On weak universality of three-dimensional Larger than Life cellular automaton
Katsunobu Imai, Kyosuke Oroji, Tomohiro Kubota
TL;DR
This paper investigates a three-dimensional extension of Larger than Life cellular automata, demonstrating that a specific radius-4 rule may be weakly universal, thus contributing to understanding their computational capabilities.
Contribution
It introduces a three-dimensional LtL automaton with a radius-4 rule as a potential weakly universal system, expanding the scope of LtL automata research.
Findings
Radius-4 3D LtL rule is a candidate for weak universality
Extends LtL automata to three dimensions
Provides groundwork for future universality proofs
Abstract
Larger than Life cellular automaton (LtL) is a class of cellular automata and is a generalization of the game of Life by extending its neighborhood radius. We have studied the three-dimensional extension of LtL. In this paper, we show a radius-4 three-dimensional LtL rule is a candidate for weakly universal one.
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Taxonomy
TopicsCellular Automata and Applications · Computability, Logic, AI Algorithms · DNA and Biological Computing