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This paper is one of a series of the papers treating stable configurations in cell space. The strong-week relations between states are introduced in the local transition rule of the cell space. The lo...cal transition rule is systematically represented by the threshold type function. The pattern of stable configuration is remarkably changed when the thresholds of the local transition rule exceeds some critical values. It is shown that the stable configurations in the $ m \times n $ cell space are dependent on both the size of the basic cell space and the type of local transition rule. Hierarchy of types of local transition rules and cluster property of stable configurations are obtained. In addition the singular stable subconfiguration is defined and it is found that a stable configuration becomes another stable configuration if a state of the singular stable subconfiguration is changed.show more
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