Evolution of Cellular Automata-Based Replicating Structures Exhibiting Unconventional Features

genetic algorithm, cellular automaton, transition function, conditional rule, replicating loop

Replicating loops represent a class of benchmarks, which is commonly studied in relation with cellular automata. Most of the known loops, for which replication rules exist in two-dimensional cellular space, create the copies of themselves using a certain construction algorithm that is common for all the emerging replicas. In such cases, the replication starts from a single instance of the loop (represented as the initial state of the cellular automaton) and is controlled by the transition function of the automaton according to which the copies of the loop are developed. Despite the fact that universal replicators in cellular automata are possible (for example, von Neumann's Universal Constructor), the process of replication of the loops is usually specific to the shape of the loop and the replication rules given by the transition function. This work presents a method for the automatic evolutionary design of cellular automata, which allows us to design transition functions for various structures that are able to replicate according to a given specification. It will be shown that new replicating loops can be discovered that exhibit some unconventional features in comparison with the known solutions. In particular, several scenarios will be presented which can, in addition to the replication from the initial loop, autonomously develop the given loop from a seed, with the ability of the loop to subsequently produce its replicas according to the given specification. Moreover, a parallel replicator will be shown that is able to develop the replicas to several directions using different replication algorithms.