This book brings together the impact of Prof. John Horton Conway, the playful and legendary mathematician's wide range of contributions in science which includes research areas―Game of Life in cellular automata, theory of finite groups, knot theory, number theory, combinatorial game theory, and coding theory. It contains transcripts where some eminent scientists have shared their first-hand experience of interacting with Conway, as well as some invited research articles from the experts focusing on Game of Life, cellular automata, and the diverse research directions that started with Conway's Game of Life. The book paints a portrait of Conway's research life and philosophical direction in mathematics and is of interest to whoever wants to explore his contribution to the history and philosophy of mathematics and computer science. It is designed as a small tribute to Prof. Conway whom we lost on April 11, 2020.
Author(s): Sukanta Das, Souvik Roy, Kamalika Bhattacharjee
Series: Emergence, Complexity and Computation, 45
Publisher: Springer
Year: 2022
Language: English
Pages: 220
City: Cham
Preface
John Horton Conway
Contents
Contributors
Transcript from Conway Memorial Lecture Series
John Horton Conway: A Master of All Trades
1 A Personal Remembrance
2 Interaction with Robert Wilson
Two Different Directions: John Conway and Stephen Wolfram
1 Conway—The Mathematical Engineer
2 Program as Model for the World
3 Computational Equivalence
4 Cellular Automata and Physics
5 Multiway Graphs
6 Limits of Physics and Mathematics
7 Interaction with Stephen Wolfram
8 Concluding Remarks
Conway Memorial Series: The Mathematical Artist of Play
1 A Personal Encounter
2 The Nim Game
3 Beyond Combinatorial Game Theory
4 Interaction with R. Ramanujam
Invited Articles
Some Notes About the Game of Life Cellular Automaton
1 The Game of Life
2 The Game of Life and Its Connection in One Dimension
3 Final Notes
References
Gliders in the Game of Life and in a Reversible Cellular Automaton
1 Game of Life and the Glider
1.1 Irreversibility of the Game of Life (GoL)
1.2 The Glider, Spaceships and a Glider Gun
1.3 Controlling a Glider
1.4 Collisions of Gliders
1.5 Collisions of Gliders with a Block
2 Elementary Triangular Partitioned Cellular Automaton
2.1 Triangular Partitioned Cellular Automaton
2.2 Elementary Triangular Partitioned Cellular Automaton (ETPCA)
2.3 Reversible ETPCA and Conservative ETPCA
2.4 Dualities in ETPCAs
2.5 Time-Symmetry in Reversible ETPCAs
3 The Glider in the Reversible ETPCA0347
3.1 Evolution from a One-Particle Pattern
3.2 The Glider and Useful Patterns
3.3 Controlling a Glider
3.4 Collisions of Gliders
3.5 Collisions of a Glider with a Fin
4 Composing Reversible Computers in ETPCA 0347 Using a Glider
4.1 Making a Reversible Logic Element with Memory
4.2 Making Reversible Turing Machines
5 Concluding Remarks and Open Problems
References
From Multiple to Single Updates Per Cell in Elementary Cellular Automata with Neighbourhood Based Priority
1 Introduction
2 Fundamentals
2.1 Definitions
2.2 Independent Neighbourhood Updates and Active State Transitions
3 From Multiple to Single Updates Per Cell Per Iteration
3.1 Overview of the Idea
3.2 Formalisation
4 Analysis of the Elementary Space with Neighbourhood Based Priority Asynchronism with Single Updates Per Cell
4.1 Dynamical Equivalence Classes
4.2 Identifying Dynamical Classes
4.3 An Example of the Full Process
5 Concluding Remarks
References
Game of Life, Athenian Democracy and Computation
1 Introduction
2 Game-of-Life and Direct Democracy
3 Athenian Democracy
4 A Model of Computation
5 Cellular Automata with Memory
6 Conclusion
References
Algorithmic Information Dynamics of Cellular Automata
1 Introduction
2 Cellular Automata
3 Algorithmic Information Dynamics (AID)
3.1 Numerical Methods
3.2 The Coding Theorem Method and Causal Discovery
3.3 The Block Decomposition Method (BDM)
3.4 Algorithmic Intervention Analysis
3.5 Information Deficiency as an Algorithmic Information Calculus
3.6 Study of Dynamical Systems in Software Space
4 AID Application to Elementary Cellular Automata
4.1 ECA Perturbation Analysis
4.2 ECA Colliding Event Quantification
5 Conclusions
References
The Game of Life in Three Dimensions, and Other Tessellations
1 Introduction—Conway's Game of Life
1.1 The Rules of Life
2 Finding a Rule for Three-Dimensional Life
2.1 The Best Rules for Three-Dimensional Versions of Life
2.2 A Comparison Between Conway's Life and Three-Dimensional Life
2.3 The Rule 4, 5/5
3 Another Game of 3D Life
4 Additional Games of Life in Two Dimensional Grids
4.1 The Triangular Grid
4.2 The Hexagonal grid
5 Conclusion
References
