1999/09/22 by J. S. Shiner, Shiner, J. S.
Economics, Econometrics and Finance · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #FOS: Physical sciences #Theoretical and Computational Physics #adap-org #nlin.AO
paper · pdf · doi:10.48550/arxiv.adap-org/9909007
11 pages, 2 figures
arxiv created 1999/09/22 · openalex publication_date 1999/09/22 · arxiv updated 2009/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
The disorder and a simple convex measure of complexity 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 power 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. Similar results are found for disorder. 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.