Naomi Kochi

Date of Award

8-1-2005

Document Type

Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

First Advisor

Dr. John Konvalina

Abstract

We explore a quantitative description of Wolfram's classification of elementary cellular automata based on fractal dimensions. We find the· fractal dimension to be a global measure in classifying elementary cellular automata independent of initial conditions. On the other hand, the results of our analysis of rules in Class 3 numerically confirm the existence of a wide range of dynamics among rules in Class 3. The main reason for this is due to the fact that the rules with the Sierpinski structure in Class 3 have the capacity to behave like rules in Class 2 depending on their initial conditions. Furthermore, we apply mutual information to investigate how elementary cellular automata handle information throughout the iterations of time steps. We discover a similarity among Rule 30, Rule 110 and Rule 22, and give further supporting evidence for Wolfram's conjecture that Rule 30 and Rule 22 may be universal.

Comments

A Thesis Presented to the Department of Mathematics and the Faculty of the Graduate College University of Nebraska In Partial Fulfillment of the Requirements for the Degree (Master of Art) University of Nebraska at Omaha. Copyright 2005 Naomi Kochi

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