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.

Therefore, it seems reasonable to ask whether rules for cellular
automata can be written in order to produce depictions of braids.  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 macrame, and we will touch on some
of these.