Recurrent Bivariate Fractal Interpolation Surfaces With Multi-parameter

The notion of fractal interpolation surface was firstly introduced by Massopust, and since then there has been a tremendous interest in the subject due to its diverse applications ranging from simulating irregular object shape to compression image. In the years that followed, the problem of the construction of fractal surfaces has been dealt by many other authors, thereby enriching the study on the fractal interpolation surface. In this paper,in order to overcome the strictly self-similar limitations of traditional fractal interpolation surface and gain more flexibility in practical application, we combines recurrent iterated function system with multi-parameters and constructs a class of recurrent bivariate fractal interpolation surfaces with multi-parameters.The main research works described in this article are as follows:Firstly, this paper briefly reviews the background and current situation of fractal theory, the main content and innovation of the paper is further summarized.Then it introduces the fundamental theory and knowledge of the fractal interpolation including the theory of fractal space and iterated function syetem,as well as the definition of fractal dimension.Secondly, this paper mainly introduces recurrent fractal interpolation function. For example, based on MATLAB, graphs of the fractal interpolation function and recurrent fractal interpolation function are drawn passing through the given interpolation data.From the graph can be seen, the application of recurrent fractal interpolation function is more flexible than the fractal interpolation function.Finally, this paper constructs a class of recurrent bivariate fractal interpolation surfaces with multi-parameters. Firstly, it constructed a class of recurrent iterated function system on a rectangular domain,then the uniqueness of the attractor is proved. Meanwhile, it is explained that the recurrent iterated function system on a rectangular domain is how to undertake iteration by a specific example. Then it is proved that the class of recurrent iteration function system attractors on a rectangular domain are continuous curved surface passing through the given interpolation data.