Quiescent string dominance parameter F and classification of one-dimensional cellular automata.
The classification of rules may be one of the most fundamental targets in the study of cellular automata. In this paper, we propose a method for achieving such a classification, in which a new quiescent string dominance parameter F, which is orthogonal to lambda, is introduced. For N -neighbor and K -state cellular automata, in the region 1/K<lambda<1-1/K, the maximum F corresponds to the class III rules, and its minimum, to the class II or class I rules. Therefore, transition of the pattern class takes place between them without fail. By using lambda and F, the phase diagram of cellular automata is determined in the (lambda, F ) plane for five-neighbor and four-state cellular automata. The phase diagram indicates that along the F axis, class III rules are distributed in a large F region, while class I and class II rules are, in a small F region, and class IV rules are found in the overlapping region of class II and III rules. These distributions are almost independent of lambda. Along the lambda axis, all four pattern classes are found in the region 0.25<lambda<0.75, and no correlation between pattern class and lambda parameter is observed.
Sakai
Sunao
S
Faculty of Education, Yamagata University, Yamagata, Japan. sakai@e.yamagata-u.ac.jp
Kanno
Megumi
M
Saito
Yukari
Y
D002477:Cells / Q000166:cytology*; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics