Research On Construction Of Fractals With IFS From Complex Function Family Of F?z?= Z^-n+c

Since the fractal is put forward clearly,it has been developing rapidly in the fields of whether practice or scientific research,people are more and more familiar with it.Theconcepts and methods of chaos and fractal are widely used in the fields of astronomy,chemistry,physics,astronomy,chemistry,physics,biology,meteorology,economy,mutual penetrationand different other disciplines,so as to promote the development of a comprehensive interdiscipliness.The rapid developments of the computer hardware and the computer graphics technology make fractal itself develop so quickly that it has been widely recognized and accepted,it is also because of the help of the computer graphics,there has so many beautiful fractal graphics.By the computer technology,we can better promote our understanding of fractals,and also can expand the application fields of fractals widerly.Because of the complexity of fractal images,its construction methods and mechanism also needs to be improved.At present,the main methods of computer drawing fractal are from these two directions:one is the visualization of the dynamic systems and the other is IFS.In inland and international the study of symmetric fractals has been mostly investigated from the two directions.The main work is about how to construct symmetric dynamic systems of two-dimensional plane or three-dimensional space or symmetric IFSs and how to construct their images.Nowadays,as an important method of construction of fractals,the iterated function system is still based on the traditional linear compression affine transformations.In the study of computer visualization of plane dynamic systems,many scholars have been interested in the study of complex analytic maps,and have achieved a lot of research results.In this paper,we try to construct IFSs by using the complex function family with negative integer power,and propose a method to construct the nonlinear iterated function system.The complex function family.f(z)= z-n + c is as the research object.Major innovations and research works are as follows:(1)We researched on the iteration features and rules of complex function family off(z)=z-n+c,including its iterative orbit,attraction basins and fixed point.Compared with the complex analytic mapping with the positive integer power.(2)We research and present a method for constructing nonlinear iterated function systems by complex function family of f(z)= z-n +c.By selecting at least two parameters in the 1-period region of the M set in the parameter plane,the iterated function system can be composed of which can be used to generate a large number of strange attractors or fractal.(3)We research the effective range of the complex function family of,f(z)= z-n+c with the negative integer powers,research how to choose the initial iteration point and research the random iterative orbit of the nonlinear iterated function system.(4)According to the geometric symmetry of the 1-period region of the M set of the complex function family,the method of construction of symmetric IFS is proposed by choosing Zn+1 parameters or Dn+1 parameters,where the parameters used to construct the fractals with Zn+1 symmetry can be obtained by selecting the symmetric parameters with Zn+1 or selecting the symmetric parameters with both Zn+1 and Dn+1 at same time.(5)We research how to significantly improve the definition the of the boundaries of the fractals by increasing iteration numbers of the some iteration functions of iterated function system.(6)Based on the M set of complex function family f(z)= z-n c,the nonlinear IFSs are constructed by selecting the parameters in the 1 period region and a large number of new or strange attractor fractals are constructed and an image database is built.