一类Weierstrass函数图像的K-维数式  

On K-dimention of a Weierstrass-type Function

作　　者：黄铭[1] 张静[2] 刘鸿博[2] 朱春梅 

机构地区：[1]四川工商职业技术学院,成都611830 [2]四川水利职业技术学院,成都611830 [3]四川水产学校,成都611731

出　　处：《四川理工学院学报（自然科学版）》2012年第2期88-90,共3页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

摘　　要：Weierstrass函数是一类处处连续不可微的函数,其函数图像具有分形性质。研究Weierstrass函数图像的分形维数在分形几何中具有非常重要的地位。K-维数是介于Hausdorff维数和Box维数之间的分形维数,通过研究一类Weierstrass函数图像的K-维数,证明了这类函数图像的K-维数为1,从而进一步揭示出这类Weierstrass函数图像的Hausdorff维数、Box维数和K-维数之间的关系。Weierstrass function is everywhere continuous and nowhere differentiable.Its graph has fractal properties.Studying the graph of Weierstrass function plays an important role in fractal geometry.K-dimension is a fractal dimension between Hausdorff dimension and Box dimension.The K-dimension of graph of Weierstrass-type function was studied.It was proved that the K-dimension is equal to 1,and the relationship between Hausdorff dimension,Box dimension and K-dimension is progressively revealed.

关 键 词：WEIERSTRASS函数 K-维数 函数图像 

分 类 号：O186[理学—数学]