The Complexity of Braids, Cables, and Weaves Modeled with Stranded Cellular Automata

Joshua Holden
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 463–466 Short Papers


In a previous Bridges paper, the author and Lana Holden presented a system for modeling the depiction of one-dimensional strands in three-dimensional space, applicable to knitting, crochet, weaving, and other forms of artistic media depicting knots and other forms of interlacing strands. This system of Stranded Cellular Automata depends on the idea of a one-dimensional grid of cells which evolves through a time dimension according to specified rules. This paper starts an investigation of the complexity of the patterns produced by Stranded Cellular Automata, as measured by the length of the maximum possible repeat for a given width of pattern. Upper and lower bounds are given for special situations, although the general case remains open.