一类三维自仿射谢宾斯基地毯的Hausdorff维数和Box维数  

Hausdorff Dimension and Box Dimension of a Kind of 3-dimensional Self-affine Sierpinski Carpets

作　　者：陈绍明[1] 龙伦海[1] 朱莉红[1] 

机构地区：[1]海南大学信息科学技术学院,海南海口570228

出　　处：《海南大学学报（自然科学版）》2012年第3期199-202,205,共5页Natural Science Journal of Hainan University

摘　　要：给出了三维空间中一类自仿射集Sierpinski Carpets的Hausdorff维数的计算公式,并通过6个引理进行了论证.同时,给出了此类自仿射集Sierpinski Carpets的Box维数的表达式,并用Box维数的定义证明了该结论.The formula of the Hausdorff dimension of a kind of 3-dimensional self-affine Sierpinski Carpets was given and proved through six lemmas. The formula of the Box dimensions of this kind of 3-dimensional self-affine Sierpinski Carpets was also obtained and proved through the definition of the box dimension.

关 键 词：SIERPINSKI CARPETS HAUSDORFF维数 BOX维数 

分 类 号：O174.12[理学—数学]