Experimental study of Elementary Cellular Automata dynamics using the density parameter

In [Gut89] Howard Gutowitz writes : “A fundamental problem in theory of cellular automata is classification. A good classification divides cellular automata into groups with meaningfully related properties. In general there are two types of classifications : phenotypic and genotypic. A phenotypic classification divides a population into groups according to their observed behaviour. A genotypic classification divides a population into groups according to the intrinsic structure of the entities in the population.” In 1984, the first phenotypic classification has been proposed by Wolfram [Wol84] dividing cellular automata (CA) according to their “observed dynamics”. This classification was very important since it motivated numerous researches but was at the same time criticised by many authors on grounds that no formal definitions of the classes were given. In 1989, Culik and Yu in [ČPY89] proposed a formal definition of the classes according to some asymptotic behaviour of the cellular automaton and showed the undecidability of the classifying scheme. The class of CA that has drawn much attention is the class of the 256, 2-state 3-neighbours CA, or so-called Elementary CA (ECA). An interesting axis of investigation was the application of topological analysis theory to cellular automata. In 1998, Cattaneo et al. in [CFM99] proposed a genotypic classification of all of the 256 ECA that has the advantage to rely on formal definitions as well as theoretical justifications.