Complex Dynamics Emerging in Rule 30 with Majority Memory

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.

Designing Complex Dynamics in Cellular Automata With Memory

“…For details please see [Wuensche & Lesser, 1992]. full-asymmetric: 10,11,14,15,24,25,28,29,42,43,46,57,60,138,142,152,156,170,184. strong: 10, 11, 15, 24, 25, 42, 46, 57, 138, 152, 170, 184. moderate: 14, 28, 29, 43, 142, 156. weak: 60.…”

“…For details please see [Ninagawa, 2008]. 3,6,7,9,10,11,14,15,18,22,24,25,26,27,30,34,35,37,38,41,42,43,45,46,54,56,57,58,60,62,74,106,110,122,126,130,134,138,142,146,152,154,162,170,184.…”

How to make dull cellular automata complex by adding memory: Rule 126 case study

“…In this way, Rule 126 provides a special case of how a chaotic behavior can be decomposed selecting a kind of memory into a extraordinary activity of gliders, glider guns, still-life structures, and a huge number of reactions. Such features can be compared to Brain Brian's rule behavior or Conway's Life but in one dimension; actually none traditional ECA could have a glider dynamics comparable to the one revealed in this ECA with memory denoted as φ R126maj (following notation described in [7,8]).…”

“…As it was explained in [7,37] a new family of evolution rules derived from classic ECA can be found selecting a kind of memory. Figure 9 illustrates dynamics for some values of τ in φ R126maj .…”

“…Such technique takes the past history of the system for constructing its present and future: the memory [1][2][3][4][5][6]. It was previously reported in [7] how the chaotic elementary cellular automaton (ECA) Rule…”