A class of nonlinear iterated function system attractors

In this article the theory of NIFS (nonlinear iterated function system) and the random iteration algorithm are expounded. By theoretical analysis, the definition domain of a class of complex polynomial hyperbolic NIFS in the complex cc-plane is given out and a series of the NIFS attractors are simulated. In the article, the changing regularity of the NIFS attractors are discussed when the control parameters are changed and the relationship between the totally disconnected NIFS attractor and its address set is discussed. Results show that: (1) the multiplicity of the NIFS inverse function leads to multiple addresses of the same region for NIFS attractors, and (2) the NIFS attractors have chaotic dynamic characteristics, and the evolution of the NIFS attractors depend on the choice of the range of the principal argument θzθz.