Radial View: Observing Fuzzy Cellular Automata with a New Visualization Method
نویسندگان
چکیده
Fuzzy Cellular Automata (FCA) are special couple map lattices that generalize Boolean cellular automata by allowing continuous values for the cell states. The local transition rule of a FCA is the “fuzzification" of the disjunctive normal form that describes the local function of the corresponding Boolean cellular automata. Recently there has been some interest in elementary Fuzzy cellular automata and, in particular, in the understanding of their dynamics. The classical observation medium for these systems whether Boolean or Fuzzy has always been the space-time diagram. In this paper we consider a new way to visualize the evolution of Fuzzy Cellular Automata that reveals interesting dynamics not observable with the space-time diagram. We then experimentally group the elementary circular Fuzzy Cellular Automata on the basis of their behavior as observed with this new visualization tool. We discover that all circular FCA have a periodic behavior. Interestingly, the periods have only lengths 1,2,4,n (where n is the size of a configuration).
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