Cyclic Behavior of Randomly Growing Digital Structures in Finite Random Environment

Computer experiments with a model of a randomly growing structure with the possibility of division are presented. In agreement with the set of conditions, the growing structures are considered as evolutionary sequences. The randomly growing digital structure could achieve unchangeable "shape" in each evolutionary generation in spite of the lack of complete predetermination of this "shape". The effect was obtained by random supplement of creative materials from the environment. The environment was assumed as random, finite, and repetitive in a cyclic way. For this environment the only stable state of evolutionary sequence is a periodic sequence (in a particular case, the same "shape" in each generation). Other sequences have either to degenerate or, after a number of nonperiodic charges, become periodic. The model, results obtained from the computer and interpretation are presented.