Deeply rooted in fundamental research in Mathematics and Computer Science, Cellular Automata (CA) are recognized as an intuitive modeling paradigm for Complex Systems. Already very basic CA, with extremely simple micro dynamics such as the Game of Life, show an almost endless display of complex emergent behavior. Conversely, CA can also be designed to produce a desired emergent behavior, using either theoretical methodologies or evolutionary techniques. Meanwhile, beyond the original realm of applications - Physics, Computer Science, and Mathematics – CA have also become work horses in very different disciplines such as epidemiology, immunology, sociology, and finance. In this context of fast and impressive progress, spurred further by the enormous attraction these topics have on students, this book emerges as a welcome overview of the field for its practitioners, as well as a good starting point for detailed study on the graduate and post-graduate level. The book contains three parts, two major parts on theory and applications, and a smaller part on software. The theory part contains fundamental chapters on how to design and/or apply CA for many different areas. In the applications part a number of representative examples of really using CA in a broad range of disciplines is provided - this part will give the reader a good idea of the real strength of this kind of modeling as well as the incentive to apply CA in their own field of study. Finally, we included a smaller section on software, to highlight the important work that has been done to create high quality problem solving environments that allow to quickly and relatively easily implement a CA model and run simulations, both on the desktop and if needed, on High Performance Computing infrastructures.

This book contains the courses given at the Fifth School on Complex Systems held at Santiago, Chile, from 9th .to 13th December 1996. At this school met researchers working on areas related with recent trends in Complex Systems, which include dynamical systems, cellular automata, symbolic dynamics, spatial systems, statistical physics and thermodynamics. Scientists working in these subjects come from several areas: pure and applied mathematics, physics, biology, computer science and electrical engineering. Each contribution is devoted to one of the above subjects. In most cases they are structured as surveys, presenting at the same time an original point of view about the topic and showing mostly new results. The paper of Bruno Durand presents the state of the art on the relationships between the notions of surjectivity, injectivity and reversibility in cellular automata when finite, infinite or periodic configurations are considered, also he discusses decidability problems related with the classification of cellular automata as well as global properties mentioned above. The paper of Eric Goles and Martin Matamala gives a uniform presentation of simulations of Turing machines by cellular automata. The main ingredient is the encoding function which must be fixed for all Turing machine. In this context known results are revised and new results are presented.

Modeling Chemical Systems using Cellular Automata provides a practical introduction to an exciting modeling paradigm for complex systems. The book first discusses the nature of scientific inquiry using models and simulations, and then describes the nature of cellular automata models. It then gives detailed descriptions, with examples and exercises, of how cellular automata models can be used in the study of a wide variety chemical, physical, and biochemical phenomena. Topics covered include models of water itself, solution phenomena, solution interactions with stationary systems, first- and second-order kinetic phenomena, enzyme kinetics, vapor-liquid equilibrium, and atomic and molecular excited-state kinetics. The student experiences these systems through hands-on examples and guided studies. This book is the first of its kind: a textbook and a laboratory manual about cellular automata modeling of common systems in chemistry. The book is designed to be used as a text in undergraduate courses dealing with complex systems and/or as a computational supplement to laboratory courses taught at the undergraduate level. The book includes: - Compact descriptions of a large variety of physical and chemical phenomena - Illustrative examples of simulations, with exercises for further study - An instructor's manual for use of the program The book will be of great value in undergraduate courses in chemistry, physics, biology, applied mathematics, and bioinformatics, and as a supplement for laboratory courses in introductory chemistry, organic chemistry, physical chemistry, medicinal chemistry, chemical engineering and other courses dealing with statistical and dynamic systems. It allows the exploration of a wide range of dynamic phenomena, many of which are not normally accessible within conventional laboratory settings due to limitations of time, cost, and experimental equipment. The book is both a textbook on applied Cellular Automata and a lab manual for chemistry (physics, engineering) courses with lab activity. It would supplement other lab work and be an additonal book the students would use in the course. The authors have assessed the emerging need for this kind of activity in science labs because of the cost of the practical activitites and the frequent failure of some exercises leading to lost didactic value of some experiments. This book is pioneering an alternative that will grow in use. There are no course directors who would use Cellular Automata exclusively. The authors see an emerging interest in this kind of work in courses that contain lab exercises. One such course is the graduate course that Lemont Kier gives in Life Sciences about complexity. He uses many examples and studies from Cellular Automata in the latter part of this course.

Cellular automata are fully discrete dynamical systems with dynamical variables defined at the nodes of a lattice and taking values in a finite set. Application of a local transition rule at each lattice site generates the dynamics. The interpretation of systems with a large number of degrees of freedom in terms of lattice gases has received considerable attention recently due to the many applications of this approach, e.g. for simulating fluid flows under nearly realistic conditions, for modeling complex microscopic natural phenomena such as diffusion-reaction or catalysis, and for analysis of pattern-forming systems. The discussion in this book covers aspects of cellular automata theory related to general problems of information theory and statistical physics, lattice gas theory, direct applications, problems arising in the modeling of microscopic physical processes, complex macroscopic behavior (mostly in connection with turbulence), and the design of special-purpose computers.

Are mathematical equations the best way to model nature? For many years it had been assumed that they were. But in the early 1980s, Stephen Wolfram made the radical proposal that one should instead build models that are based directly on simple computer programs. Wolfram made a detailed study of a class of such models known as cellular automata, and discovered a remarkable fact: that even when the underlying rules are very simple, the behaviour they produce can be highly complex, and can mimic many features of what we see in nature. And based on this result, Wolfram began a program of research to develop what he called A Science of Complexity."The results of Wolfram's work found many applications, from the so-called Wolfram Classification central to fields such as artificial life, to new ideas about cryptography and fluid dynamics. This book is a collection of Wolfram's original papers on cellular automata and complexity. Some of these papers are widely known in the scientific community others have never been published before. Together, the papers provide a highly readable account of what has become a major new field of science, with important implications for physics, biology, economics, computer science and many other areas.

Cellular automata make up a class of completely discrete dynamical systems, which have became a core subject in the sciences of complexity due to their conceptual simplicity, easiness of implementation for computer simulation, and their ability to exhibit a wide variety of amazingly complex behavior. The feature of simplicity behind complexity of cellular automata has attracted the researchers' attention from a wide range of divergent fields of study of science, which extend from the exact disciplines of mathematical physics up to the social ones, and beyond. Numerous complex systems containing many discrete elements with local interactions have been and are being conveniently modelled as cellular automata. In this book, the versatility of cellular automata as models for a wide diversity of complex systems is underlined through the study of a number of outstanding problems using these innovative techniques for modelling and simulation.

Michael Batty offers a comprehensive view of urban dynamics in the context of complexity theory, presenting models that demonstrate how complexity theory can embrace a myriad of processes and elements that combine into organic wholes.

This fascinating, colourful book offers in-depth insights and first-hand working experiences in the production of art works, using simple computational models with rich morphological behaviour, at the edge of mathematics, computer science, physics and biology. It organically combines ground breaking scientific discoveries in the theory of computation and complex systems with artistic representations of the research results. In this appealing book mathematicians, computer scientists, physicists, and engineers brought together marvelous and esoteric patterns generated by cellular automata, which are arrays of simple machines with complex behavior. Configurations produced by cellular automata uncover mechanics of dynamic patterns formation, their propagation and interaction in natural systems: heart pacemaker, bacterial membrane proteins, chemical rectors, water permeation in soil, compressed gas, cell division, population dynamics, reaction-diffusion media and self-organisation. The book inspires artists to take on cellular automata as a tool of creativity and it persuades scientists to convert their research results into the works of art. The book is lavishly illustrated with visually attractive examples, presented in a lively and easily accessible manner.

The theory and practice of modeling cities and regions as complex, self-organizing systems, presenting widely used cellular automata-based models, theoretical discussions, and applications. Cities and regions grow (or occasionally decline), and continuously transform themselves as they do so. This book describes the theory and practice of modeling the spatial dynamics of urban growth and transformation. As cities are complex, adaptive, self-organizing systems, the most appropriate modeling framework is one based on the theory of self-organizing systems—an approach already used in such fields as physics and ecology. The book presents a series of models, most of them developed using cellular automata (CA), which are inherently spatial and computationally efficient. It also provides discussions of the theoretical, methodological, and philosophical issues that arise from the models. A case study illustrates the use of these models in urban and regional planning. Finally, the book presents a new, dynamic theory of urban spatial structure that emerges from the models and their applications. The models are primarily land use models, but the more advanced ones also show the dynamics of population and economic activities, and are integrated with models in other domains such as economics, demography, and transportation. The result is a rich and realistic representation of the spatial dynamics of a variety of urban phenomena. The book is unique in its coverage of both the general issues associated with complex self-organizing systems and the specifics of designing and implementing models of such systems.

Theory of Computation -- Computation by Abstracts Devices.