In this section, we’ll go through some examples from Chapter 2. This includes some basic code in Mathematica.
What are the bones of a simple program? Initial conditions, and update rules. So say you start out with a finite array of black and white cells, represented by 1’s and 0’s. Your update rules would be those rules which determine which cells of some initial array change in the next step of their evolution.
Elementary cellular automaton (ECA) rules take a look at the two nearest neighbors of the “active” cell one is updating, and uses that list of three colors to determine how the center “active” cell will change in the next step of the evolution.
Let’s first take a look at how update rules are constructed in general:
Now let’s take a look at how one can get the update rules for each of the 256 ECAs:
There’s a great Demonstration, created by Paul-Jean Letourneau, which illustrates how ECAs are created.
Stay tuned for the first installment of Chapter 3.