Self-Organized Criticality: Self-Organized Complexity? The Disorder and "Simple Complexities" of Power Law Distributions

  • Authors:

  • J. S. Shiner

  • Affiliations:

  • Abteilung Nephrologie, Inselspital, Bern, Switzerland E-mail: shiner@alumni.duke.edu

  • Venue:
  • Open Systems & Information Dynamics
  • Year:
  • 2000

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Abstract

Simple measures of complexity, showing either a monotonic or a convex dependence on disorder, are studied for rank ordered power law distributions, indicative of criticality, in the case where the total number of ranks is large. It is found that a pwoer law distribution may produce a high level of complexity only for a restricted range of system size (as measured by the total number of ranks), with the range depending on the exponent of the distribution. Self-organized criticality thus does not guarantee a high level of complexity, and when complexity does arise, it is self-organized itself only if self-organized criticality is reached at an appropriate system size.