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This book presents a proof of universal computation in the Game of Life cellular automaton by using a Turing machine construction. It provides an introduction including background information and an extended review of the literature for Turing Machines, Counter Machines and the relevant patterns in Conway´s Game of Life so that the subject matter is accessibly to non specialists.

The book contains a description of the author´s Turing machine in Conway´s Game of Life including an unlimited storage tape provided by growing stack structures and it also presents a fast universal Turing machine designed to allow the working to be demonstrated in a convenient period of time.

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Introduction.- Background.- Literature Review / Related Work.- Game of Life Turing Machine.- Game of Life Universal Turing Machine.- Optimizing Transition Order.- Forty Five Degree Stack.- Stack Constructor.- Universal Counter Machine - Turing Machine.- Wolfram´s two State Three Symbol UTM.- Conclusions and Discussion.- Further Work.

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"The book contains numerous detailed illustrations ... . an avid reader who is a Game of Life enthusiast to the core will cherish every word. However, less detail-oriented readers may also enjoy this manuscript, focusing more on the tale told by the illustrations and their accompanying captions. These in themselves provide much insight into the fascinating universe of cellular automata-and into the amazing feats they can accomplish." (Moshe Sipper, Genetic Programming and Evolvable Machines, Vol. 18, 2017)

"Rendell´s volume reports an extended project on such engineering of universal computers in the GoL. ... individual chapters have references to the literature relevant to each of them. Aficionados of the Game of Life will welcome this volume as the journal of a fellow enthusiast as he explores new ways to configure and manipulate the simple potential of this fascinating algorithm." (H. Van Dyke Parunak, Computing Reviews, November, 2015)

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