Gliders on the Stranded Cellular Automata Model

TL;DR

This paper introduces an algebraic framework for the Stranded Cellular Automata model, classifies all simple gliders, and provides algorithms for their generation, advancing understanding of pattern dynamics in this automaton.

Contribution

It offers a formal algebraic definition of patterns and gliders in the SCA model, including classification and generation algorithms for simple gliders.

Findings

Classified all 1- and 2-stranded gliders in the SCA model.

Proved an equivalence between two classes of gliders.

Developed an algorithm to generate all elements of a specific glider class.

Abstract

The Stranded Cellular Automata (SCA) model consists of a grid of cells which can each contain between zero and two strands apiece and two turning rules that control when strands turn and when they cross. While patterns on this model have been studied previously, such research has not needed an algebraic description of the model. We provide a formal algebraic definition of patterns on the model, define gliders on the model in a way which is semi-compatible with definitions of gliders in other cellular automata models, and classify all 1- and 2-stranded gliders on this model. In addition, we prove an equivalence of two classes of gliders and design an algorithm to generate all such elements of that class.