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  • 1
    Electronic Resource
    Electronic Resource
    Computation theory of cellular automata (1984)
    Springer
    Communications in mathematical physics 96 (1984), S. 15-57 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Self-organizing behaviour in cellular automata is discussed as a computational process. Formal language theory is used to extend dynamical systems theory descriptions of cellular automata. The sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages. Many examples are given. The sizes of the minimal grammars for these languages provide measures of the complexities of the sets. This complexity is usually found to be non-decreasing with time. The limit sets generated by some classes of cellular automata correspond to regular languages. For other classes of cellular automata they appear to correspond to more complicated languages. Many properties of these sets are then formally non-computable. It is suggested that such undecidability is common in these and other dynamical systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01217347
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  • 2
    Electronic Resource
    Electronic Resource
    Algebraic properties of cellular automata (1984)
    Springer
    Communications in mathematical physics 93 (1984), S. 219-258 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Cellular automata are discrete dynamical systems, of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata. The complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities. The systems are usually irreversible, and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01223745
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  • 3
    Electronic Resource
    Electronic Resource
    Cellular automata as models of complexity (1984)
    [s.l.] : Nature Publishing Group
    Nature 311 (1984), S. 419-424 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Natural systems from snowflakes to mollusc shells show a great diversity of complex patterns. The origins of such complexity can be investigated through mathematical models termed ‘cellular automata’. Cellular automata consist of many identical components, each simple., but together ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/311419a0
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  • 4
    Electronic Resource
    Electronic Resource
    Two- and three-point energy correlations in Hadronice + e − annihilation (1980)
    Springer
    The European physical journal 4 (1980), S. 237-256 
    Details
    ISSN: 1434-6052
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Correlations between the energies incident on two or three detectors arounde + e − annihilation events are considered as a probe of the QCD structure of the events. Practical methods for deducing two-detector energy correlations (which give the mean product of energies incident on two detectors as a function of their angular separation) from measured events are devised. Analytical formulae for energy correlations from QCD perturbation theory are given, but it is found that large corrections from hadron formation obscure these symptotic predictions at available energies. Correlations between the final state and the incominge ± beam direction are discussed, and observables are presented which measure the angular distributions of planes of final particles with respect to the beam axis (but do not require explicit determination of the planes). Finally, three-detector energy correlatons and their moments are treated, and methods for investigating planar structures ine + e − annihilation events are devised.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01421803
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  • 5
    Electronic Resource
    Electronic Resource
    QCD expectations for high-energy hadronic collisions (1982)
    Springer
    The European physical journal 15 (1982), S. 111-114 
    Details
    ISSN: 1434-6052
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is argued that perturbative QCD effects could be important in low-momentum transfer hadronic collisions at very high energies and should then give rise to several distinctive phenomena.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01571991
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  • 6
    Electronic Resource
    Electronic Resource
    Cellular automaton fluids 1: Basic theory (1986)
    Springer
    Journal of statistical physics 45 (1986), S. 471-526 
    Details
    ISSN: 1572-9613
    Keywords: Cellular automata ; derivation of hydrodynamics ; molecular dynamics ; kinetic theory ; Navier-Stokes equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Continuum equations are derived for the large-scale behavior of a class of cellular automaton models for fluids. The cellular automata are discrete analogues of molecular dynamics, in which particles with discrete velocities populate the links of a fixed array of sites. Kinetic equations for microscopic particle distributions are constructed. Hydrodynamic equations are then derived using the Chapman-Enskog expansion. Slightly modified Navier-Stokes equations are obtained in two and three dimensions with certain lattices. Viscosities and other transport coefficients are calculated using the Boltzmann transport equation approximation. Some corrections to the equations of motion for cellular automaton fluids beyond the Navier-Stokes order are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01021083
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  • 7
    Electronic Resource
    Electronic Resource
    Two-dimensional cellular automata (1985)
    Springer
    Journal of statistical physics 38 (1985), S. 901-946 
    Details
    ISSN: 1572-9613
    Keywords: Discrete models ; dynamical systems ; pattern formation ; computation theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A largely phenomenological study of two-dimensional cellular automata is reported. Qualitative classes of behavior similar to those in one-dimensional cellular automata are found. Growth from simple seeds in two-dimensiona! cellular automata can produce patterns with complicated boundaries, characterized by a variety of growth dimensions. Evolution from disordered states can give domains with boundaries that execute effectively continuous motions. Some global properties of cellular automata can be described by entropies and Lyapunov exponents. Others are undecidable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01010423
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  • 8
    Book
    Book
    ¬The¬ Mathematica book (1996)
    Cambridge; Wolfram :Cambridge Univ. Pr.,
    Details
    Title: ¬The¬ Mathematica book
    Author: Wolfram, Stephen
    Publisher: Cambridge; Wolfram :Cambridge Univ. Pr.,
    Year of publication: 1996
    Pages: 1403 S.
    Type of Medium: Book
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  • 9
    Book
    Book
    Mathematica: a system for doing mathematics by computer (1988)
    Reading, MA u.a. :Addison-Wesley,
    Details
    Title: Mathematica: a system for doing mathematics by computer
    Author: Wolfram, Stephen
    Publisher: Reading, MA u.a. :Addison-Wesley,
    Year of publication: 1988
    Pages: 749 S.
    Type of Medium: Book
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  • 10
    Book
    Book
    Mathematica: a system for doing mathematics by computer (1991)
    Reading, MA u.a. :Addison-Wesley,
    Details
    Title: Mathematica: a system for doing mathematics by computer
    Author: Wolfram, Stephen
    Publisher: Reading, MA u.a. :Addison-Wesley,
    Year of publication: 1991
    Pages: 961 S.
    Type of Medium: Book
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