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

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

2004-10-19

arxiv.org/abs/nlin/0410037v1

Phys. Rev. E 71, 067103 (2005)

Nonlinear Sciences

Cellular Automata and Lattice Gases

4 pages (3 figs included)

Scientific paper

10.1103/PhysRevE.71.067103

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 $1/f^{\alpha}$ 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.

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