Phys. Rev. E 71, 067103 (2005) [4 pages]1∕fα spectra in elementary cellular automata and fractal signalsReceived 20 October 2004; revised 13 April 2005; published 28 June 2005 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. © 2005 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.71.067103
DOI:
10.1103/PhysRevE.71.067103
PACS:
89.75.Da, 82.40.Np, 05.45.Df, 45.70.Qj
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