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.

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.  .