MF-DFA离散小波方法下初等元胞自动机的多重分形性质
Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFA
摘要：
2005年，Nagler和Claussen（Phys.Rev.E71（2005）067103）研究了基本元胞自动机（ECA）的时间序列的可能的（多重）分形行为。他们通过直接拟合多项式系数a和b消除了^b处的多项式背景。在这里，我们重新考虑他们的工作，消除多项式的趋势，通过基于多重分形的去趋势波动分析（MF-DFA），其中小波多分辨率属性被用来过滤出的趋势，在一个更快的方式比直接多项式拟合，也相对于小波变换模极大值（WTMM）的程序。在该算法中，离散快速小波变换被用来计算的趋势作为一个局部特征，进入所谓的细节信号。我们说明了我们的结果为三个代表ECA规则：90，105，和150。我们证实了它们的多重分形行为，并给出了标度参数的结果
英文摘要：
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
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