Copyright © 2009 Xingyuan Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper contrastively researches the structural characteristic and the fission-evolution law of four different kinds of generalized Julia set (generalized J set in short) with different parameter c, which includes the generalized J set without any perturbation, the generalized J set perturbed by additive noises, the generalized J set perturbed by multiplicative noise, and the generalized J set perturbed by composing additive and multiplicative noises, analyzes the effect of random perturbation to the generalized J set, and illuminates the stability of the generalized J set.