Braids on the Stranded Cellular Automata Model

Abstract

The Stranded Cellular Automata (SCA) model is a grid of cells such that each cell can contain 0, 1, or 2 strands, together with two cellular automata that control when and how strands turn and cross. It was developed to study patterns occurring in fiber arts. We define a notion of what it means for a braid, in the sense of an element of a braid group, to be represented by an SCA pattern, and provide several algorithms to determine when a braid has an SCA representation with certain additional properties.

arXiv comment11 figures, 27 pages, this is the version with full detail