Nagler Jan, Claussen Jens Christian
Institut für Theoretische Physik, Universität Bremen, Otto-Hahn-Allee, D-28334 Bremen, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 2):067103. doi: 10.1103/PhysRevE.71.067103. Epub 2005 Jun 28.
We systematically compute the power spectra of the one-dimensional elementary cellular automata introduced by Wolfram. On the one hand our analysis reveals that one automaton displays 1/f spectra though considered as trivial, and on the other hand that various automata classified as chaotic or complex display no 1/f spectra. We model the results generalizing the recently investigated Sierpinski signal to a class of fractal signals that are tailored to produce 1/f(alpha) spectra. From the widespread occurrence of (elementary) cellular automata patterns in chemistry, physics, and computer sciences, there are various candidates to show spectra similar to our results.
我们系统地计算了由沃尔夫勒姆引入的一维基本元胞自动机的功率谱。一方面，我们的分析表明，尽管有一种元胞自动机被认为是平凡的，但它却呈现出1/f谱；另一方面，各种被归类为混沌或复杂的元胞自动机却没有呈现出1/f谱。我们对结果进行建模，将最近研究的谢尔宾斯基信号推广到一类经专门设计以产生1/f(α)谱的分形信号。鉴于（基本）元胞自动机模式在化学、物理和计算机科学中的广泛存在，有各种候选对象可能会呈现出与我们的结果相似的谱。
