TY  - BOOK
AU  - Hadeler,K.P.
AU  - M©ơller,Johannes
ED  - Ohio Library and Information Network.
TI  - Cellular automata: analysis and applications 
T2  - Springer monographs in mathematics
SN  - 3319530437
AV  - QA267.5.C45 
U1  - 006.3/822 23
PY  - 2017///
CY  - Cham
PB  - Springer
KW  - Cellular automata
KW  - Electronic books
N1  - Includes bibliographical references and index; List of Symbols; 1 Introduction; 1.1 Discreteness; 1.2 The Game of Life; 1.3 Contact Automata; 1.4 Some Wolfram Automata; 1.5 Greenberg-Hastings Automata; 1.6 Langton's Ant and Life Without Death; 1.7 A Nice Little Automaton; 1.8 History and Applications; 1.9 Outline of This Work; 2 Cellular Automata: Basic Definitions; 2.1 The Grid; 2.1.1 Abelian or Regular Grids; 2.1.2 Non-Abelian Grids; 2.2 The Neighborhood; 2.3 Elementary State and the Global State; 2.4 The Local and the Global Function; 2.5 Excursion: The Growth Function of a Cayley Graph; 3 Cantor Topology of Cellular Automata. 3.1 Prelude: Cantor Sets and Cantor Spaces3.1.1 The Classical Mid-Third Cantor Set; 3.1.2 Cantor Spaces; 3.2 Cantor Metric for Cellular Automata; 3.3 The Curtis-Hedlund-Lyndon Theorem; 3.4 Spatial Structure and Simplifications; 3.4.1 Examples: Structures That Are Not CellularAutomata; 3.4.2 Simplification of the State Space; 3.4.3 Simplification of the Neighborhood; 3.4.4 Simplification of the Grid; 3.5 Cellular Automata and Continuous Maps on Cantor Spaces; 3.5.1 Bijective Maps; 3.5.2 General Maps: The Universal Cellular Automaton; 4 Besicovitch and Weyl Topologies. 5.6 Structure of Attractors-Infinite Grids: Hurley Classification6 Chaos and Lyapunov Stability; 6.1 Topological Chaos; 6.2 Permuting Cellular Automata; 6.2.1 Surjective Cellular Automata; 6.2.2 Topological Transitivity; 6.2.3 Denseness of Periodic Points; 6.3 Lyapunov Stability and Gilman Classification; 6.3.1 Class Gilman 1; 6.3.2 Class Gilman 2; 6.3.3 Class Gilman 3; 6.3.4 Class Gilman 4; 7 Language Classification of Kůrka; 7.1 Grammar; 7.2 Finite Automata; 7.3 Finite Automata and Regular Languages; 7.4 Cellular Automata and Language: Kůrka Classification; 7.4.1 Class Kůrka 1; Available to OhioLINK libraries
N2  - This book focuses on a coherent representation of the main approaches to analyze the dynamics of cellular automata. Cellular automata are an inevitable tool in mathematical modeling. In contrast to classical modeling approaches as partial differential equations, cellular automata are straightforward to simulate but hard to analyze. In this book we present a review of approaches and theories that allow the reader to understand the behavior of cellular automata beyond simulations. The first part consists of an introduction of cellular automata on Cayley graphs, and their characterization via the fundamental Cutis-Hedlund-Lyndon theorems in the context of different topological concepts (Cantor, Besicovitch and Weyl topology). The second part focuses on classification results: What classification follows from topological concepts (Hurley classification), Lyapunov stability (Gilman classification), and the theory of formal languages and grammars (Kůrka classification). These classifications suggest to cluster cellular automata, similar to the classification of partial differential equations in hyperbolic, parabolic and elliptic equations. This part of the book culminates in the question, whether properties of cellular automata are decidable. Surjectivity, and injectivity are examined, and the seminal Garden of Eden theorems are discussed. The third part focuses on the analysis of cellular automata that inherit distinct properties, often based on mathematical modeling of biological, physical or chemical systems. Linearity is a concept that allows to define self-similar limit sets. Models for particle motion show how to bridge the gap between cellular automata and partial differential equations (HPP model and ultradiscrete limit). Pattern formation is related to linear cellular automata, to the Bar-Yam model for Turing pattern, and Greenberg-Hastings automata for excitable media. Also models for sandpiles, the dynamics of infectious diseases and evolution of predator-prey systems are discussed. Mathematicians find an overview about theory and tools for the analysis of cellular automata. The book contains an appendix introducing basic mathematical techniques and notations, such that also physicists, chemists and biologists interested in cellular automata beyond pure simulations will benefit
UR  - https://drive.google.com/file/d/17QlKrk2GO4A5AFkzTu4ftI22CK3BM7RS/view?usp=sharing
ER  -