一类分形插值曲面的截线及其维数  

Profile Curves of Fractal Interpolation Surface 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：《鞍山师范学院学报》2009年第4期1-4,共4页Journal of Anshan Normal University

基　　金：江苏省自然科学基金项目(BK2002003)

摘　　要：对一类分形插值曲面和它的截线进行探讨.根据生成分形插值曲面的迭代函数系,导出了其截线的迭代函数系,证明了它的不变集(即分形插值曲面的截线)是具有间断点的分形插值函数的图像,并通过计算得到分形插值曲面的盒维数与其截线的盒维数之间的关系.In this paper we construct a class of iterated function system and study the profile curves of fractal surface generated by the constructed. We prove the invariant set which is the graph of fractal interpolation functions with discontinuous points. Then we give the relationship between the box-counting dimension of FIS and the dimension of its Profile curves by counting them.

关 键 词：迭代函数系 分形插值曲面 截线 盒维数 

分 类 号：O184[理学—数学]