Moran-Sierpinski地毯及Moran-Sierpinski海绵的维数结果  

Dimensional results for the Moran-Sierpinski carpet and Moran-Sierpinski sponge

作　　者：胡晓梅 HU Xiaomei(Editorial Department of Journal of Central China Normal University,Wuhan 430079,China)

机构地区：[1]华中师范大学学报编辑部,武汉430079

出　　处：《华中师范大学学报（自然科学版）》2023年第6期793-798,共6页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11271148)。

摘　　要：该文研究了Moran-Sierpinski地毯和Moran-Sierpinski海绵的维数,得到若干结果.Moran-Sierpinski地毯和Moran-Sierpinski海绵具有Moran结构,是Sierpinski地毯及Sierpinski海绵利用Moran理论的推广.该文利用分形几何中的技巧,通过计算分别得到它们的Hausdorff维数,packing维数和上盒维数结果.Sierpinski地毯及Sierpinski海绵的维数结果可以看作是本文的特例.In this paper,the dimensional results of Moran-Sierpinski carpet and Moran-Sierpinski sponge are considered.Moran-Sierpinski carpet and Moran-Sierpinski sponge have the Moran structure,which is an extension of the Sierpinski carpet and Sierpinski sponge by the method of Moran set.By the techniques in fractal geometry and calculation,the Hausdorff dimensions,packing dimensions,and upper box dimensions of the Moran-Sierpinski carpet and Moran-Sierpinski sponge are obtained.The dimensional results of the Sierpinski carpet and Sierpinski sponge can be seen as special cases of this paper.

关 键 词：Sierpinski地毯 Sierpinski海绵 MORAN集 Hausdorff维数 PACKING维数 上盒维数 

分 类 号：O174.12[理学—数学]