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Oбзор последних исследований в области клеточно-автоматических (КА) моделей физических систем, возникающих явлений, вычислительной универсальности, хаоса, явлений роста, фазовых переходов, самоорганизованной критичности, систем реакции-диффузии, самовоспроизведения, параллельных вычислений, и более.
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.
Cellular Automata in Triangular, Pentagonal, and Hexagonal Tessellations
Cellular Automata in Hyperbolic Spaces
Structurally Dynamic Cellular Automata
Asynchronous Cellular Automata
Quantum Cellular Automata
Reversible Cellular Automata
Additive Cellular Automata
Cellular Automata with Memory
Classification of Cellular Automata
Tiling Problem and Undecidability in Cellular Automata
Cellular Automata and Groups
Self-Replication and Cellular Automata
Gliders in Cellular Automata
Basins of Attraction of Cellular Automata and Discrete Dynamical Networks
Growth Phenomena in Cellular Automata
Emergent Phenomena in Cellular Automata
Dynamics of Cellular Automata in Noncompact Spaces
Orbits of Bernoulli Measures in Cellular Automata
Chaotic Behavior of Cellular Automata
Ergodic Theory of Cellular Automata
Topological Dynamics of Cellular Automata
Control of Cellular Automata
Algorithmic Complexity and Cellular Automata
Graphs Related to Reversibility and Complexity in Cellular Automata
Cellular Automata as Models of Parallel Computation
Cellular Automata and Language Theory
Evolving Cellular Automata
Cellular Automata Hardware Implementation
Firing Squad Synchronization Problem in Cellular Automata
Universality of Cellular Automata
Cellular Automata Modeling of Physical Systems
Stochastic Cellular Automata as Models of Reaction–Diffusion Processes
Phase Transitions in Cellular Automata
Self-Organized Criticality and Cellular Automata
Identification of Cellular Automata