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517.96 --- Finite differences. Functional and integral equations --- 517.96 Finite differences. Functional and integral equations

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This penultimate volume contains numerous original, elegant, and surprising results in 1-dimensional cellular automata. Perhaps the most exciting, if not shocking, new result is the discovery that only 82 local rules, out of 256, suffice to predict the time evolution of any of the remaining 174 local rules from an arbitrary initial bit-string configuration. This is contrary to the well-known folklore that 256 local rules are necessary, leading to the new concept of quasi-global equivalence . Another surprising result is the introduction of a simple, yet explicit, infinite bit string called the

Cellular automata. --- Computational complexity. --- Dynamics. --- Nonlinear theories. --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Complexity, Computational --- Electronic data processing --- Machine theory --- Computers, Iterative circuit --- Iterative circuit computers --- Structures, Tessellation (Automata) --- Tessellation structures (Automata) --- Parallel processing (Electronic computers) --- Pattern recognition systems --- Sequential machine theory --- Wolfram, Stephen. --- Wolfram, Stephen,

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Electric networks, Nonlinear --- Nonlinear theories --- Réseaux électriques non linéaires --- Théories non linéaires

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This novel book introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. A surprisingly useful interpretations of cellular automata in terms of neural networks is also given. The book provides a scientifically sound and original analysis, and classifications of the empirical results presented in Wolfram's monumental "New Kind of Science."

Cellular automata. --- Computational complexity. --- Dynamics. --- Nonlinear theories. --- Wolfram, Stephen, --- Wolfram, Stephen.

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Volume IV continues the author's odyssey on l-D cellular automata as chronicled in Volumes I, II and III, by uncovering a novel quasi-ergodicity phenomenon involving orbits meandering among omega-limit orbits of complex (group 5) and hyper (group 6) Bernoulli rules. This discovery is embellished with analytical formulas characterizing the fractal properties of characteristic functions, as well as explicit formulas for generating colorful and pedagogically revealing isomorphic basin tree diagrams. Many new results were derived and proved by uncovering subtle symmetries endowed by various subset

Cellular automata. --- Computational complexity. --- Dynamics. --- Nonlinear theories. --- Wolfram, Stephen,