One-Dimensional Cellular Automata: Pascal's Triangle and an Extension of Rule 90 for a Non-Abelian Group
Date of Award
2009
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
Poimenidou, Eirini
Keywords
Cellular Automata, Dihedral Group, Pascal's Triangle
Area of Concentration
Mathematics
Abstract
This thesis is a study of one-dimensional cellular automata. We begin by developing new properties of binomial coefficients that were discovered from patterns seen in Pascal's triangle modulo a prime. Then, motivated by Wolfram, Martin and Odlyzko's "Algebraic Properties of Cellular Automata", we study an extension of Rule 90 for multiplicative groups and develop the necessary and sufficient conditions for a state in this automaton to have a predecessor. We then apply this method to show the fraction of states reachable through evolution for this extension of Rule 90 over the dihedral group.
Recommended Citation
Craig, Erin, "One-Dimensional Cellular Automata: Pascal's Triangle and an Extension of Rule 90 for a Non-Abelian Group" (2009). Theses & ETDs. 4075.
https://digitalcommons.ncf.edu/theses_etds/4075