Complex Systems

Universal Emergence of 1/f Noise in Asynchronously Tuned Elementary Cellular Automata

Daisuke Uragami
Department of Mathematical Information Engineering
College of Industrial Technology
Nihon University, Chiba, Japan
uragami.daisuke@nihon-u.ac.jp

Yukio-Pegio Gunji
Department of Intermedia Art and Science
School of Fundamental Science and Engineering
Waseda University, Tokyo, Japan
yukio@waseda.jp

Abstract

In this paper, we propose asynchronously tuned elementary cellular automata (AT_ECA) as models that implement a new type of self-organized criticality (SOC). SOC in AT_ECA is based on asynchronously updating and locally tuning the consistency between dual modes of transition. A previous work showed that AT_ECA generate class 4-like spacetime patterns over a wide area of the rule space, and the density decay follows a power law for some of the rules. In this study, we performed a spectral analysis of AT_ECA, of which a great number of rules were found to exhibit 1/f noise, suggesting that AT_ECA realize critical states without selecting specific rules or fine-tuning parameters.

Keywords: cellular automata; 1/f noise; self-organizing criticality; asynchronous