Fire Experiment

Description and Use

The forest consists of a rectangular lattice of trees. Each tree in the forest is in one of three possible states:

Healthy trees are colored green.
On fire trees are colored red.
Burnt trees are colored black.

Time is discrete and the dynamics of the fire process are as follows:

A tree that is on fire at time t will be burnt at time t + 1.
Once a tree is burnt it remains burnt.
If a tree is healthy at time t and is directly above or below or to the right or to the left of a tree on fire at time t, then the healthy tree will catch on fire at time, t + 1 independently, with respective probabilities p_u, p_d, p_r, and p_l.
Trees that are healthy at time t catch on fire at time t +1 independently of one another.

The forest is shown in the large graph box in the center. You can choose either a 100 by 50 forest or a 500 by 250 forest. with the first list box. To change the state of a tree, select the desired state with the second list box and then click on the tree. In particular, to set a tree on fire, make sure that Set State: Red is selected and click on the tree. The vertices of the tree pointed to by the mouse are shown.

The fire spread probabilities can be varied with scroll bars. The simulation automatically stops when no more trees are on fire. The number of trees that are healthy, on fire, and burnt are recorded at each time unit in the table.

This experiment illustrates a conceptually simple yet mathematically rich particle system. The process exhibits critical or phase-change behavior: when the fire spread probabilities are below certain thresholds, the fire burns out with probability 1. When the fire spread probabilities are above the thresholds, the fire has positive probability of burning forever. For a more detailed mathematical analysis, see

the fire process

Instructions for Downloading and Installing

Click on the link below to download the Java archive file:

FireExperiment.jar (23 KB)

To add the applet to your web page, insert the following in the html file, at the point where you want the applet to appear:

<applet code="edu.uah.math.experiments.FireExperiment.class" archive="FireExperiment.jar" width="600" height="500"></applet>

The jar file and the html file must be in the same folder.

This width and height dimensions are simply suggestions and can be varied. Generally, components such as graphs and tables expand and contract proportionally, while components such as buttons, scrollbars, dice, and coins are fixed in size.

Metadata

Type

Java Applet

Keywords

probability
interacting particle system
fire process
random variable
phase transition

Version

August, 2003

Browser Requirements

Support for the Java 2 runtime environment (version 1.4 or later). Click on the icon to download the appropriate plug-in.

Authors

Kyle Siegrist
Dawn Duehring

Copyright

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public License for more details.

Related Resources

If you are interested in the Java source code or the Java documentation and object model for this applet, please visit FireExperiment in the Object section of the Library.