Comparing the Dynamical Behavior of Elementary CA Rules

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This Demonstration compares the dynamical behavior of the 256 elementary cellular automata (CA) rules, aligning them in just one graphic, starting from the same random initial condition.

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The CA dynamics are obtained by calculating the total of black cells at each CA step along the time axis.

You can see the four classes of CA rule behavior:

Class I CA tend to stabilize quickly to just one value with a short transitory state (e.g. rules 0 and 250).

Class II CA tend to vary between periodic values, becoming stable (e.g. rules 94 and 156).

Class III CA tend to keep behaving randomly (e.g. rule 30).

Class IV CA tend to have local random behavior (e.g. rule 110).

It is hard to tell the difference visually between classes III and IV, even with an algorithm.

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Contributed by: Daniel de Souza Carvalho (March 2011)
Open content licensed under CC BY-NC-SA


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