Autoreplicators and hypercycles in typogenetics

Abstract

A simplified formal system typogenetics, closely related to concepts of molecular genetics and introduced by Hofstadter in his seminal book Dialogues with G ö del, Escher, Bach: An Eternal Golden Braid [Basic books, New York, 1979 (Chapters XVI and XVII)] is discussed. Concepts of autoreplicators and hypercycles, defined within typogenetics, belong to basic entities in current perception of artificial life. A metaphor of chemical reactions (chemostat) is applied to study emergence of autoreplicators and hypercycles. The initial version of evolutionary approach, designed for construction of autoreplicators, is able to produce only small hypercycles composed of two or at most three autoreplicators. An emergence of larger hypercycles represents extremely complicated combinatorial optimization problem. Therefore, we turn our attention to a sequential technique of their construction, where a smaller hypercycle is enlarged by another autoreplicator. Both components are thus integrated into one hypercycle. This method of successive construction of hypercycles substantially reduces combinatorial complexity of the original approach where whole hypercycles are simultaneously optimized.