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Table of Contents
Intro
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
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