1/f noise in elementary cellular automaton rule 110

Authors:
Shigeru Ninagawa
Affiliations:
Division of Information and Computer Science, Kanazawa Institute of Technology, Ishikawa, Japan
Venue:
UC'06 Proceedings of the 5th international conference on Unconventional Computation
Year:
2006

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Abstract

Cellular Automata are considered to be discrete dynamical systems as well as computing systems. Spectral analysis has been employed to investigate the behavior of dynamical systems. We calculated the power spectra from the evolutions starting from a random initial configuration to analyze the temporal behavior in elementary cellular automata. As a result, rule 110 has 1/f spectrum for the longest time steps. Rule 110 alone has proved to be capable of supporting universal computation in elementary cellular automata. These results suggest that there is a relationship between computational universality and 1/f noise in cellular automata.