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تسجيل مستخدم جديدA New Parameter $F$ to Classify Cellular Automata Rule Table Space and a Phase Diagram in $lambda-F$ Plane
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It is shown that for the N-neighbor and K-state cellular automata, the class II, class III and class IV patterns coexist at least in the range $frac{1}{K} le lambda le 1-frac{1}{K} $. The mechanism which determines the difference between the pattern classes at a fixed $lambda$ is found, and it is studied quantitatively by introducing a new parameter $F$. Using the parameter F and $lambda$, the phase diagram of cellular automata is obtained for 5-neighbor and 4-state cellular automata. PACS: 89.75.-k Complex Systems
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In addition to the $lambda$ parameter, we have found another parameter which characterize the class III, class II and class IV patterns more quantitatively. It explains why the different classes of patterns coexist at the same $lambda$. With this par
ameter, the phase diagram for an one dimensional cellular automata is obtained. Our result explains why the edge of chaos(class IV) is scattered rather wide range in $lambda$ around 0.5, and presents an effective way to control the pattern classes. oindent PACS: 89.75.-k Complex Systems
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for the N-neighbor and K-state cellular automata, the class I, class II, class III and class IV patterns coexist at least in the range, $frac{1}{K} le lambda le 1-frac{1}{K} $. The mechanism is studied quantitatively by introducing a new parameter $F$, which we call quiescent string dominance parameter. It is taken to be orthogonal to $lambda$. Using the parameter F and $lambda$, the rule tables of one dimensional 5-neighbor and 4-state cellular automata are classified. The distribution of the four pattern classes in ($lambda$,F) plane shows that the rule tables of class III pattern class are distributed in larger $F$ region, while those of class II and class I pattern classes are found in the smaller $F$ region and the class IV behaviors are observed in the overlap region between them. These distributions are almost independent of $lambda$ at least in the range $0.25 leq lambda leq 0.75$, namely the overlapping region in $F$, where the class III and class II patterns coexist, has quite gentle $lambda$ dependence in this $lambda$ region. Therefore the relation between the pattern classes and the $lambda$ parameter is not observed. PACS: 89.75.-k Complex Systems
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