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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Bibliography
P. Bak, C. Tank, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).
P. Bak, How Nature Works: the Science of Self-organized Criticality, Springer-Verlag, New York, 1996.
N. Gutenberg and C. F. Richter, Seismicity of the Earth, Princeton University Press, Princeton, 1949.
A. C. Johnston and S. Nava, J. Geophys. Res. 90, 6737 (1985).
B. Mandelbrot, J. Bus. (Chicago) 36, 307 (1963).
B. Mandelbrot, J. Bus. (Chicago) 37, 393 (1964).
D. M. Raup and J. J. Sepkoski, Proc. Natl. Acad. Sci. (USA) 81, 801 (1984).
D. M. Raup, Science 231, 1528 (1986).
M. E. J. Newman, Proc. R. Soc. London B 263, 1605 (1996).
G.K. Zipf, Human Behavior and the Principle of Least Effort, Addison-Wesley, Cambridge, 1949.
S. Glassman, Comp. Networks ISDN Systems 27, 165 (1994).
B. A. Huberman and L. A. Adamic, Nature 401, 131 (1999); see also http://www.parc.xerox.com/istl/groups/iea/www/growth.html.
R. Wackerbauer, A. Witt, H. Atmanspacher, J. Kurths and H. Scheingraber, Chaos, Solitons Fractals 4, 133 (1994).
H. Atmanspacher, J. Consciousness Studies 1, 168 (1994).
H. Atmanspacher, C. Räth and G. Wiedenmann, Physica A 234, 819 (1997).
This classication scheme may not encompass all proposed complexity measures, however;see [28].
J. S. Shiner, M. Davison and P. T. Landsberg, in Dynamics, Synergetics, Autonomous Agents —Nonlinear Systems Approaches to Cognitive Psychology and Cognitive Science, edited by W. Tschacher and J.-P. Dauwalder, World Scientific, Singapore, 1999.
J. S. Shiner, M. Davison and P. T. Landsberg, Phys. Rev. E 59, 145 (1999).
P. T. Landsberg, Phys. Lett. A 102, 171 (1984).
P. T. Landsberg, Int. J. Quantum Chem., Symp 11A, 55 (1984).
P. T. Landsberg, in On Self-Organization, edited by R.K. Mishra, D. Maass, and E. Zwierlein, Springer-Verlag, Berlin, 1994.
When referring to specic measures of disorder, order or complexity, we enclose these words in quotation marks to distinguish the measures from the general concepts.
J. S. Shiner, in: Self-Organization of Complex Structures: From Individual to Collective Dynamics, edited by F. Schweitzer, Gordon and Breach, London, 1997.
A. Rényi, Probability Theory North-Holland, Amsterdam, 1970.
P. Grassberger, Phys. Lett. A 97, 227 (1983).
H. G. E. Hentschel and I. Procaccia, Physica D 8, 435 (1983).
P. T. Landsberg and J. S. Shiner, Phys. Lett. A 245, 228 (1998).
J. S. Shiner, M. Davison, and P.T. Landsberg, “Reply to comments on 'simple Measure for Complexity'”, accepted in Phys. Rev. E (2000).
J. P. Crutchéld, D.P. Feldman, and C. R. Shalizi, “Comment on 'simple Measure for Complexity'”, to be published, Phys. Rev. E (2000).
P.-M. Binder and N. Perry, “Comment on 'simple measure for complexity'”, to be published, Phys. Rev. E (2000).
B. Mandelbrot, in: Structures of Language and Its Mathematical Aspects, edited by R. Jacobson, American Mathematical Society, New York, 1961. (See also [34])
R. Dawkins, The Blind Watchmaker, Penguin, London, 1988.
M. Schroeder, Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, W. H. Freeman, New York, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shiner, J.S. Self-Organized Criticality: Self-Organized Complexity? The Disorder and "Simple Complexities" of Power Law Distributions. Open Systems & Information Dynamics 7, 131–138 (2000). https://doi.org/10.1023/A:1009652708715
Issue Date:
DOI: https://doi.org/10.1023/A:1009652708715