This textbook offers a rigorous mathematical introduction to cellular automata (CA). Numerous colorful graphics illustrate the many intriguing phenomena, inviting undergraduates to step into the rich field of symbolic dynamics. Beginning with a brief history, the first half of the book establishes t...

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Bibliographische Detailangaben

1. Verfasser:	Hawkins, Jane 1954- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Providence, Rhode Island American Mathematical Society [2024]
Schriftenreihe:	Student mathematical library volume 108
Schlagworte:	Cellular automata Dynamical systems and ergodic theory > Topological dynamics > Cellular automata Dynamical systems and ergodic theory > Topological dynamics > Symbolic dynamics Computer science > Theory of computing > Cellular automata Dynamical systems and ergodic theory > Low-dimensional dynamical systems Lehrbuch Aufgabensammlung
Zusammenfassung:	This textbook offers a rigorous mathematical introduction to cellular automata (CA). Numerous colorful graphics illustrate the many intriguing phenomena, inviting undergraduates to step into the rich field of symbolic dynamics. Beginning with a brief history, the first half of the book establishes the mathematical foundations of cellular automata. After recapping the essentials from advanced calculus, the chapters that follow introduce symbolic spaces, equicontinuity, and attractors. More advanced topics include the Garden of Eden theorem and Conway's Game of Life, and a chapter on stochastic CA showcases a model of virus spread. Exercises and labs end each chapter, covering a range of applications, both mathematical and physical. Designed for undergraduates studying mathematics and related areas, the text provides ample opportunities for end-of-semester projects or further study. Computer use for the labs is largely optional, providing flexibility for different preferences and resources. Knowledge of advanced calculus and linear algebra is essential, while a course in real analysis would be ideal. Cover -- half title page -- title page -- Copyright -- Contents -- Preface -- Basic notation -- Chapter 1. Introduction to Symbolic Dynamics and Cellular Automata -- 1.1. Coding and symbolic dynamics -- 1.2. Cellular automata -- 1.3. Exercises -- 1.4. Labs -- Chapter 2. Properties of Symbol Spaces -- 2.1. Symbol spaces for cellular automata -- 2.2. Open and closed sets in metric spaces: The bigger picture -- 2.3. Convergence and Cauchy sequences in metric spaces -- 2.4. Dimension -- 2.5. Zero-dimensional metric spaces -- 2.6. Exercises -- 2.7. Labs -- Chapter 3. Dynamics of CAs: Equicontinuity and attractors -- 3.1. Continuous functions on ℝ -- 3.2. Continuous functions on metric spaces -- 3.3. Equicontinuity and dynamics -- 3.4. Limit sets, accumulation points, and attractors -- 3.5. Exercises -- 3.6. Labs -- Chapter 4. Dynamics and Classification of Cellular Automata -- 4.1. A labeling scheme for elementary CAs -- 4.2. Two classifications of one-dimensional CAs -- 4.3. Classes 1 and 2: Equicontinuity in CAs -- 4.4. Classes 3 and 4: Chaotic dynamics in CAs -- 4.5. Chaotic dynamics of cellular automata -- 4.6. Exercises -- 4.7. Labs -- Chapter 5. Surjectivity and the Garden of Eden Theorem -- 5.1. Surjective maps -- 5.2. Surjectivity and dynamics for CAs -- 5.3. Exercises -- 5.4. Labs -- Chapter 6. Two-dimensional CAs and Conway's Game of Life -- 6.1. The basic setup for 2D CAs -- 6.2. Conway's Game of Life -- 6.3. The classification scheme for 2D CAs -- 6.4. Exercises -- 6.5. Labs -- Chapter 7. Stochastic Cellular Automata -- 7.1. An overview of probability distributions among CAs: Making random choices -- 7.2. The first examples -- 7.3. Equicontinuity and classification of SCAs -- 7.4. A detailed definition of a stochastic cellular automaton in one dimension -- 7.5. An application of SCAs: Modeling viral spread -- 7.6. Exercises.
Beschreibung:	Literaturverzeichnis: Seite 223-226. - Index
Beschreibung:	xv, 228 Seiten Illustrationen 22 cm
ISBN:	9781470475376