About the embedding of one dimensional cellular automata into hyperbolic cellular automata

Abstract

In this paper, we look at two ways to implement determinisitic one dimensional cellular automata into hyperbolic cellular automata in three contexts: the pentagrid, the heptagrid and the dodecagrid, these tilings being classically denoted by $\{5,4\}$, $\{7,3\}$ and $\{5,3,4\}$ respectively.

19 pages, 9 figures

References in corpus (2)

• A new universal cellular automaton on the ternary heptagrid
• A weakly universal cellular automaton in the hyperbolic 3D space with three states

Cited by in corpus (2)

• An upper bound on the number of states for a strongly universal hyperbolic cellular automaton on the pentagrid
• A new weakly universal cellular automaton in the 3D hyperbolic space with two states