Emergence of non-local effects in rule dynamical systems

'Rule-dynamics' is a framework for simple models of rule-changing systems using cellular automata (CA) rules. It is known that the mechanism of some cluster formation can be explained in terms of the spatio-temporal action of only two local rules. Among the various self-organizing patterns which are induced by the relationships between the local rules, 'switching phenomena' are especially interesting. The pattern of one cluster can be exchanged with the pattern of another cluster due to boundary interactions between nearest neighboring clusters. That is, a non-local effect can be generated instantaneously beyond the direct interaction range assumed in the original system. The significance of the switching phenomena is briefly discussed in relation to information transfer in biological systems.