Computational Universality and 1/f Noise in Elementary Cellular Automata

TL;DR

This paper investigates the potential link between 1/f noise and computational universality in elementary cellular automata by using genetic algorithms to identify rules with 1/f-type spectra.

Contribution

It introduces a genetic algorithm-based method to find cellular automata with 1/f noise, highlighting a possible connection to computational universality.

Findings

Identified cellular automata with 1/f noise spectra.

Rules with 1/f spectra exhibit propagating structures similar to universal automata.

Computational universality of the identified rules remains unproven.

Abstract

It is speculated that there is a relationship between 1/f noise and computational universality in cellular automata. We use genetic algorithms to search for one-dimensional and two-state, five-neighbor cellular automata which have 1/f-type spectrum. A power spectrum is calculated from the evolution starting from a random initial configuration. The fitness is estimated from the power spectrum in consideration of the similarity to 1/f-type spectrum. The result shows that the rule with the highest average fitness has a propagating structure like other computationally universal cellular automata, although computational universality of the rule has not been proved yet.