Stranded cellular automata model explains patterns in braided strands
Braids on the Stranded Cellular Automata Model
Formal Languages and Automata Theory
Summary
The paper looks at a special kind of grid model called stranded cellular automata (SCA), where each cell can hold up to two strands that move and cross based on simple rules. This model helps study how braided patterns, like those in fiber arts, can be formed and represented mathematically. The authors connect these patterns to something called braid groups, which describe ways to twist and cross strands. They also provide ways to check if a given braid pattern can be made using the SCA model and under what conditions.
Stranded cellular automataBraid groupsCellular automataBraidsFiber artsStrand crossingGrid modelAlgorithmMathematical representation
Authors
Alexa Renner
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.