Dynamics and Computation in Cellular Automata

Class 1 Almost all initial configurations relax after a transient period to the same fixed configuration (e.g., all Is). 

Class 2 Almost all initial configurations relax after a transient period to some fixed point or some temporally periodic cycle of configurations, but which one depends on the initial configuration. (It should be pointed out that on finite lattices , there is only a finite number k ) of possible configurations, so all rules ultimately lead to periodic behavior. Class 2 refers not to this type of periodic behavior but rather to cycles with periods much shorter than. ) 

Class 4- Some initial configurations result in complex localized structures, sometimes long-lived. 

Subsequent to Wolfram s work, several researchers have asked how static properties of CA rules relate to the dynamical behavior of the CAs. Christopher Langton, for example, studied the relationship between the average dynamical behavior of cellular automata and a particular statistic (A) of a CA rule table (Langton, 1990). For binary-state CAs, A is simply the fraction of Is in the output bits of the rule table. For CAs with A 2, A is defined as the fraction of non-quiescent states in the rule table, where one state is arbitrarily chosen to be quiescent. 

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