Computational universality and 1/f noise in elementary cellular automata

Abstract

Elementary (one-dimensional two-state three-neighbor) cellular automaton rule 110 is capable of supporting universal computation and exhibits 1/f noise. However, the power spectra of rule 110 do not always exhibit 1/f-type spectrum because of periodic background particular to rule 110. Since periodic background in rule 110 does not play any role in supporting universal computation, we can expect that the removal of periodic background does not change the behavior essential to supporting universal computation. As a result of removing periodic background, we found that the power spectra fit better to 1/f noise. This result suggests 1/f noise is an intrinsic property of computational universality in cellular automata.