Multifractal analyses of row sum signals of elementary cellular automata
Rosu Barbus, Haret-Codratian
We ﬁrst apply the WT-MFDFA, MFDFA, and WTMM multifractal methods to binomial multifrac-tal time series of three diﬀerent binomial parameters and ﬁnd that the WTMM method indicates an enhanced diﬀerence between the fractal components than the known theoretical result. Next, we make use of the same methods for the time series of the row sum signals of the two comple-mentary ECA pairs of rules (90,165) and (150,105) for ten initial conditions going from a single 1 in the central position up to a set of ten 1’s covering the ten central positions in the ﬁrst row. Since the members of the pairs are actually similar from the statistical point of view, we can check which method is the most stable numerically by recording the diﬀerences provided by the methods between the two members of the pairs for various important quantities of the scaling analyses, such as the multifractal support, the most frequent H¨older exponent, and the Hurst exponent and considering as the better one the method that provides the minimum diﬀerences. According to this criterion, our results show that the MFDFA performs better than WT-MFDFA and WTMM in the case of the multifractal support, while for the other two scaling parameters the WT-MFDFA is the best. The employed set of initial conditions does not generate any speciﬁc trend in the values of the multifractal parameters.
Fecha de publicación2012
Palabras claveElementary cellular automata
Extended initial conditions
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