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

Abstract

Triangular Automata (TA) stands for cellular automata in the triangular grid. This work focuses on the simplest type 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. The 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.