A new universal cellular automaton on the ternary heptagrid

2009/03/12 by Maurice Margenstern, Margenstern, Maurice · 2 citations
Computer Science · #Cellular Automata and Applications #Computational Geometry (cs.CG) #F.2.2 #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #cs.CG #cs.FL

paper · pdf · doi:10.48550/arxiv.0903.2108

35 pages, 33 figures

arxiv created 2009/03/12 · openalex publication_date 2009/03/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct a new weakly universal cellular automaton on the ternary heptagrid. The previous result, obtained by the same author and Y. Song required six states only. This time, the number of states is four. This is the best result up to date for cellular automata in the hyperbolic plane.

Cited by

• About the embedding of one dimensional cellular automata into hyperbolic cellular automata
• A family of weakly universal cellular automata in the hyperbolic plane with two states

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