Complex Fractal Interpolation Surface And Its Box Dimension

The rough and complex phenomena can be described realistically in fractal interpolation which exists widely in nature.The theory of fractal interpolation are implemented in real space,has not yet been found in complex space.Therefore a method of construction for the iterated function system with given interpolation nodes is proposed on the complex domain.So that the invariant set of the iterated function system is an image of the interpolation function.This paper is divided into five chapters.The first chapter explains the background of research,development of fractal interpolation function and the main contents and innovations.The second chapter is concerned with the basic knowledge of fractal theory and complex function.In the third chapter,the method of constructing a complex fractal interpolation function is proposed.In order to ensure the continuity of the fractal interpolation function,this chapter uses two construction methods to solve the continuity of the boundary.Firstly,defining the boundary interpolation nodes on the square domain are co-linear,then the constant vertical scaling factors are introduced.Secondly,the boundary interpolation nodes on the rectangular area can be arbitrarily selected by using the special function vertical scaling factors.The fourth chapter introduces the dimension of fractal interpolation surface.According to the theory of complex variable function,the real part and imaginary part of complex fractal interpolation function are binary real functions,and then the box dimension of fractal interpolation surface is calculated by using the dimension theorem.In the last chapter sums up the main ideas and prospect of this thesis.Firstly,summaries the main contents of this paper,and some prospects are put forward for further research on this subject.