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The mathematical study of braids combines aspects of topology and group theory to study mathematical representations of onedimensional strands in threedimensional space. These strands are also sometimes viewed as representing the movement through a time dimension of points in twodimensional space. On the other hand, the study of cellular automata usually involves a one or twodimensional 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 macramé, and we will touch on some of these.
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Modeling knots that 'bounce' off the top and bottom of the pattern, or otherwise do anything besides basically going from the bottom to the top of the design, seems like it would require a very different mathematical idea than the one I've been using. Possibly a 2D cellular automaton would be the way to handle it, but I haven't thought about that yet. Maybe in the future....
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