Hausdorff Dimension of Two Classes of Modified Sierpinski Carpets

Shan Jiajun; Long Lunhai; Yang Cheng; Wang Sichen

doi:10.15886/j.cnki.hdxbzkb.2016.0002

Shan Jiajun, Long Lunhai, Yang Cheng, Wang Sichen. Hausdorff Dimension of Two Classes of Modified Sierpinski Carpets[J]. Natural Science of Hainan Unversity, 2016, 34(1): 7-11. DOI: 10.15886/j.cnki.hdxbzkb.2016.0002

Citation:

Hausdorff Dimension of Two Classes of Modified Sierpinski Carpets

Graphical Abstract

Graphical Abstract

Abstract

Abstract

In the report, a bi Lipschitz map between square and sector ring whose central angle was less than 180° was constructed. Firstly, it was proved that if we change the initial set of Sierpinski carpet from square to sector ring, the Hausdorff dimension are equal. Secondly, it was also showed that the Hausdorff dimension of the Modified Sierpinski carpet remain the same even the initial set is replaced into the sector whose central angle is less than 180°.