Power Spectral Analysis of Elementary Cellular Automata

Abstract

Spectral analysis of elementary cellular automata is performed. A power spectrum is calculated from the evolution of 88 independent rules starting from random initial configurations. As a result, it is found that rule 110 exhibits 1/f noise during the longest time steps. Rule 110 has proved to be capable of supporting universal computation. These results suggest that there is a relationship between computational universality and 1/f noise in cellular automata.