Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFAJ. S. Murguia1, J. E. Pérez-Terrazas2 and H. C. Rosu2
1 Departamento de Físico Matemáticas, Universidad Autónoma de San Luis Potosí - Alvaro Obregón 64, 78000 San Luis Potosí, S.L.P., Mexico
2 IPICYT - Instituto Potosino de Investigación Científica y Tecnológica - Camino a la presa San José 2055, 78216, San Luis Potosí, SLP, Mexico
received 28 March 2009; accepted in final form 13 July 2009; published July 2009
published online 18 August 2009
In 2005, Nagler and Claussen (Phys. Rev. E, 71 (2005) 067103) investigated the time series of the elementary cellular automata (ECA) for possible (multi)fractal behavior. They eliminated the polynomial background atb through the direct fitting 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.
89.75.Da - Systems obeying scaling laws.
05.45.Tp - Time series analysis.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
© EPLA 2009