The mathematical study of braids combines aspects of topology and
group theory to study 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.
Previous work as been shown that rules for cellular automata can be
written in order to produce depictions of braids. This talk will
extend the previous system into a more flexible one which more
realistically captures the behavior of strands in certain media, such
as knitting. Some theorems about what can and cannot be represented
with these cellular automata will be presented.