Nanotechnology Group,Kansai Advanced Research Centre,National Institute of Information and Communications Technology.
588-2 iwaoka, Nishi-ku, Kobe, 651-2401, Japan

Received 28 October 2002; received in revised form 21 December 2003; accepted 18 April 2004
Communicated by I. Mezic

Abstract

　ln this paper we propose a cellular array model whose transition function is based on a continuously valued expression that
includes a temperature parameter T and two shift parameters Eo and xo. This transition function coincides with the transition
function of the Game of Life cellular automaton model when the temperature approaches the limit T→0. States in this model
are continuously valued for T > 0, and cell state transitions, though deterministic, are affected by thermal fluctuation. Spectral
analysis of the cell state's time series shows a 1/f spectrum in the low temperature region, as in the Game of Life, and a
Lorentzian spectrum in the high temperature region. Analysis of the average entropy shows a division along approximately the
same critical point into a low temperature region indicative of the Game of Life and a high temperature region with different
behavior. We show that model is robust to deviations in the values of parameters Eo and xo, but that the robustness declines
with an increase in temperature, up to a critical temperature at which all robustness is lost.
©2004 Elsevier B.V. All rights reserved.

PACS: 05.40.+J; 02.50.-r; 89.80.+h

keywords: Cellular automata; The Game of Life; Spectral analysis; 1/f fluctuation; Entropy; Computational universality