Fractal Interpolation And Its Application

The concept of fractal interpolation functions was firstly proposed by the American mathematician Barnsely in 1986. Comparing with the traditional interpolation, we find that fractal interpolation function has a great advantage on describing those phenomenon and things which have fractal feature or look very complex. Fractal interpolation function is defined by the given interpolation nodes and Iterated Function System(IFS), so it is meaningful and vital to discuss the influence of free parameters on FIF. Many outstanding and famous specialists have made a smash hit on the research of the fractal interpolation and its application within recent decades.In chapter 1, we give the history of the fractal geometry and the current condition of fractal interpolation theory, furthermore the major content of the article is summarized.In chapter 2, we give some traditional interpolation methods and fractal interpolation theory.In chapter 3, we show the influences of the parameter on fractal interpolation function image and its dimension by numerical analysis. Then we give a method of choosing the proper parameter and analyze the rationality with an case.In chapter 4, we discuss the impact of the change of the interpolation nodes on fractal interpolation function with numerical experiment on the base of chapter 3.In chapter 5, we construct a more flexible fractal interpolation system on rectangular region and prove it has the only one attractor; finally we show its flexibility by twice fractal interpolation on the broken surface of rock.In chapter 6, we make a conclusion and a forecast to the future.