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Topological structure of fractal squares

Published online by Cambridge University Press:  01 March 2013

KA–SING LAU ,
JUN JASON LUO  and
HUI RAO
KA–SING LAU
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, P.R. China. e-mail: kslau@math.cuhk.edu.hk
JUN JASON LUO
Affiliation:
Department of Mathematics, Shantou University, Shantou 515063, Guangdong, P.R. China. e-mail: luojun2011@yahoo.com.cn
HUI RAO
Affiliation:
Department of Mathematics, Hua Zhong Normal University, Wuhan 430079, P.R. China. e-mail: hrao@mail.ccnu.edu.cn
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Abstract

Given an integer n ≥ 2 and a digit set ⊊ {0,1,. . .,n − 1}2, there is a self-similar set F ⊂ ℝ2 satisfying the set equation: F=(F+)/n. We call such F a fractal square. By studying a periodic extension H= F + ℤ2, we classify F into three types according to their topological properties. We also provide some simple criteria for such classification.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 1 , July 2013 , pp. 73 - 86
Copyright
Copyright © Cambridge Philosophical Society 2013 

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