Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2004-09-10
Physical Review Letters, vol. 93, no. 11 (10 September 2004), article 118701
Nonlinear Sciences
Adaptation and Self-Organizing Systems
Four pages, two color figures
Scientific paper
10.1103/PhysRevLett.93.118701
Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we propose a new criterion, namely an internally-generated increase in the statistical complexity, the amount of information required for optimal prediction of the system's dynamics. We precisely define this complexity for spatially-extended dynamical systems, using the probabilistic ideas of mutual information and minimal sufficient statistics. This leads to a general method for predicting such systems, and a simple algorithm for estimating statistical complexity. The results of applying this algorithm to a class of models of excitable media (cyclic cellular automata) strongly support our proposal.
Haslinger Robert
Shalizi Cosma Rohilla
Shalizi Kristina Lisa
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