Cellular Automata And Complexity

Collected Papers

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Author: Stephen Wolfram

Publisher: CRC Press

ISBN: 0429973721

Category: Mathematics

Page: 608

View: 3735

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.

New Kind of Science

Notes from the Book

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Author: Stephen Wolfram

Publisher: N.A

ISBN: 9781579550196

Category: Science

Page: 348

View: 670

Cellular Automata Machines

A New Environment for Modeling

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Author: Tommaso Toffoli,Norman Margolus

Publisher: MIT Press

ISBN: 9780262200608

Category: Computers

Page: 259

View: 828

Theory of Computation -- Computation by Abstracts Devices.

Cellular Automata

A Discrete Universe

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Author: Andrew Ilachinski

Publisher: World Scientific Publishing Company

ISBN: 981310256X

Category: Science

Page: 840

View: 9891

Cellular automata are a class of spatially and temporally discrete mathematical systems characterized by local interaction and synchronous dynamical evolution. Introduced by the mathematician John von Neumann in the 1950s as simple models of biological self-reproduction, they are prototypical models for complex systems and processes consisting of a large number of simple, homogeneous, locally interacting components. Cellular automata have been the focus of great attention over the years because of their ability to generate a rich spectrum of very complex patterns of behavior out of sets of relatively simple underlying rules. Moreover, they appear to capture many essential features of complex self-organizing cooperative behavior observed in real systems. This book provides a summary of the basic properties of cellular automata, and explores in depth many important cellular-automata-related research areas, including artificial life, chaos, emergence, fractals, nonlinear dynamics, and self-organization. It also presents a broad review of the speculative proposition that cellular automata may eventually prove to be theoretical harbingers of a fundamentally new information-based, discrete physics. Designed to be accessible at the junior/senior undergraduate level and above, the book will be of interest to all students, researchers, and professionals wanting to learn about order, chaos, and the emergence of complexity. It contains an extensive bibliography and provides a listing of cellular automata resources available on the World Wide Web.

Game of Life Cellular Automata

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Author: Andrew Adamatzky

Publisher: Springer Science & Business Media

ISBN: 9781849962179

Category: Computers

Page: 579

View: 7685

In the late 1960s British mathematician John Conway invented a virtual mathematical machine that operates on a two-dimensional array of square cell. Each cell takes two states, live and dead. The cells’ states are updated simultaneously and in discrete time. A dead cell comes to life if it has exactly three live neighbours. A live cell remains alive if two or three of its neighbours are alive, otherwise the cell dies. Conway’s Game of Life became the most programmed solitary game and the most known cellular automaton. The book brings together results of forty years of study into computational, mathematical, physical and engineering aspects of The Game of Life cellular automata. Selected topics include phenomenology and statistical behaviour; space-time dynamics on Penrose tilling and hyperbolic spaces; generation of music; algebraic properties; modelling of financial markets; semi-quantum extensions; predicting emergence; dual-graph based analysis; fuzzy, limit behaviour and threshold scaling; evolving cell-state transition rules; localization dynamics in quasi-chemical analogues of GoL; self-organisation towards criticality; asynochrous implementations. The volume is unique because it gives a comprehensive presentation of the theoretical and experimental foundations, cutting-edge computation techniques and mathematical analysis of the fabulously complex, self-organized and emergent phenomena defined by incredibly simple rules.

Cellular Automata

9th International Conference on Cellular Automata for Research and Industry, ACRI 2010, Ascoli Piceno, Italy, September 21-24, 2010, Proceedings

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Author: Stefania Bandini,Sara Manzoni,Hiroshi Umeo,Vizzari Giuseppe

Publisher: Springer

ISBN: 3642159796

Category: Computers

Page: 672

View: 1625

Cellular Automaton Modeling of Biological Pattern Formation

Characterization, Examples, and Analysis

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Author: Andreas Deutsch,Sabine Dormann

Publisher: Birkhäuser

ISBN: 1489979808

Category: Mathematics

Page: 464

View: 2363

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

The MATHEMATICA ® Book, Version 4

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Author: Stephen Wolfram

Publisher: Cambridge University Press

ISBN: 9780521643146

Category: Computers

Page: 1470

View: 7633

With over a million users around the world, the Mathematica software system created by Stephen Wolfram has defined the direction of technical computing for the past decade. The enhanced text and hypertext processing and state-of-the-art numerical computation features will ensure that Mathematica 4, takes scientific computing into the next century.The Mathematica Book continues to be the definitive reference guide to this revolutionary software package and is released in this new edition to coincide with the release of the new version of Mathematica.The Mathematica Book is a must-have purchase for anyone who wants to understand the opportunities in science, technology, business, and education made possible by Mathematica 4. This encompasses a broad audience of scientists and mathematicians; engineers; computer professionals; financial analysts; medical researchers; and students at high-school, college, and graduate levels.Written by the creator of the system, The Mathematica Book includes both a tutorial introduction and complete reference information, and contains comprehensive description of how to take advantage of Mathematica's ability to solve myriad technical computing problems and its powerful graphical and typesetting capabilities.New to this version:* Major efficiency enhancements in handling large volumes of numerical data.* Internal packed array technology to make repetitive operations on large numerical datasets radically more efficient in speed and memory.*Improved algebraic computation facilities, including support for assumptions within Simplify, and related functions, and specification of domains for variables, as well as full support of symbolic Laplace, Fourier, and Z transforms.* Additional Mathematica functions, including Dirac Delta, Stuve, Harmonic numbers, etc.* Enhanced graphics and sound capabilities, including faster graphic generation and additional format support for graphics and sound.* Full-function spell checking including special technical dictionaries.

Designing Beauty: The Art of Cellular Automata

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Author: Andrew Adamatzky,Genaro J. Martínez

Publisher: Springer

ISBN: 3319272705

Category: Technology & Engineering

Page: 191

View: 8603

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.

Modelling Urban Development with Geographical Information Systems and Cellular Automata

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Author: Yan Liu

Publisher: CRC Press

ISBN: 9781420059908

Category: Technology & Engineering

Page: 186

View: 4322

Urban development and migration from rural to urban areas are impacting prime agricultural land and natural landscapes, particularly in the less developed countries. These phenomena will persist and require serious study by those monitoring global environmental change. To address this need, various models have been devised to analyze urbanization and the physical, socioeconomic, and institutional factors impacting urban development. The most promising and rapidly developing of these paradigms take advantage of new Geographical Information System (GIS) technology. Modelling Urban Development with Geographical Information Systems and Cellular Automata presents one such cutting-edge model that is more than just predictive. It describes how the model simulates the urbanization process, and it provides theoretical context to promote understanding. Starting with a practical overview of the modelling techniques used in urban development research, the author focuses on the cellular automata model and its greatest strength – the incorporation of fuzzy set and fuzzy logic approaches through which urban development can be viewed as a spatially and temporally continuous process. Real-Life Application to Develop Future Planning Methods The text describes a landmark study underway, in which the fuzzy constrained cellular automata model has been implemented in a GIS environment to simulate urban development in Sydney, Australia. Featuring a survey of associated research and a geographical database for the Sydney simulation, this book answers many general "what if" questions for urban planners and details a new approach that they can adapt to their own testing and evaluation needs. This modeling method will provide researchers and planners with the means to not just predict population trends, but to better prepare for their consequences.

Cellular Automata and Groups

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Author: Tullio Ceccherini-Silberstein,Michel Coornaert

Publisher: Springer Science & Business Media

ISBN: 9783642140341

Category: Computers

Page: 440

View: 4142

Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.

Hydrodynamic Limits and Related Topics

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Author: Shui Feng,Anna T. Lawniczak,S. R. S. Varadhan

Publisher: American Mathematical Soc.

ISBN: 9780821871331

Category: Science

Page: 141

View: 6498

This book presents the lecture notes and articles from the workshop on hydrodynamic limits held at The Fields Institute (Toronto). The first part of the book contains the notes from the mini-course given by Professor S. R. S. Varadhan. The second part contains research articles reviewing the diverse progress in the study of hydrodynamic limits and related areas. This book offers a comprehensive introduction to the theory and its techniques, including entropy and relative entropy methods, large deviation estimates, and techniques in nongradient systems. This book, especially the lectures of Part I, could be used as a text for an advanced graduate course in hydrodynamic limits and interacting particle systems.

Additive Cellular Automata

Theory and Applications

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Author: Parimal Pal Chaudhuri,Dipanwita Roy Chowdhury,Sukumar Nandi,Santanu Chattopadhyay

Publisher: John Wiley & Sons

ISBN: 9780818677175

Category: Mathematics

Page: 364

View: 1752

CA and its applications: a brief survey; group CA characterization; Characterization of nongroup CA; CA as a universal pattern generator; CA-based error correcting code; Design of CA-based cipher system; Generation of hashing functions; CA-based testable logic synthesis; Theory and application of two-dimensional CA; Bibliography; Index.

Informatics in Control, Automation and Robotics I

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Author: José Braz,Helder Araújo,Alves Vieira,Bruno Encarnação

Publisher: Springer Science & Business Media

ISBN: 1402045433

Category: Computers

Page: 290

View: 6301

This is a collection of papers presented at the 1st International Conference on Informatics in Control, Automation and Robotics (ICINCO). The papers focus on real world applications, covering three main themes: Intelligent Control Systems, Optimization, Robotics and Automation, Signal Processing, Systems Modeling and Control. The book will interest professionals in the areas of control and robotics.

Complexity Approach To Sustainability, A: Theory And Application (Second Edition)

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Author: Espinosa Angela,Walker Jon

Publisher: World Scientific

ISBN: 1786342057

Category: Business & Economics

Page: 584

View: 715

Business sustainability and sustainable development are of great importance in modern-day socio-economic study. Despite this, the impact of recent contributions from systems and complexity sciences in addressing these issues has not yet filtered down into effective practice. This book argues that there is a need for urgency in the application of analytical tools which embody the principles of complexity management in sustainability research, in particular in the context of the global climate change. The approach presented is based on the concept of clusters of whole systems coming together through collaboration, in order to create larger wholes capable of dealing with the issues facing our socio-economic environmental systems. In this updated second edition, the authors further clarify the viability and sustainability (V&S) approach, and the criteria and framework needed for sustainable governance. It includes a more detailed perspective on the implications of the V&S approach to businesses and networks towards changes in structure, strategy and processes, inspired by specific case studies. Key additions include a criteria for designing more viable and sustainable self-governed organizations, the methodologies and tools to design and implement self-transformations towards sustainability, and how these tools support sustainability management individually and globally, for businesses and society.

The Global Dynamics of Cellular Automata

An Atlas of Basin of Attraction Fields of One-dimensional Cellular Automata

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Author: Andrew Wuensche,Mike Lesser

Publisher: Andrew Wuensche

ISBN: 9780201557404

Category: Mathematics

Page: 250

View: 5126

Subtitled, An atlas of basin of attraction fields of one-dimensional cellular automata. Contains work previously unpublished in scientific journals that may have profound significance in many areas of the sciences of complexity, introducing a powerful global perspective for the study of discrete dynamical systems. The atlas is intended, with accompanying software, as an aid to navigation into rule behavior space and will be of interest to those involved with cellular automata theory, complex systems, dynamical systems, computational theory, artificial life, neural networks, and aspects of genetics. Annotation copyrighted by Book News, Inc., Portland, OR

The Mathematica GuideBook for Programming

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Author: Michael Trott

Publisher: Springer

ISBN: 1441985034

Category: Mathematics

Page: 1028

View: 7349

This comprehensive, detailed reference provides readers with both a working knowledge of Mathematica in general and a detailed knowledge of the key aspects needed to create the fastest, shortest, and most elegant implementations possible. It gives users a deeper understanding of Mathematica by instructive implementations, explanations, and examples from a range of disciplines at varying levels of complexity. The three volumes -- Programming, Graphics, and Mathematics, total 3,000 pages and contain more than 15,000 Mathematica inputs, over 1,500 graphics, 4,000+ references, and more than 500 exercises. This first volume begins with the structure of Mathematica expressions, the syntax of Mathematica, its programming, graphic, numeric and symbolic capabilities. It then covers the hierarchical construction of objects out of symbolic expressions, the definition of functions, the recognition of patterns and their efficient application, program flows and program structuring, and the manipulation of lists. An indispensible resource for students, researchers and professionals in mathematics, the sciences, and engineering.

Automata-2008

Theory and Applications of Cellular Automata

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Author: Andrew Adamatzky,R. Alonso-Sanz,A. Lawniczak

Publisher: Luniver Press

ISBN: 1905986165

Category: Computers

Page: 616

View: 1324

Cellular automata are regular uniform networks of locally-connected finite-state machines. They are discrete systems with non-trivial behaviour. Cellular automata are ubiquitous: they are mathematical models of computation and computer models of natural systems. The book presents results of cutting edge research in cellular-automata framework of digital physics and modelling of spatially extended non-linear systems; massive-parallel computing, language acceptance, and computability; reversibility of computation, graph-theoretic analysis and logic; chaos and undecidability; evolution, learning and cryptography. The book is unique because it brings together unequalled expertise of inter-disciplinary studies at the edge of mathematics, computer science, engineering, physics and biology.

Soft Computing in Engineering Design and Manufacturing

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Author: Pravir K. Chawdhry,Rajkumar Roy,Raj K. Pant

Publisher: Springer Science & Business Media

ISBN: 9783540762140

Category: Computers

Page: 454

View: 6504

This book is a collection of some 47 research papers that were presented in June 1997 at the 2nd Online World Conference in soft computing. It covers the state-of-the-art techniques and applications of soft computing which will stimulate further advances towards the next generation of intelligent machines. The papers are organised into eight sections which cover areas such as genetic algorithms, engineering design, manufacturing and robotics. The book's main focus, though, is on the existence and interaction of fuzzy, neural and evolutionary computing techniques. Though fundamentally quite different from one another, these techniques can work incredibly well together when building intelligent systems. Soft Computing in Engineering Design and Manufacturing will be of interest to graduate students and researchers involved in soft computing. It will also be useful for those working in related industrial environments.