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$1/f^α$ spectra in elementary cellular automata and fractal signals

Jan Nagler·Jens Christian Claussen
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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/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 $1/f^α$ 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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BibTeXRIS

Jan Nagler, Jens Christian Claussen. 2004-10-19. $1/f^α$ spectra in elementary cellular automata and fractal signals. https://doi.org/10.1103/physreve.71.067103

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