Recurrent Fractal Interpolation Curve And Its Box Dimension

Fractal curve is an important research direction in fractal geometry.Fractal curve can be used to describe many natural phenomena in nature.Dimension is an important research content in the research process of fractal curve or surface.We can understand the graphic properties better through dimension.Structural fractal interpolation functions can be interpolated by fractal interpolation or recursion fractal interpolation.But many experimental data or natural phenomena tend to occur in complex curves,rather than in the image of a function.In this paper,the method of constructing plane fractal interpolation curve by recursion fractal interpolation is presented.The formula of calculating box dimension is obtained after the properties of recursion fractal interpolation curve dimension being studied.In Chapter 1,it introduces the research background,domestic and overseas research development status of this paper briefly,and presents the main content and innovation points of this paper.In Chapter 2,it reviewed the relevant basic knowledge,fractal interpolation function,which include the definitions of iterated function system and the affine transformation.It also introduced the definitions of the fractal interpolation function(FIF),recursive fractal interpolation function(RIFS)and related concepts of box dimension.In Chapter 3,the interpolation points are classified.Then he interpolation function of x or y is formed on each segment.The recursive fractal interpolation curve for the whole point column is obtained.Then it proves its continuity and gives examples.In Chapter 4,it introduces the dimension formula of fractal interpolation function first.The image of a particular fractal function is obtained by rotation and translation the image of each segment of the recursive fractal interpolation curve.We find the relationship between the curve and the iteration function.The formula for calculating the dimension of recursion fractal interpolation curve is obtained by the box dimension of recursive fractal interpolation function image.In Chapter 5,there are summary and prospect.This chapter summarizes the main research contents of this paper and gives some suggestions for future research.