Classification of Discrete Dynamical Systems Based on Transients


In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method is based on classifying the asymptotic behavior of the average computation time in a given system before entering a loop. We were able to identify a critical region of behavior that corresponds to a phase transition from ordered behavior to chaos across various classes of dynamical systems. To show that our approach can be applied to many different computational systems, we demonstrate the results of classifying cellular automata, Turing machines, and random boolean networks. Further, we use this method to classify 2D cellular automata to automatically find those with interesting, complex dynamics. We believe that our work can be used to design systems in which complex structures emerge. Also, it can be used to compare various versions of existing attempts to model open-ended evolution (Ray (1991), Ofria and Wilke (2004), Channon (2006)).

Artificial Life Journal, Special Issue (currently in the review process)

We extend our previous paper about a novel method of classifying the dynamics of discrete dynamical systems. Currently, it’s in the review process for a special issue of the ALife Journal. After we receive the feedback and adjust the paper accordingly, I will publish the results here.