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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. The 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. --- Cellular automata --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Computer Science --- Algebra --- Computers, Iterative circuit --- Iterative circuit computers --- Structures, Tessellation (Automata) --- Tessellation structures (Automata) --- Computer science. --- Computers. --- Algorithms. --- Computer logic. --- Computer science --- Artificial intelligence. --- Computer Science. --- Logics and Meanings of Programs. --- Algorithm Analysis and Problem Complexity. --- Artificial Intelligence (incl. Robotics). --- Theory of Computation. --- Computation by Abstract Devices. --- Discrete Mathematics in Computer Science. --- Mathematics. --- Parallel processing (Electronic computers) --- Pattern recognition systems --- Sequential machine theory --- Logic design. --- Computer software. --- Information theory. --- Computational complexity. --- Artificial Intelligence. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Software, Computer --- Computer systems --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Complexity, Computational --- Informatics --- Science --- Communication theory --- Communication --- Cybernetics --- Computer science—Mathematics. --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Calculators --- Cyberspace --- Algorism --- Arithmetic --- Computer science logic --- Logic, Symbolic and mathematical --- Foundations --- Discrete mathematics. --- Computer Science Logic and Foundations of Programming. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Computer mathematics

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This book is devoted to Slime mould Physarum polycephalum, which is a large single cell capable for distributed sensing, concurrent information processing, parallel computation and decentralized actuation. The ease of culturing and experimenting with Physarum makes this slime mould an ideal substrate for real-world implementations of unconventional sensing and computing devices The book is a treatise of theoretical and experimental laboratory studies on sensing and computing properties of slime mould, and on the development of mathematical and logical theories of Physarum behavior. It is shown how to make logical gates and circuits, electronic devices (memristors, diodes, transistors, wires, chemical and tactile sensors) with the slime mould. The book demonstrates how to modify properties of Physarum computing circuits with functional nano-particles and polymers, to interface the slime mould with field-programmable arrays, and to use Physarum as a controller of microbial fuel cells. A unique multi-agent model of slime is shown to serve well as a software slime mould capable for solving problems of computational geometry and graph optimization. The multiagent model is complemented by cellular automata models with parallel accelerations. Presented mathematical models inspired by Physarum include non-quantum implementation of Shor's factorization, structural learning, computation of shortest path tree on dynamic graphs, supply chain network design, p-adic computing and syllogistic reasoning. The book is a unique composition of vibrant and lavishly illustrated essays which will inspire scientists, engineers and artists to exploit natural phenomena in designs of future and emergent computing and sensing devices. It is a 'bible' of experimental computing with spatially extended living substrates, it spanstopics from biology of slime mould, to bio-sensing, to unconventional computing devices androbotics, non-classical logics and music and arts. .

Computer Science --- Engineering & Applied Sciences --- Bionics. --- Myxomycetes. --- Acellular slime molds --- Aerogastres --- Molds, Slime --- Mycetozoa --- Myxogastres --- Plasmoidial slime molds --- Slime fungi --- Slime molds --- Slime moulds --- True slime molds --- Intellectronics --- Engineering. --- Artificial intelligence. --- Bioinformatics. --- Computational intelligence. --- Complexity, Computational. --- Robotics. --- Automation. --- Complexity. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- Applications of Nonlinear Dynamics and Chaos Theory. --- Robotics and Automation. --- Automatic factories --- Automatic production --- Computer control --- Engineering cybernetics --- Factories --- Industrial engineering --- Mechanization --- Assembly-line methods --- Automatic control --- Automatic machinery --- CAD/CAM systems --- Robotics --- Automation --- Machine theory --- Complexity, Computational --- Electronic data processing --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Bio-informatics --- Biological informatics --- Biology --- Information science --- Computational biology --- Systems biology --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Construction --- Industrial arts --- Technology --- Data processing --- Rhizopoda --- Bioengineering --- Biophysics --- Cybernetics --- Systems engineering --- Artificial Intelligence. --- Computational complexity. --- Statistical physics. --- Physics --- Mathematical statistics --- Statistical methods

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Reaction-diffusion and excitable media are amongst most intriguing substrates. Despite apparent simplicity of the physical processes involved the media exhibit a wide range of amazing patterns: from target and spiral waves to travelling localisations and stationary breathing patterns. These media are at the heart of most natural processes, including morphogenesis of living beings, geological formations, nervous and muscular activity, and socio-economic developments.   This book explores a minimalist paradigm of studying reaction-diffusion and excitable media using locally-connected networks of finite-state machines: cellular automata and automata on proximity graphs. Cellular automata are marvellous objects per se because they show us how to generate and manage complexity using very simple rules of dynamical transitions. When combined with the reaction-diffusion paradigm the cellular automata become an essential user-friendly tool for modelling natural systems and designing future and emergent computing architectures.   The book brings together hot topics of non-linear sciences, complexity, and future and emergent computing. It shows how to discover  propagating localisation and perform computation with them in very simple two-dimensional automaton models.  Paradigms, models and implementations presented in the book strengthen the theoretical foundations in the area for future and emergent computing and  lay key stones towards physical embodied information processing systems.  .

Artificial intelligence. --- Cellular automata. --- Complexity. --- Computer networks. --- Engineering & Applied Sciences --- Computer Science --- Computers, Iterative circuit --- Iterative circuit computers --- Structures, Tessellation (Automata) --- Tessellation structures (Automata) --- Engineering. --- Computational intelligence. --- Complexity, Computational. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- Complexity, Computational --- Electronic data processing --- Machine theory --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Construction --- Industrial arts --- Technology --- Parallel processing (Electronic computers) --- Pattern recognition systems --- Sequential machine theory --- Artificial Intelligence. --- Computational complexity.

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This book is a tribute to Kenichi Morita’s ideas and achievements in theoretical computer science, reversibility and computationally universal mathematical machines. It offers a unique source of information on universality and reversibility in computation and is an indispensable book for computer scientists, mathematicians, physicists and engineers. Morita is renowned for his works on two-dimensional language accepting automata, complexity of Turing machines, universality of cellular automata, regular and context-free array grammars, and undecidability. His high-impact works include findings on parallel generation and parsing of array languages by means of reversible automata, construction of a reversible automaton from Fredkin gates, solving a firing squad synchronization problem in reversible cellular automata, self-reproduction in reversible cellular spaces, universal reversible two-counter machines, solution of nondeterministic polynomial (NP) problems in hyperbolic cellular automata, reversible P-systems, a new universal reversible logic element with memory, and reversibility in asynchronous cellular automata. Kenichi Morita’s achievements in reversibility, universality and theory of computation are celebrated in over twenty high-profile contributions from his colleagues, collaborators, students and friends. The theoretical constructs presented in this book are amazing in their diversity and depth of intellectual insight, addressing: queue automata, hyperbolic cellular automata, Abelian invertible automata, number-conserving cellular automata, Brownian circuits, chemical automata, logical gates implemented via glider collisions, computation in swarm networks, picture arrays, universal reversible counter machines, input-position-restricted models of language acceptors, descriptional complexity and persistence of cellular automata, partitioned cellular automata, firing squad synchronization algorithms, reversible asynchronous automata, reversible simulations of ranking trees, Shor’s factorization algorithms, and power consumption of cellular automata.

Engineering. --- Computational intelligence. --- Complexity, Computational. --- Complexity. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Construction --- Industrial arts --- Technology --- Complexity, Computational --- Electronic data processing --- Machine theory --- Computational complexity.

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This volume of the Encyclopedia of Complexity and Systems Science, Second Edition, provides an authoritative introduction and overview of the latest research in cellular automata (CA) models of physical systems, emergent phenomena, computational universality, chaos, growth phenomena, phase transitions, self-organised criticality, reaction-diffusion systems, self-replications, parallel computation, and more. Fundamental topics of algorithmic complexity, algebraic groups, language theory, evolving CA, ergodic theory, synchronisation, tiling problems and undecidability and topological dynamics of CA are addressed. Cellular automata are regular uniform networks of locally-connected finite-state machines, and represent discrete systems with non-trivial behavior, including waves, patterns and travelling localisations. CA are ubiquitous: they are mathematical models of computation and computer models of natural systems. Classes of CA presented in this book include additive CA, automata in hyperbolic spaces and non-compact spaces, CA in triangular, pentagonal and hexagonal tessellations, automata with memory, quantum and reversible automata, structurally-dynamic CA, and asynchronous automata. Topics added to the second edition include: asynchronous cellular automata, stochastic cellular automata as models of reaction-diffusion processes, cellular automata hardware implementation, cellular automata basins of attraction, orbits of Bernoulli measures in cellular automata, and graphs related to reversibility and complexity in cellular. This state-of-the-art reference is unique in bringing together unequalled expertise of interdisciplinary studies at the edge of mathematics, computer science, and physics.

Logic design. --- Engineering mathematics. --- Computer science. --- Computational complexity. --- Logics and Meanings of Programs. --- Discrete Mathematics. --- Complex Systems. --- Mathematical and Computational Engineering. --- Computation by Abstract Devices. --- Discrete Mathematics in Computer Science. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Informatics --- Science --- Engineering --- Engineering analysis --- Mathematical analysis --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Mathematics --- Cellular automata. --- Cellular automata --- Computer logic. --- Discrete mathematics. --- Statistical physics. --- Dynamical systems. --- Applied mathematics. --- Computers. --- Computer science—Mathematics. --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Calculators --- Cyberspace --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Computer science logic --- Logic, Symbolic and mathematical --- Statistical methods --- System theory. --- Computer science --- Computer Science Logic and Foundations of Programming. --- Mathematical and Computational Engineering Applications. --- Theory of Computation. --- Data processing. --- Mathematics. --- Computer mathematics --- Systems, Theory of --- Systems science --- Philosophy