Generation of the Correlation between Rule and Density in Rule-Dynamical Systems

'Rule-dynamics' is a framework for simple models of rule-changing systems using cellular automata (CA) rules. We realize the transition process from CA to rule-dynamics by adjusting one parameter. Through this process, we show that a correlation between the rule and the density is generated, and also show that this correlation increases although the entropies of the density and the rule increase respectively. This suggests that we can extract the density information from the local rule description.