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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,

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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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Les disciplines scientifiques et littéraires sont généralement perçues dans ce qui les différencie, les divise et parfois même les oppose. Pensée scientifique et pensée poétique s’expriment dans des modes de discours bien distincts. Il arrive pourtant qu’elles se rejoignent : c’est quand la pensée ne peut plus s’exprimer dans le mode qui lui était propre et que, recourant à une mise en forme directe, elle grave dans un schéma – du plus simple au plus complexe – le chemin qui la ramènera vers la parole. On dit bien souvent : « une image vaut 100 000 mots » ou bien encore, plus familièrement : « je fais vous faire un dessin" . Parmi les « auteurs » nous retrouvons Goethe, Darwin, Leibnitz, Freud, P. Valery, W. Benjamin, J. Malaurie, C. Simon, F. Lang, I. Nabokov, R. Queneau, un schéma présentant Internet…

Thought and thinking in art --- Thought and thinking --- Drawing --- Pensée dans l'art --- Pensée --- Dessin --- Psychological aspects --- Aspect psychologique --- Sémiologie de l'image --- Sémiologie --- Croquis --- Processus de conception --- kunst --- tekenkunst --- schetsen --- ontwerp --- kunst en wetenschap --- Agassiz Jean Louis Rodolphe --- Averty Jean-Christophe --- Axelos Kostas --- Barr Alfred H. --- Belyj Andrej --- Benjamin Walter --- kunst en filosofie --- kunst en literatuur --- Beuys Joseph --- Cache Bernard --- Cunningham Merce --- Czapski Joseph --- Darwin Charles --- De Jonckheere Philippe --- Descartes René --- Dreyfus Alfred --- Fischli Peter --- Florenski Pavel --- Freud Sigmund --- Geve Thomas --- Goethe Johann Wolfgang --- Gould Augustus Addison --- Griaule Marcel --- Hirschhorn Thomas --- Hundertwasser Friedensreich --- Itten Johannes --- Kahn Louis I. --- Kentridge William --- Klee Paul --- Klucis Gustav --- Korzyksbi Alfred --- Lang Fritz --- Langlois Henri --- Lombardi Mark --- Malaurie Jean --- Marinetti Filippo Tommaso --- Martin Etienne --- Mendeleïev Dimitri --- de Montgolfier Jospeh Michel --- Nabokov Vladimir --- Nelson Theodor H. --- Ogotemmêli --- Otlet Paul --- Pairault Pierre --- Perec Georges --- Queneau Raymond --- Rekacewicz Philippe --- Rice Peter --- Ricoeur Paul --- Simon Claude --- Steiner Rudolf --- Steinweg Marcus --- Strickland Hugh E. --- Valéry Paul --- Vertov Dziga --- Vig Lars --- Villani Cedric --- Weiss David --- Wolfram Stephen --- Wul Stefan --- Xenakis Iannis --- Zanzotto Andrea --- 741.03 --- 741.036 --- Pensée dans l'art --- Pensée --- Barr Alfred H --- Kahn Louis I --- Nelson Theodor H --- Strickland Hugh E --- Mind --- Thinking --- Thoughts --- Educational psychology --- Philosophy --- Psychology --- Intellect --- Logic --- Perception --- Psycholinguistics --- Self --- Art