John Conway developed this game in 1970 and was interested whether he could get patterns repeating itself. You can explore the Netlogo model “Life” in the “computer science” library, and see how the cells keep on changing their states (Figure 9). Sometimes this gives the impressing that blocks of cells remain alive. For example, the "glider" and the "blinker". The glider is composed of 5 cells which form a small arrow-headed shape, like the following, with x representing alive state:

    X
    X
  XXX

This glider will crawl across the world, retaining its shape. A blinker is a block of three cells (either up and down or left and right) that rotates between horizontal and vertical orientations

Figure 9: Game of life.

Application: Forest Fire

There are many applications of cellular automata varying from the growth of cancer cells to models of land use change. Here we present an application of cellular automata for the simulation of forest fires.

Cells can have the following states:

• tree
• tree on fire
• no tree

If a tree has a neighbor in a Von Neumann neighborhood that is on fire, the tree will change its state to fire. We can now investigate the impact of the density of trees on the spread of a fire. Suppose there is a density of 55%, meaning that the probability a cell has a tree is 0.55. Then what happens if the trees in the left column are on fire? We see in Figure 10 below that the fire stops quickly.

Figure 10: Forest fire model with 55% density of trees.

 However, if we increase the density to 58%, we see that the fire spreads through the whole forest (Figure 11). Deeper analysis shows that around 0.58 there is a so-called percolation threshold, a tipping point of density that lead the fire to spread.  

Figure 11: Forest fire with 58% density of trees.