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We discuss a characterization of complexity based on successiveapproximations of the probability density describing a system by means ofmaximum entropy methods, thereby quantifying the respective role played bydifferent orders of interaction. This characterization is applied on simplecellular automata in order to put it in perspective with the usual notion ofcomplexity for such systems based on Wolfram classes. The overlap is shown tobe good, but not perfect. This suggests that complexity in the sense of Wolframemerges as an intermediate regime of maximum entropy-based complexity, but alsogives insights regarding the role of initial conditions in complexity-relatedissues.

Assessing complexity by means of maximum entropy models