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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the boundaries of self-similar tiles in $ \mathbb{R}^1$


Author: Xing-Gang He
Journal: Proc. Amer. Math. Soc. 134 (2006), 3163-3170
MSC (2000): Primary 28A80, 05B45
Published electronically: June 5, 2006
MathSciNet review: 2231899
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Abstract: The aim of this note is to study the construction of the boundary of a self-similar tile, which is generated by an iterated function system $ \{\phi_i(x)=\frac{1}{N} (x+d_i)\}_{i=1}^N$. We will show that the boundary has complicated structure (no simple points) in general; however, it is a regular fractal set.


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Additional Information

Xing-Gang He
Affiliation: Department of Mathematics, Central China Normal University, Wuhan, 430079, People’s Republic of China
Email: xingganghe@sina.com

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08643-6
PII: S 0002-9939(06)08643-6
Keywords: Box dimension, Hausdorff dimension, self-similar set, self-similar tile, iterated function system.
Received by editor(s): April 14, 2005
Published electronically: June 5, 2006
Additional Notes: This research was supported in part by SRF for ROCS(SEM)
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.