On the boundaries of self-similar tiles in

Author:
Xing-Gang He

Journal:
Proc. Amer. Math. Soc. **134** (2006), 3163-3170

MSC (2000):
Primary 28A80, 05B45

DOI:
https://doi.org/10.1090/S0002-9939-06-08643-6

Published electronically:
June 5, 2006

MathSciNet review:
2231899

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Abstract | References | Similar Articles | Additional Information

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 . 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:
https://doi.org/10.1090/S0002-9939-06-08643-6

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.