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DY: Dynamik und Statistische Physik

DY 40: Statistical Physics (General) I

DY 40.10: Talk

Tuesday, March 8, 2005, 12:30–12:45, TU H3010

1/f^α spectra in elementary cellular automata and fractal signals — •Jan Nagler¹ and Jens Christian Claussen² — ¹Institut für Theoretische Physik, Universität Bremen, Otto-Hahn-Allee, 28334 Bremen, Germany — ²Institut für Theoretische Physik und Astrophysik, Universität Kiel, Leibnizstraße 15, 24098 Kiel, Germany

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 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. Because of the widespread applications of (elementary) cellular automata our findings may be relevant in chemistry, physics and computer sciences.