一类Weierstrass型函数图像的Box维数  

Box Dimension of a Class of Weierstrass Function

作　　者：张静[1] 刘鸿博[1] 

机构地区：[1]四川水利职业技术学院,成都611830

出　　处：《四川理工学院学报（自然科学版）》2013年第5期74-76,共3页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

摘　　要：Weierstrass函数是一类处处不可微的函数,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。通过研究一类Weierstrass型函数W(x)=∑∞k=1a kφt k(b k x+θk)的图像的Box维数,证明了这类函数图像的Box维数为2+lim n→∞(loga n/logb n),从而进一步揭示出这类Weierstrass函数图像的Hausdorff维数与Box维数之间的关系。Weierstrass function is everywhere continuous and nowhere differentiable. Its graph has fractal properties. Studying the fractal dimension of Weierstrass function graph plays an important role in fractal geometry. The Box-dimension of graph of a kind of Weierstrass-type function is studied. It is proved that its Box-dimension is equal to 2＋lim n→∞（logan/logbn）,and the relationship between Hausdorff dimension and Box dimension is progressively revealed.

关 键 词：Weierstrass型函数 函数图像 BOX维数 

分 类 号：O172[理学—数学]