2009/07/01 by J. S. Murguia, J.S. Murguía, Jaime Enrique Pérez-Terrazas +2
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Fractal and DNA sequence analysis #Theoretical and Computational Physics #nlin.CD #nlin.CG #physics.data-an
paper · pdf · doi:10.1209/0295-5075/87/28003
published as Europhys. Lett. 87 (2009) 28003 · 8 pages, 5 figures, 21 references
openalex publication_date 2009/07/01 · arxiv created 2009/08/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 at b 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.