Construction Of Recurrent Fractal Interpolation Surface With Polynomials And Its Dimension

In the past, people constructed fractal interpolation surface under the condition of interpolation points which are collinear in boundary or interpolation points are collinear in the local boundary or vertical scaling factor is equal or scaling factor is a complex function which made the study is limited. In this paper, based on the polynomial interpolation theory, by interpolation polynomial of the interpolation points, in the case of arbitrary interpolation points in the rectangle domain and constant vertical scaling factor, we discuss the construction method of recurrent fractal interpolation surface and ensure the continuity of the interpolation surface. Then, on the basis of the study of the variation and the box counting dimension, we give the theorem of calculating the fractal dimension of the surface box, and then calculate the theoretical value of the box dimension. At last, by means of paper[41], in case of non equidistant, using MATLAB to calculate the variation of calculated surface. By the relationship of variation and box dimension, calculating the box dimension of the recursive fractal interpolation surface, and then compare it with theory box dimension values.In Chapter 1, research backgrounds, research status and the main research contents and innovative points of this paper are presented.In Chapter 2, it gives the fractal basic theory and basic knowledge. First of all, the related knowledge of the iterated function system are discussed. Followed, the related knowledge of fractal interpolation function is provided, which including fractal interpolation function dimension and variation. At last, the relevant knowledge of the unary recurrent fractal interpolation function is provided.In Chapter 3, firstly, based on the learning theory of polynomial interpolation, we give the method of construction of recurrent fractal interpolation surface. Then through an example image to show the correctness of the method of fractal interpolation surface.In Chapter 4, calculating the dimension of the fractal interpolation surface.In Chapter 5, the summary and the prospect of this thesis are presented.