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Cellular Automata.

Author: Karl-Peter Hadeler; Johannes Müller
Publisher: Cham : Springer International Publishing, 2017.
Series: Springer monographs in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Hadeler, Karl-Peter.
Cellular Automata: Analysis and Applications.
Cham : Springer International Publishing, ©2017
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Karl-Peter Hadeler; Johannes Müller
ISBN: 9783319530437 3319530437
OCLC Number: 988869713
Notes: 8.5.4 Undecidability of the Domino Problem in Z 2.
Description: 1 online resource (467 pages).
Contents: 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.
Series Title: Springer monographs in mathematics.

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