Description

The forest consists of an \(n \times n\) square 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.

Initially, one tree in the center of the forest is on fire. The fire spread probabilities can be varied with the input controls. The simulation automatically stops when no more trees are on fire. An additional stop option allows the simulation to run until this happens. The random variables of interest are the number of healty (green) trees \(X\), the number of trees on fire (red) \(Y\), and the number of burnt trees (black) \(Z\). The parameter \(n\) can be varied with the scrollbar.