Observations on Complex Multi-state CAs

Abstract

A genetic algorithm, with a fitness function based on input-entropy, was developed to search for rules with complex behaviour for multi-state CAs. The surprising presence of complex rules founded allows the observation that, in this context too, complexity organises itself through various behaviour of emergent structures, which interact within regular or uniform domains, creating many different configurations, previously noticed for elementary CAs. In this paper observations on the behaviour of multi-state CAs are reported, through the dynamics of the emergent structures or gliders. In particular, it is discovered that the more particles follow local rules, the more complexity develops. This seems to be also validated by input entropy plots, which the particles produce in the dynamics of their related CAs. The paper re-opens the CAs classification problem and gives birth to new insights into some of the mathematical capability of building special configurations, attempting to measure in some way complexity.