In 2005, Nagler and Claussen (Phys. Rev. E 71 (2005) 067103) investigated thetime series of the elementary cellular automata (ECA) for possible(multi)fractal behavior. They eliminated the polynomial background at^b throughthe direct fitting of the polynomial coefficients a and b. We here reconsidertheir work eliminating the polynomial trend by means of the multifractal-baseddetrended fluctuation analysis (MF-DFA) in which the wavelet multiresolutionproperty is employed to filter out the trend in a more speedy way than thedirect polynomial fitting and also with respect to the wavelet transformmodulus maxima (WTMM) procedure. In the algorithm, the discrete fast wavelettransform is used to calculate the trend as a local feature that enters theso-called details signal. We illustrate our result for three representative ECArules: 90, 105, and 150. We confirm their multifractal behavior and provide ourresults for the scaling parameters
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机译：在2005年，Nagler和Claussen（Phys。Rev. E 71（2005）067103）研究了基本元胞自动机（ECA）可能的（多重）分形行为的时间序列。他们通过直接拟合多项式系数a和b消除了多项式背景at ^ b。我们在这里重新考虑通过基于多重分形的趋势波动分析（MF-DFA）消除多项式趋势的工作，在该分析中，小波多分辨率属性用于比直接多项式拟合更快速地滤除趋势，并且相对于小波最大变换模量（WTMM）过程。在该算法中，离散快速小波变换用于计算趋势，作为进入所谓的细节信号的局部特征。我们举例说明了三个代表性ECArule的结果：90、105和150。我们确认了它们的多重分形行为，并提供了缩放参数的结果
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