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Braids, Cables, and Cells I: An Interesting Intersection of Mathematics, Computer Science, and Art

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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 ...

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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  • joshuarbholden Joshua Holden, Professor of Mathematics at Rose-Hulman Institute of Technology Reed: Thanks for posting the sample so I could use it! Yes, Rule 47 does seem to be one of the most artistic --- most of the rules only a mathematician could love. :)

    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 2-D cellular automaton would be the way to handle it, but I haven't thought about that yet. Maybe in the future....

    Thanks for your comment!
    4 years ago
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  • guesta083ec8 guesta083ec8 Thanks for including one of my samples! Interesting topic. Your Rule 47 appears to be closest to actual IC-style knotwork. How does the rule handle interruptions (please see http://mysite.verizon.net/mihaloew/celtic/class_adv.shtml for information on this topic), I wonder? 4 years ago
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  • abhishekshah Abhishek Shah, Co Founder at Propberg Real Estate Advisors really interesting 4 years ago
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Braids, Cables, and Cells I: An Interesting Intersection of Mathematics, Computer Science, and Art Braids, Cables, and Cells I: An Interesting Intersection of Mathematics, Computer Science, and Art Presentation Transcript