具有间断点的分形插值函数及其维数  

Fractal Interpolation Function with Discontinuous Points and Its Dimension

作　　者：彭涛[1] 冯志刚[1] 

机构地区：[1]江苏大学理学院,江苏镇江212013

出　　处：《信阳师范学院学报（自然科学版）》2008年第4期497-500,共4页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：江苏省自然科学基金项目(BK2002003)

摘　　要：文献[1]提出了具有间断点的分形插值方法,根据给定的插值结点和给定的纵向压缩因子构造出二维空间上的一个映射,其不变集为通过插值结点的具有间断点的分形曲线.本文给出了具有间断点的仿射分形插值函数和递归仿射分形插值函数的关系,从而得到分形插值函数图像的计盒维数定理.A fractal interpolation algorithm with discontinuous points was proposed in paper[ 1 ]. Based on the given interpolation nodes and given longitudinal compressibility factor, a mapping on 2D space was constructed. It was also observed that its invariant set was a through-interpolation nodes rough curve with discontinuous points. The relationship between the affine fraetal interpolation functions with discontinuous points and reeursive affine fractal interpolation functions is given. And then the box-counting dimension theorem of the graph of the fractal interpolation functions with discontinuous points is obtained.

关 键 词：间断点 迭代函数系 递归分形插值函数 计盒维数 

分 类 号：O184[理学—数学]