The Complexity of Braids, Cables, and Weaves Modeled with Stranded Cellular Automata

Year: 2017 Authors: Joshua Holden

Core claim

For certain stranded cellular automata configurations, the maximum possible repeat length can be bounded above and below by explicit functions of the pattern width.

Topics

cellular automata complexity, braids and weaves, repeat length bounds, interlacing strands

Domains

cellular automata, combinatorics, Möbius function, least common multiple, textile arts, weaving, knitting, crochet

Methods

rule-based modeling, periodicity analysis, upper and lower bounds, exhaustive case analysis

Media

strands, knitted patterns, crocheted cables, loom weaves

Source status

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