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1∕fα spectra in elementary cellular automata and fractal signals

Jan Nagler1 and Jens Christian Claussen2,*

  • 1Institut für Theoretische Physik, Universität Bremen, Otto-Hahn-Allee, D-28334 Bremen, Germany
  • 2Institut für Theoretische Physik und Astrophysik, Universität Kiel, Leibnizstraße 15, D-24098 Kiel, Germany

  • *Electronic address: claussen@theo-physik.uni-kiel.de
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Phys. Rev. E 71, 067103 – Published 28 June, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.067103

Abstract

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∕fα 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.

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Phys. Rev. E 71, 067103– Published 28 June, 2005
  • Received 20 October 2004

© 2005 American Physical Society

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