Game of Life Cellular Automata

1. Front Matter

   Pages I-XIX

   PDF

2. Introduction to Cellular Automata and Conway’s Game of Life

   • Carter Bays

   Pages 1-7

3. Historical

   1. Front Matter

      Pages 9-9

      PDF

   2. Conway’s Game of Life: Early Personal Recollections

      • Robert Wainwright

      Pages 11-16

   3. Conway’s Life

      • Harold V. McIntosh

      Pages 17-33

   4. Life’s Still Lifes

      • Harold V. McIntosh

      Pages 35-50

   5. A Zoo of Life Forms

      • Harold V. McIntosh

      Pages 51-68

4. Classical Topics

   1. Front Matter

      Pages 69-69

      PDF

5. Classical topics

   1. Growth and Decay in Life-Like Cellular Automata

      • David Eppstein

      Pages 71-97

   2. The B36/S125 “2x2” Life-Like Cellular Automaton

      • Nathaniel Johnston

      Pages 99-114

   3. Object Synthesis in Conway’s Game of Life and Other Cellular Automata

      • Mark D. Niemiec

      Pages 115-134

   4. Gliders and Glider Guns Discovery in Cellular Automata

      • Emmanuel Sapin

      Pages 135-165

   5. Constraint Programming to Solve Maximal Density Still Life

      • Geoffrey Chu, Karen Elizabeth Petrie, Neil Yorke-Smith

      Pages 167-175

6. Asynchronous, Continuous and Memory-Enriched Automata

   1. Front Matter

      Pages 177-177

      PDF

7. Asynchronous, Continuous and Memory-Enriched Automata

   1. Larger than Life’s Extremes: Rigorous Results for Simplified Rules and Speculation on the Phase Boundaries

      • Kellie Michele Evans

      Pages 179-221

   2. RealLife

      • Marcus Pivato

      Pages 223-234

   3. Variations on the Game of Life

      • Ferdinand Peper, Susumu Adachi, Jia Lee

      Pages 235-255

   4. Does Life Resist Asynchrony?

      • Nazim Fatès

      Pages 257-274

   5. LIFE with Short-Term Memory

      • Ramón Alonso-Sanz

      Pages 275-290

   6. Localization Dynamics in a Binary Two-Dimensional Cellular Automaton: The Diffusion Rule

      • Genaro J. Martínez, Andrew Adamatzky, Harold V. McIntosh

      Pages 291-315

In the late 1960s British mathematician John Conway invented a virtual mathematical machine that operates on a two-dimensional array of square cell. Each cell takes two states, live and dead. The cells’ states are updated simultaneously and in discrete time. A dead cell comes to life if it has exactly three live neighbours. A live cell remains alive if two or three of its neighbours are alive, otherwise the cell dies. Conway’s Game of Life became the most programmed solitary game and the most known cellular automaton. The book brings together results of forty years of study into computational, mathematical, physical and engineering aspects of The Game of Life cellular automata. Selected topics include phenomenology and statistical behaviour; space-time dynamics on Penrose tilling and hyperbolic spaces; generation of music; algebraic properties; modelling of financial markets; semi-quantum extensions; predicting emergence; dual-graph based analysis; fuzzy, limit behaviour and threshold scaling; evolving cell-state transition rules; localization dynamics in quasi-chemical analogues of GoL; self-organisation towards criticality; asynochrous implementations. The volume is unique because it gives a comprehensive presentation of the theoretical and experimental foundations, cutting-edge computation techniques and mathematical analysis of the fabulously complex, self-organized and emergent phenomena defined by incredibly simple rules.

• Automat
• Extension
• Turing machine
• automata
• cellular automaton
• complexity
• modeling
• algorithm analysis and problem complexity

From the reviews:

“This volume’s 27 papers offer some systematic methods and rigorous theorems that exhibit the study of Conway’s game and its variations, emerging out of the realm of merely recreational mathematics. … this unique book will have great value as both a state-of-the-art summary and a collection of proposals for new directions to explore. Summing Up: Highly recommended. Upper-division undergraduates through professionals.” (D. V. Feldman, Choice, Vol. 48 (4), December, 2010)

“Andrew Adamatzky has assembled a superb collection of papers on Life that encompass work going back more than 20 years. … maintains a good balance between interconnectedness and recognition of the papers as independent contributions. … This book is a treasure trove of history, concepts, and models. It is a good starting place for a newcomer to the study of Conway’s Game of Life, an opening of vistas for the amateur hobbyist, and a serious handbook for the professional researcher.” (Anthony J. Duben, ACM Computing Reviews, February, 2011)

• Fac. of Computing, Engineering and, Mathematical Sciences (CEMS), University of the West of England, Bristol, United Kingdom

  Andrew Adamatzky

Andrew Adamatzky is a Professor in Unconventional Computing in the Department of Computer Science, and a member of Bristol Robotics Lab. He does research in reaction-diffusion computing, cellular automata, physarum computing, massive parallel computation, applied mathematics, collective intelligence and robotics.

Policies and ethics