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SIn this thesis four important problems are discussed: modeling and rendering of NIFS (Nonlinear Iterated Function System), the theory and research means of NMIFS (Nonlinear Markov IFS), the convergence and structure of the attractive basin and the repulsive basin of the free critical 'points in Julia set of the Schroder iterated functions of a one-parameter family with high degree polynomials, and the structure characteristic of a class generalized M-J set.The theory of NIFS is extended from IFS, but its essence has been another thing. In this thesis the basic theory and its application in the simulation of natural scene are mainly discussed. The result has been published on the kernel journal computer science.In the following by combining the Markov process with NIFS, the author generalizes Dekking's work on linear Markov IFS and puts focus on some important aspects such as balanced vector measures, the recursive computation of moments, and the computer simulation of the attractors of some NMIFSs. The result has been accepted by the journal Progress in Nature Science and will be published soon.Among the many means to get the roots of any equation, Schroder iteration is a very useful one. However, extra fixed points will be introduced in this procedure. To analyze the convergence and structure of the attractive basin and the repulsive basin of the free critical points in the extra fixed points is very important way to study Mandelbrot and Julia set. In this paper, the author generalizes others work and gives a beautiful way to solve the problem of the Julia set of the Schroder functions of one-parameter family polynomials with high degree.The structure and the construction of generalized M-J set are also a meaningful subject. With escaping-time algorithm and the cycle-finding algorithm two different Julia sets are studied and the structure character of a class of generalized M-J set is discussed...