Cellular Automata: Analysis and Applications

Karl Peter Hadeler, Dr.rer.nat. 1965  (U. of Hamburg), Habilitation 1967 (U. of Hamburg). In 1963/1964 visiting Moscow State University (MGU), 1968/1969 Visiting Associate Professor,U. of Minnesota. 1970 Associate Professor, Technical Department, U. of Erlangen. 1971 Professor of Mathematics, U. of Tübingen. Retired 2005, then 2005-2011 Non-permanent Professor, Arizona State University. Visiting Professor Aarhus, Nijmegen, Georgia Tech, Emory. 2009 John von Neumann Professorship, Technical University of Munich. Member of Center of Excellence (DFG/German NSF). Research interests: Ordinary and partial differential equations (reaction diffusion equations), delay equations, matrix theory, mathematical biology. Since 2011 about ten publications in mathematics. Johannes Müller studied in Karlsruhe and Tübingen, where he did his habilitation in 2001. After stays in Utrecht and Cologne, he became head of a research group in the Institute for Biomathematics and Biometry in the Helmholtz Center, Munich. Since 2004 he is teaching as a professor at the Technische Universität München. The research interests of Johannes Müller is on the interface of mathematics and life sciences. In particular his research is concerned with the theory of dynamical systems, cellular automata, and stochastic processes respectively their application.

• 1.Introduction.- 2.Cellular automata - basic definitions.- 3.Cantor topology of cellular automata.- 4.Besicovitch and Weyl topologies.- 5 Attractors.- 6 Chaos and Lyapunov stability.- 7 Language classification of Kůrka.- 8.Turing machines, tiles, and computability.- 9 Surjectivity and injectivity of global maps.- 10.Linear Cellular Automata.- 11 Particle motion.- 12.- Pattern formation.- 13.Applications in various areas.- A.Basic mathematical tools.

“I have enjoyed reading this book. It provides a clear account, with many examples and nice proofs, of the most important and general rigorous results of cellular automata in a way that is accessible to a wide readership. Advanced undergraduate and beginning graduate students of several fields … will find here a valuable toolbox. The book is also valuable for self-study and as a reference, and does a great service in bridging the gap between applications/simulations and rigorous mathematical results.” (Vladimir García Morales, Mathematical Reviews, January, 2018)“This book gives a comprehensive overview of the methods of analysis that are applicable to these dynamical systems. ... this is the first work that gives a comprehensive overview of the methods that have been proposed to derive a cellular automaton from a partial differential equation, and vice versa. ... this book is a must-have for researchers in the field.” (Jan Baetens, zbMATH 1382.37001, 2018)