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First Advisor

Joshua Holden


Interlacing strands have been used to create artistic weaving patterns. Repeated patterns form aesthetically pleasing products. This research is a mathematical modeling of weaving products in the real world by using Cellular Automata. The research is conducted by observing the evolution of the model to better understand products in the real world. Specifically, this research focuses on the repeat length of a weaving pattern given the rule of generating it and the configuration of the starting row. Previous studies have shown the range of the repeat length in specific situations. This paper will generalize the precise repeat length in one of those situations using mathematical proofs. In the future, the goal is to further generalize the findings to more situations.