2014/08/02 by Gregor Chliamovitch, Chliamovitch, Gregor, Bastien Chopard +3
Physics and Astronomy · #Cellular Automata and Lattice Gases (nlin.CG) #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #nlin.CG #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.1408.0368
10 pages, 7 figures. Submitted to Phys. Rev. X
arxiv created 2014/08/02 · arxiv updated 2014/08/05
We discuss a characterization of complexity based on successive approximations of the probability density describing a system by means of maximum entropy methods, thereby quantifying the respective role played by different orders of interaction. This characterization is applied on simple cellular automata in order to put it in perspective with the usual notion of complexity for such systems based on Wolfram classes. The overlap is shown to be good, but not perfect. This suggests that complexity in the sense of Wolfram emerges as an intermediate regime of maximum entropy-based complexity, but also gives insights regarding the role of initial conditions in complexity-related issues.