International Journal of Theoretical Physics

, Volume 25, Issue 9, pp 907–938 | Cite as

Toward a quantitative theory of self-generated complexity

  • Peter Grassberger


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.


Entropy Field Theory Elementary Particle Quantum Field Theory Computational Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • Peter Grassberger
    • 1
  1. 1.Physics DepartmentUniversity of WuppertalGauss-Strasse 20West Germany

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