A Class Of Many Parameters Of Fractal Interpolation Surfaces And Its Variation

This article mainly focuses on the multi-parameter interpolation surface, and gives a class of multi-parameter fractal interpolation surface structure. That is, on the base of two sets of parameters fractal interpolation surface on R~2, we improve the two sets of parameters upon a multi-set of parameters in three-dimensional space, compared with traditional iterated function systems, it has greater flexibility. In certain conditions, this paper proves that this kind of attractor is result from the given interpolation points set of the fractal interpolation surface. Due to variation and dimension are important parameters to characterize the roughness of the surface, but binary fractal interpolation function is a kind of continuous function, its graph can fit the nature's rough surface greatly. So this paper discusses the properties of amplitude and variation of the binary continuous function, and especially argues about the variations' property of the multi-parameter fractal interpolation surface we proposed. Also we give the order's estimate, and find out the box-counting dimension's calculation formulas of this fractal interpolation surface.Firstly, we briefly review the generation and development of fractal geometry, and summarize the study of this topic status and the main contents. Secondly this article mainly discusses the basic theory and knowledge of the fractal, including several common dimensions, iterated function systems and fractal interpolation theory. Then the mainly study is: the variation and its property of fractal interpolation function, and the relationship with box-counting dimension. Finally, using the variation's property this article discusses a class of multi-parameter fractal interpolation surface, and variation order estimate of fractal interpolation surface.