Toward a quantitative theory of self-generated complexity View Full Text


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Article Info

DATE

1986-09

AUTHORS

Peter Grassberger

ABSTRACT

Quantities are defined operationally which qualify as measures of complexity of patterns arising in physical situations. Their main features, distinguishing them from previously used quantities, are the following: (1) they are measuretheoretic concepts, more closely related to Shannon entropy than to computational complexity; and (2) they are observables related to ensembles of patterns, not to individual patterns. Indeed, they are essentially Shannon information needed to specify not individual patterns, but either measure-theoretic or algebraic properties of ensembles of patterns arising ina priori translationally invariant situations. Numerical estimates of these complexities are given for several examples of patterns created by maps and by cellular automata. More... »

PAGES

907-938

References to SciGraph publications

  • 1979-12. The universal metric properties of nonlinear transformations in JOURNAL OF STATISTICAL PHYSICS
  • 1984-03. Computation theory of cellular automata in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1984-06. Algebraic properties of cellular automata in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1983. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields in NONE
  • 1978-07. Quantitative universality for a class of nonlinear transformations in JOURNAL OF STATISTICAL PHYSICS
  • 1985-12. An answer to a question by J. Milnor in COMMENTARII MATHEMATICI HELVETICI
  • 1985-09. The evidence in THE MATHEMATICAL INTELLIGENCER
  • 1980. Periodic points and topological entropy of one dimensional maps in GLOBAL THEORY OF DYNAMICAL SYSTEMS
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    http://scigraph.springernature.com/pub.10.1007/bf00668821

    DOI

    http://dx.doi.org/10.1007/bf00668821

    DIMENSIONS

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