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.
- 245 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
The Mathematics of Cellular Automata
About this book
Information
Subtopic
Mathematics GeneralIndex
MathematicsTable of contents
- half title page
- title page
- Copyright
- Contents
- Preface
- Basic notation
- Chapter 1. Introduction to Symbolic Dynamics and Cellular Automata
- Chapter 2. Properties of Symbol Spaces
- Chapter 3. Dynamics of CAs: Equicontinuity and attractors
- Chapter 4. Dynamics and Classification of Cellular Automata
- Chapter 5. Surjectivity and the Garden of Eden Theorem
- Chapter 6. Two-dimensional CAs and Conway’s Game of Life
- Chapter 7. Stochastic Cellular Automata
- Chapter 8. Further directions
- Bibliography
- Index
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Yes, you can access The Mathematics of Cellular Automata by Jane Hawkins in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over 1.5 million books available in our catalogue for you to explore.