Self-Organized Criticality: Self-Organized Complexity? The Disorder and ``Simple Complexity'' of Power Law Distributions

摘要

The disorder and a simple convex measure of complexity are studied for rankordered power law distributions, indicative of criticality, in the case wherethe total number of ranks is large. It is found that a power law distributionmay produce a high level of complexity only for a restricted range of systemsize (as measured by the total number of ranks), with the range depending onthe 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 ifself-organized criticality is reached at an appropriate system size.