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An abstract of the thesis of Andreas Rechtsteiner for the Master of Science in Physics presented November 14, 1995. Title: Complexity Properties of the Cellular Automaton Game of Life The Game of life is probably the most famous cellular automaton. Life shows all the characteristics of Wolfram's complex Class N cellular automata: long-lived transients, static and propagating local structures, and the ability to support universal computation. We examine in this thesis questions about the geometry and criticality of Life. We find that Life has two different regimes with different dimensionalities. In the small scale regime Life shows a fractal dimensionality with Ds = 0.658 and in the large scale regime D1 = 2.0, suggesting that the objects of Life are randomly distributed. We find that Life differentiates between different spatial directions in the universe. This is surprising because Life's transition rules do not show such a differentiation. We find further that the correlations between alive cells extend farthest in the active period and that they decrease in the glider period, suggesting that Life is sub-critical. Finally, we find a size-distribution of active clusters which does not depend on the lattice size and amount of activity, except for the largest clusters. We suggest that this result also indicates that Life is sub-critical. Complexity Properties of the Cellular Automaton Game of Life By Andreas Rechtsteiner A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in PHYSICS Portland State University 1995