1/f(alpha) spectra in elementary cellular automata and fractal signals.
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/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.
Nagler
Jan
J
Institut für Theoretische Physik, Universität Bremen, Otto-Hahn-Allee, D-28334 Bremen, Germany.
Claussen
Jens Christian
JC