Modeling Braids, Cables, and Weaves with Stranded Cellular Automata

The mathematical study of braids involves with mathematical representations of one-dimensional strands in three-dimensional space. These strands are also sometimes viewed as representing the movement through a time dimension of points in two-dimensional space. On the other hand, the study of cellular automata usually involves a one- or two-dimensional grid of cells which evolve through a time dimension according to specified rules. This time dimension is often represented as an extra spacial dimension. The ideas of representing both strands in space and cellular automata have also been explored in many artistic media, including drawing, sculpture, knitting, crochet, and weaving. This paper presents a system of Stranded Cellular Automata which realistically captures the behavior of strands in certain media, such as knitting and crochet