Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:C3L-B
Session:
Number:C3L-B2
Fluctuations of fuzzy cellular automata around their convergence point
Heather Betel, Paola Flocchini,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
In this paper, we study the oscillating behavior of a class of fuzzy cellular automata as they converge toward their fixed point. We first prove that they all converge to 1/2, we then describe their dynamics as values approach this point of convergence. In all cases the fluctuations around 1/2 obey a Boolean rule. We show that for some fuzzy rules the oscillations follow precisely the corresponding Boolean rule itself, while for others they obey a different rule. Finally, we characterize the class of elementary cellular automata that fluctuate according to their corresponding Boolean rule showing that only those studied in this paper display this behavior. These results explain and generalize those of.