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Braids, Cables, and Cells: An Interesting Intersection of Mathematics, Computer Science, and Art
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Desc: 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 macramé, and we will touch on some of these.
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- Slide 1: Braids, Cables, and Cells: An Interesting
Intersection of Mathematics, Computer Science, and
Art
Joshua Holden
Rose-Hulman Institute of Technology
http://www.rose-hulman.edu/~holden
Joshua Holden (RHIT) Braids, Cables, and Cells 1 / 13
- Slide 2:“Knotwork” in graphic arts
Figure: Left: by A. Reed Mihaloew, Right: by Christian Mercat
Joshua Holden (RHIT) Braids, Cables, and Cells 2 / 13
- Slide 3:“Cables” in fiber arts
Figure: Design by Barbara McIntire, knitted by Lana Holden
Joshua Holden (RHIT) Braids, Cables, and Cells 3 / 13
- Slide 4:“Braids” in group theory
Two braids which are the same except for “pulling the strands” are
considered equal
All strands are