Replication Error and Time Evolution of a Self-Replicating System

A self-replicating system where the elements belonging to a solution category can replicate themselves by copying their own informations, is considered. The information carried by each element is defined by an element of all the n multiple tensor product of a base space that consists of m different base elements. We assume that in the replication the processes of copying each base information are the same and independent from one another and that the copying error distribution in each process is characterized by a small variation with a quite small mean value. Concentrating on the number fluctuation of the informations in the copying process, we analyze the time evolution of the system. We illustrate the change of averaged number of informations carried by system objects and the variation of the number distribution as a function of time. Especially, it is shown that the averaged number of information grows in general after large number of generations.