Abstract
In cellular automata with memory, the unchanged maps of the conventional cellular automata are applied to cells endowed with memory of their past states in some specified interval. We implement Rule 30 automata with a majority memory and show that using the memory function we can transform quasi-chaotic dynamics of classical Rule 30 into domains of travelling structures with predictable behaviour. We analyse morphological complexity of the automata and classify dynamics of gliders (particle, self-localizations) in memory-enriched Rule 30. We provide formal ways of encoding and classifying glider dynamics using de Bruijn diagrams, soliton reactions and quasi-chemical representations.
Highlights
An elementary cellular automaton (CA) is a one-dimensional array of finite automata, where each automaton takes two states and updates its state in discrete time depending on its own state and the states of its two closest neighbors
We inferred a sophisticated system of quasi-chemical reactions between the gliders
It was shown that the majority memory increases nominal complexity but decreases statistical complexity of patterns generated by the CA
Summary
An elementary cellular automaton (CA) is a one-dimensional array of finite automata, where each automaton takes two states and updates its state in discrete time depending on its own state and the states of its two closest neighbors. Known as the class of complex rules. Class IV is of particular interest because the rules exhibit nontrivial behavior with rich and diverse patterns, as shown for rule 54 in [2, 3]
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