Triangular Automata: The 256 Elementary Cellular Automata of the Two-Dimensional Plane

Cellular automata (CAs) in the triangular grid are here called triangular automata (TAs). This paper focuses on the simplest type of TAs, called elementary TAs (ETAs). They are argued to be the two-dimensional counterpart of Wolfram’s elementary CAs. Conceptual and computational tools for their study are presented, along with an initial analysis. This paper is accompanied by the author’s website [1], where the results can be explored interactively. The source code is available in the form of a Wolfram Language package at [2].