trees will grow at a certain grid-square Pgrowth.
4. Designated time step number t.
By changing these four values, some interesting results can be obtained.
This model uses the following rules(taken from the Cornell page):
- Cells can be in 3 different states. State=0 is empty, state=1 is burning and state=2 is forest.
- If one or more of the 4 neighbors of a cell is burning and it is forest (state=2) then the new state is burning (state=1).
- There is a low probability (say 0.000005) of a forest cell (state=2) starting to burn on its own (from lightning).*
- A cell which is burning (state=1) becomes empty (state=0).
- There is a low probability (say, 0.01) of an empty cell becoming forest to simulate growth.*
- The array is considered to be toroidly connected, so that fire which burns to left side will start fires on the right. The top and bottom are similarly connected.
Because of limitations in computing speed, I will limit my grid size to no more than n = 200.
Analysis
Because of the random nature of this model, results at small n-values tend to be highly unpredictable.
Click on images to enlarge.
Click on images to enlarge.
Holding n and Plightning steady and increasing Pgrowth, the oscillatory motion is smoothed out.
Holding n and Pgrowth steady, the below images are obtained: ()