Triangular Automata: The 256 Elementary Cellular Automata of the 2D Plane

TL;DR

This paper introduces Elementary Triangular Automata as a 2D counterpart to Wolfram's elementary cellular automata, providing tools, analysis, and interactive resources for their study.

Contribution

It defines and explores the simplest class of cellular automata on a triangular grid, offering new computational tools and initial analysis for this class.

Findings

Introduction of Elementary Triangular Automata (ETA) as 2D automata.

Development of conceptual and computational tools for ETA analysis.

Availability of interactive exploration tools and source code.

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.