一类Weierstrass函数图像的盒维数  

Box Dimensions of the Graphs of a Class of Weierstrass Functions

作　　者：李本秀[1] 魏毅强[1] 

机构地区：[1]太原理工大学数学系,太原030024

出　　处：《太原科技大学学报》2010年第4期314-316,共3页Journal of Taiyuan University of Science and Technology

摘　　要：函数图像的分形维数是分形几何研究中的一个非常重要并且在当前十分活跃的课题。本文研究了一类形如∑∞k=1aktk(bkx+θk)的Weierstrass函数,证明了它的连续而不可微性,并给出了其图像的盒维数。The fractal dimension of the graph of the function is a very important and active in the current topic in the study of fractal geometry,especially the Box dimension.In this paper,the Box dimension of a more generalized Weierstrass function ∑∞k=1aktk（bkx＋θk） is studied,and its continuity and nowhere differentiability are also studied.

关 键 词：WEIERSTRASS函数 分形 盒维数 

分 类 号：O172[理学—数学]