Classification of Discrete Dynamical Systems Based on Transients
This work addresses the challenge of designing systems with emergent complex structures for researchers in artificial evolution and computational modeling, though it appears incremental by building on prior attempts to model open-ended evolution.
The authors tackled the problem of identifying systems capable of producing complex behavior for artificial evolution by developing a novel classification method based on the asymptotic behavior of average computation time before entering a loop, identifying a critical region corresponding to a phase transition from order to chaos across systems like cellular automata and Turing machines.
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 et al. (2004), Channon (2006)).