Mathematics of cellular automata
Hawkins, Jane
Mathematics of cellular automata - India : Universities Press, 2025. - xv, 228p. : ill. ; 22 cm - Student mathematical library, v. 108 1520-9121 ; .
Includes bibliographical references and index.
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.
Readership: Undergraduate students interested in an accessible introduction to dynamical systems, e.g. Conway's Game of Life.
9789349750647
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
510.5 / HAW-M
Mathematics of cellular automata - India : Universities Press, 2025. - xv, 228p. : ill. ; 22 cm - Student mathematical library, v. 108 1520-9121 ; .
Includes bibliographical references and index.
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.
Readership: Undergraduate students interested in an accessible introduction to dynamical systems, e.g. Conway's Game of Life.
9789349750647
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
510.5 / HAW-M
