Relationship between Generation Overlapping and Fractal Dimension in Secular Change of ALife Population

Kenichi Kamijo and Masahide Yoneyama
Toyo University

Abstract:

The idealized artificial life (ALife) ecological system has been structured on a computer, in order to investigate the essential behavior of actual organisms. Under a given environment, which can be controlled by the environment parameter, the secular population change of ALife entities conforming to a logistic reproduction rule has been simulated on it. The fractal dimension in both the original chaotic population change and the population change converted by the generation overlapping, which means the so-called moving total conversion in the population change process, can be well denoted by the polynomial of degree 5 with the environment parameter except near the several values. Also the relationship between the generation overlap number and the fractal dimension has been investigated in the secular change of the ALife entities. It has been shown that the fractal dimension will decrease in proportion to the increase of the generation overlap number. For this ALife ecological system, the fractal dimension in some cases of the environment parameter can be well denoted by the polynomial of degree 5 with the generation overlap number.