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From chapters 2 and 3 it seems that Wolfram groups behavior of the cellular automata according to three types: one group consisted of cellular automata that demonstrated pure repitition and a very simple pattern, a second group consisted of those with many details but had a regular nested structure overall, and a third group where there does not appear to be much regularity and the behavior of the cellular automata seems random.

Wolfram notes common themes between the 256 rules: one common behavior he states is where a pattern consisting of a single cell or group of cells persists such as in rules 2, 4, 103 and 123. Another common feature of some patterns is that they remain a fixed size while other patterns go on forever. Of the patterns that continue to grow some are repetitive while others are not.  Repition and nesting patters Wolframs states are common patterns among the cellular automata. What is interesting to note is that Wolfram claims that only 10 out of the 256 rules yield apparent randomness.  Even more interesting is rule 110 which is unique in that it has parts that demonstrate both regularity and irregularity.  

Another degree of complexity is introduced when you look at rules which involve three colors rather than two. The total number of possible rules in this case would be much greater.  What is significant about looking at rules which involve more than two colors is that they produce behavior similar to cellular automata that only involve two colors. This lead Wolfram to state that, “having more complicated underlying rules has not led to much greater complexity in overall behavior.” This is interesting to me because it would seem that logically involving more colors and having more complicated rules would result in more complicated behavior. It also seems like since many more rules are possible with more colors involved it would be hard to find several common themes. I wonder what the “essential ingredents” of the elementary elementary rules are that producecomplicated behavior.