The Property Of A Class Of Nonliner And Multi-parameter Fractal Interpolation Surface

In1986, Since Barnsley first put forward the concept of fractal interpolation function, It became a new and important theoretical tool of data fitting, approximation of function. It can simulate the shape of material object distinctly and It achieved a important significance of non-smooth curve and surface fitting. Compared to the traditional research which focusing on the linear aspect, In this paper, a class of nonlinear and multi-parameter iterated function system is constructed and a class of more general fractal function will be discussed, as follows:In the introduction of this paper, we review the development of fractal geometry, the current situation of this project and the major content of the article is summarized.In chapter1, we mainly introduced the basic knowledge of the fractal theoryIn Chapter2, we discussed the properties of amplitude and variation of the binary continuous function, and argue about the relationship of the variation and the dimension.In Chapter3, we construct a class of nonlinear iterated function system, including three arbitrary parameters, It can better control the interpolation surface by adjusting the parameters properly. Under certain conditions, we prove the uniqueness of the attractor and the attractor is the image of a fractal interpolation function. Moreover, we discuss the continuity of the fractal interpolation surface. Under the boundary contour, the parameter-dependent of the surface is obtained. Numerical experiment demonstrate the effectiveness of the parameter control.In Chapter4, Through the discussion of the properties of variation, We give calculation formula of the box-dimension of interpolation surface.