Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFA
Rosu Barbus, Haret-Codratian
In 2005, Nagler and Claussen (Phys. Rev. E 71, 067103 (2005)) investigated the time series of the elementary cellular automata (ECA) for possible (multi)fractal behavior. They eliminated the polynomial background atb through the direct ﬁt-ting of the polynomial coeﬃcients a and b. We here reconsider their work eliminating the polynomial trend by means of the multifractal-based detrended ﬂuctuation analysis (MF-DFA) in which the wavelet multiresolution property is employed to ﬁlter out the trend in a more speedy way than the direct polynomial ﬁtting and also with respect to the wavelet transform modulus maxima (WTMM) procedure. In the algorithm, the discrete fast wavelet transform is used to calculate the trend as a local feature that enters the so-called details signal. We illustrate our result for three representative ECA rules: 90, 105, and 150. We conﬁrm their multifractal behavior and provide our results for the scaling parameters.
Fecha de publicación2009
Palabras claveStatistical physics and nonlinear systems
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