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

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**134**(2006), 3163-3170 Request permission

## 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.## References

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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
- 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
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2231899