 This simple representation is also at the core of the widely adopted Wolfram code (Wolfram 1983), assigning to each rule a number: with black = 1 and white = 0, the bottom row can be read as a binary number (01011010); converting to decimal gives you the rule’s name (in this case, Rule 90). Since rules for CA with \(r = 1\) and \(k = 2\) differ just in the bottom row of the diagram, this encoding scheme effectively identifies each possible rule in the class. One-dimensional CA with \(r = 1\) and \(k = 2\) are among the simplest CA one can define, yet their behavior is at time quite interesting. When Stephen Wolfram started to explore this field in the Eighties, that class seemed a perfect fit. With \(r = 1\), there are 8 possible neighbors (see  Fig. 4  above) to be mapped to \({1, 0}\), giving a total of \(2^8 = 256\) rules. Starting with random initial conditions, Wolfram went on to observe the behavior of each rule in many simulations. As a result, he was able to classify the qualitative behavior of each rule in one of four distinct classes. Repeating the original experiment, we simulated the evolution of two rules for each class of Wolfram’s scheme.