The book introduces a powerful new global perspective for the study of discrete dynamical systems. After first looking at the unique trajectory of a system's future, an algorithm is also presented that directly computes the multiple merging trajectories that may have constituted the system's past. A given set of cellular parameters will, in a sense, crystallize state space into a set of basins of attraction that will typically have the topology of branching trees rooted on attractor cycles. The book makes accessible the explicit portraits of these mathematical objects through computer-generated graphics. (Book/disk package disk requires an 80286, or higher, IBM PC or compatible with 640K of memory, VGA graphics, and DOS 2.0 or higher.

Theory of Computation -- Computation by Abstracts Devices.

The book deals with analytical and computational studies of spatially-extended discrete dynamical systems: one-dimensional cellular automata. The topics included are non-constructible configurations, reversibility, probabilistic analysis and De Bruijn diagrams. Techniques discussed are based on topology, matrix theory, formal languages and probability theory. The book is an excellent reading for anybody interested in non-linearity, emergency, complexity and self-organization.

EXPLORING DISCRETE DYNAMICS is a comprehensive guide to studying cellular automata and discrete dynamical networks with the classic software Discrete Dynamics Laboratory (DDLab). These collective networks are at the core of complexity and emergent self-organisation. With interactive graphics, DDLab is able to explore an huge diversity of behaviour -- mostly terra incognita -- space-time patters, but also basins of attraction, mathematical objects representing the convergent flow in state-space. Applications range within physics, mathematics, biology, cognition, society, economics and computation, and more specifically in neural and genetic networks, artificial life, and a theory of memory.

This text explores the use of cellular automata in modeling pattern formation in biological systems. It describes several mathematical modeling approaches utilizing cellular automata that can be used to study the dynamics of interacting cell systems both in simulation and in practice. New in this edition are chapters covering cell migration, tissue development, and cancer dynamics, as well as updated references and new research topic suggestions that reflect the rapid development of the field. The book begins with an introduction to pattern-forming principles in biology and the various mathematical modeling techniques that can be used to analyze them. Cellular automaton models are then discussed in detail for different types of cellular processes and interactions, including random movement, cell migration, adhesive cell interaction, alignment and cellular swarming, growth processes, pigment cell pattern formation, tissue development, tumor growth and invasion, and Turing-type patterns and excitable media. In the final chapter, the authors critically discuss possibilities and limitations of the cellular automaton approach in modeling various biological applications, along with future research directions. Suggestions for research projects are provided throughout the book to encourage additional engagement with the material, and an accompanying simulator is available for readers to perform their own simulations on several of the models covered in the text. QR codes are included within the text for easy access to the simulator. With its accessible presentation and interdisciplinary approach, Cellular Automaton Modeling of Biological Pattern Formation is suitable for graduate and advanced undergraduate students in mathematical biology, biological modeling, and biological computing. It will also be a valuable resource for researchers and practitioners in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science. PRAISE FOR THE FIRST EDITION “An ideal guide for someone with a mathematical or physical background to start exploring biological modelling. Importantly, it will also serve as an excellent guide for experienced modellers to innovate and improve their methodologies for analysing simulation results.” —Mathematical Reviews

This book highlights both theoretical and applied advances in cellular learning automata (CLA), a type of hybrid computational model that has been successfully employed in various areas to solve complex problems and to model, learn, or simulate complicated patterns of behavior. Owing to CLA’s parallel and learning abilities, it has proven to be quite effective in uncertain, time-varying, decentralized, and distributed environments. The book begins with a brief introduction to various CLA models, before focusing on recently developed CLA variants. In turn, the research areas related to CLA are addressed as bibliometric network analysis perspectives. The next part of the book presents CLA-based solutions to several computer science problems in e.g. static optimization, dynamic optimization, wireless networks, mesh networks, and cloud computing. Given its scope, the book is well suited for all researchers in the fields of artificial intelligence and reinforcement learning.