Dissertation/Thesis Abstract

Cellular Automata, Game of Life and Chance
by Alvandipour, Mehrdad, M.S., Southern Illinois University at Edwardsville, 2017, 43; 10615332
Abstract (Summary)

Cellular automata (CA) is shortly reviewed and different approaches to CAs are introduced, while the major focus is put on the Game of Life (GoL). While the GoL has deterministic rules, we suggest a method to make the game stochastic. An analysis of the new stochastic game is studied which focuses on a macroscopic characteristic of the field, the population density. The stochastic game is simulated with various different rules to compare the exact results with the analysis. The applicability of Markov chains and Markov random fields to such games is also studied briefly, while the final chapter of our work consists of a stochastic game inside a finite grid which is modeled by Markov chains. The structure of the states, the transition probabilities and other aspects of the model is both analyzed and simulated. And finally relevant directions to expand this study is suggested.

Indexing (document details)
Advisor: Budzban, Gregory
Commitee: Sewell, Edward C., Staples, George S.
School: Southern Illinois University at Edwardsville
Department: Mathematics and Statistics
School Location: United States -- Illinois
Source: MAI 57/01M(E), Masters Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics
Keywords: Markov chains, Markov random fields, Probability theory, Simulation, Stochastic games
Publication Number: 10615332
ISBN: 978-0-355-25504-1
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