Triangular Automata: The 256 Elementary Cellular Automata of the 2D Plane
Cellular Automata and Lattice Gases
2025-11-11 v7
Abstract
Cellular automata on the triangular grid are here referred to as Triangular Automata (TA). This paper focuses on the simplest class of TA, called Elementary Triangular Automata (ETA). They are argued to be the two-dimensional counterpart of Wolfram's Elementary Cellular Automata. Conceptual and computational tools for their study are presented, along with an initial analysis. This paper is accompanied by a website where the results can be explored interactively. The source code is available in the form of a Mathematica package.
Keywords
Cite
@article{arxiv.2309.15795,
title = {Triangular Automata: The 256 Elementary Cellular Automata of the 2D Plane},
author = {Paul Cousin},
journal= {arXiv preprint arXiv:2309.15795},
year = {2025}
}