Chapter: Landscapes and Trees

In this assignment, you will simulate a forest fire using "trees" on a "landscape". Here, the landscape is going to be 2-dimensional grid of cells, each of which either either contains a tree of some kind or else is devoid of trees. This rudimentary landscape is useful in studying burn patterns, safety measures and the effects of a "controlled burn".

For example, here is a 5 x 5 grid with 17 trees, represented with ones, twos and zeroes (1 = pine tree, 2 = oak tree, 0 = no tree).

   1 2 1 0 1
   0 0 2 0 1
   0 1 1 1 0
   1 0 2 2 1
   1 1 0 1 1

The following "rules" determine the behavior of the system:

• The rows of an m x m grid are numbered 0,...,m-1. Thus, row number 0 in the first example is:

     1 2 1 0 1
  

• Likewise, the columns are numbered 0,...,m-1 (from left to right). Thus, in the above 5 x 5 example, Cell (2,3) contains a pine tree, but (3,1) has no tree.
• The neighbors of a cell are the four cells to the north, south, east and west of the cell. Thus, Cell (1,1) has neighbors (0,1), (2,1), (1,0) and (1,2). Cells at the four corners have only two neighbors each and cells on the boundary (but not at the corners) have three neighbors each.
• When a pine tree catches fire, it will in the next time-period ignite every pine tree that is in a neighboring cell. An ignited tree does not ignite its non-neighbors.

Let us consider what happens when a pine tree is ignited. The tree itself catches fire and ignites its pine neighbors, which in turn ignite their pine neighbors, and so on. All these trees eventually burn down. Eventually, the burning stops and we are left with the stumps of a cluster. Thus, a pine-cluster is a collection of pine trees, such that any two pine trees in the cluster are connected to each other via a string of neighboring pine trees. Hence, in the example below

   1 1 1
   0 0 0
   0 1 1

   x x x
   0 0 0
   0 1 1

   1 1 1
   0 0 0
   0 x x

Oaks are trees with different "burn" properties:

• Pine trees are the trees described already: We know that if any neighboring pine tree catches fire, they will ignite. It is the case that if a neighboring oak tree catches fire, a pine tree will catch fire.
• Oak trees are "sturdier". It requires two neighboring trees (either oaks or pines) to be on fire simultaneously for an oak tree to catch fire.

Your goal in this project is to consider the effects of a controlled burn on mixed forests. This simulation that you will write is part of a long tradition of simulating "macro" behaviors (for example: a complete burn) that arise from local behavior of small units (a burning tree ignites its neighbors). These types of simulations are often called agent or artificial society simulations.