$1/f^{\alpha }$ spectra in elementary cellular automata and fractal signals

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 $1/f^{\alpha }$ 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.

4 pages (3 figs included)

References in corpus (1)

• Sierpinski signal generates $1/f^{\alpha }$ spectra

Cited by in corpus (6)

• Outer-totalistic cellular automata on graphs
• Analysis of self-organized criticality in Ehrenfest's dog-flea model
• Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFA
• Improvement and analysis of a pseudo random bit generator by means of cellular automata
• Quantum walks with spatiotemporal fractal disorder
• Deterministic many-body dynamics with multifractal response