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ISSN 1088-6826(e) ISSN 0002-9939(p)

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
Posted: 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 $\{\phi_i(x)=\frac{1}{N} (x+d_i)\}_{i=1}^N$ . 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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