Complex Dynamics Emerging in Rule 30 with Majority Memory

In cellular automata (CAs) with memory, the unchanged maps of conventional CAs are applied to cells endowed with memory of their past states in some specified interval. We implement the rule 30 automaton and show that by using the majority memory function we can transform the quasi-chaotic dynamics of classical rule 30 into domains of traveling structures with predictable behavior. We analyze morphological complexity of the automata and classify glider dynamics (particle, self-localizations) in the memory-enriched rule 30. Formal ways of encoding and classifying glider dynamics using de Bruijn diagrams, soliton reactions, and quasi-chemical representations are provided.