About Strongly Universal Cellular Automata
Maurice Margenstern
TL;DR
This paper constructs strongly universal cellular automata with minimal states on the line and extends these constructions to hyperbolic spaces, demonstrating universality in complex geometric settings.
Contribution
It introduces the first strongly universal cellular automaton on the line with 11 states and extends universality to hyperbolic geometries with 10 states.
Findings
Constructed a strongly universal cellular automaton with 11 states on the line.
Embedded the automaton into hyperbolic tilings to achieve universality.
Reduced the number of states to 10 in hyperbolic space constructions.
Abstract
In this paper, we construct a strongly universal cellular automaton on the line with 11 states and the standard neighbourhood. We embed this construction into several tilings of the hyperbolic plane and of the hyperbolic 3D space giving rise to strongly universal cellular automata with 10 states.
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Taxonomy
TopicsCellular Automata and Applications · Quasicrystal Structures and Properties · DNA and Biological Computing