title: Statistical distributions and self-organizing phenomena: what conclusions should be drawn?
abstract: Some salient properties of the inverse power law distribution, the exponential distribution, catastrophe distributions, and the relationships among them were explored and compared. Self-organizing events may display any of these distributions. Catastrophe functions and their distributions do not display fractional (fractal) dimensions. Thus it is possible to have self-organization without the fractal. An empirical example from leadership emergence research illustrated a situation where a power law distribution provided a poor characterization of the data, but a swallowtail catastrophe model did so quite well. The results call into question some simplistic assumptions about the relationships among fractals, inverse power laws, self-organization and so-called pink noise.
authors.affiliation: Marquette University, Milwaukee, WI 53201-1881, USA. stephen.guastello@marquette.edu
authors.forename: Stephen J
authors.initials: SJ
authors.lastname: Guastello
mesh_terms: D017709:Fractals; D006126:Group Processes; D006801:Humans; D007857:Leadership; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D011340:Problem Solving