The main purpose of this work is to understand some limitations introduced by the classical definitions of cellular automata (CA). To this end, we have defined a new model of CAs (fuzzy CAs) which allows the observation of interesting "chaotic" properties of elementary CAs. To date neither a formal nor a precise definition of "chaos" in CAs exists; we believe that the proposed model provides a "sharper" tool to detect which properties can be associated to a "chaotic" behavior. We also define a measure (rule entropy) which gives information about the CA's dynamics solely on the basis of the rule table and provides theoretical explanations to some of the empirical observations
Cattaneo, G., Flocchini, P., Mauri, G., Quaranta Vogliotti, C., Santoro, N. (1997). Cellular automata in fuzzy backgrounds. PHYSICA D-NONLINEAR PHENOMENA, 105(1-3), 105-120 [10.1016/S0167-2789(96)00233-3].
Cellular automata in fuzzy backgrounds
MAURI, GIANCARLO;
1997
Abstract
The main purpose of this work is to understand some limitations introduced by the classical definitions of cellular automata (CA). To this end, we have defined a new model of CAs (fuzzy CAs) which allows the observation of interesting "chaotic" properties of elementary CAs. To date neither a formal nor a precise definition of "chaos" in CAs exists; we believe that the proposed model provides a "sharper" tool to detect which properties can be associated to a "chaotic" behavior. We also define a measure (rule entropy) which gives information about the CA's dynamics solely on the basis of the rule table and provides theoretical explanations to some of the empirical observations
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