## 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

2. Probability that lightning will strike a particular grid-square

3. Probability that trees will grow at a certain grid-square

4. Designated time step number

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

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.

*****These rules will be ignored in this analysis.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: ()