A Cellular Automaton

What is in this chapter? Cellular automata are widely used models in mathematical physics and in theoretical biology. These systems start from a random state and then evolve using deterministic rules, with time being discrete. We concentrate on a specific model in this chapter. We define the initial configuration as follows. For each site in Z2 we put a 1 with probability p or a 0 with probability 1 — p. This is done independently for each site. The rules of evolution for the cellular automaton are the following. If there is 1 at a site it remains there forever. If there is a 0 at a given site and if at least one neighbor in each of the orthogonal directions is a 1 then we replace the 0 by a 1 at the next update.