A random version of McMullen-Bedford general Sierpinski carpets and its application

Yongxin Gui; Wenxia Li

doi:10.1088/0951-7715/21/8/004

A random version of McMullen-Bedford general Sierpinski carpets and its application

Yongxin Gui^*
, Wenxia Li

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We consider a random version of the McMullen-Bedford general Sierpinski carpet which is constructed by randomly choosing patterns in each step instead of a single pattern in its original form. Their Hausdorff, packing and box-counting dimensions are determined. A sufficient condition and a necessary condition for the Hausdorff measures in their dimensions to be positive are given. As an application, we discuss the issue on the intersection of the general Sierpinski carpet with its translations.

Original language	English
Pages (from-to)	1745-1758
Number of pages	14
Journal	Nonlinearity
Volume	21
Issue number	8
DOIs	https://doi.org/10.1088/0951-7715/21/8/004
State	Published - 1 Aug 2008

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10.1088/0951-7715/21/8/004

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title = "A random version of McMullen-Bedford general Sierpinski carpets and its application",

abstract = "We consider a random version of the McMullen-Bedford general Sierpinski carpet which is constructed by randomly choosing patterns in each step instead of a single pattern in its original form. Their Hausdorff, packing and box-counting dimensions are determined. A sufficient condition and a necessary condition for the Hausdorff measures in their dimensions to be positive are given. As an application, we discuss the issue on the intersection of the general Sierpinski carpet with its translations.",

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AB - We consider a random version of the McMullen-Bedford general Sierpinski carpet which is constructed by randomly choosing patterns in each step instead of a single pattern in its original form. Their Hausdorff, packing and box-counting dimensions are determined. A sufficient condition and a necessary condition for the Hausdorff measures in their dimensions to be positive are given. As an application, we discuss the issue on the intersection of the general Sierpinski carpet with its translations.

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A random version of McMullen-Bedford general Sierpinski carpets and its application

Abstract

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