Topological properties of self-similar fractals with one parameter |
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Authors: | Jun Jason Luo Lian Wang |
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Affiliation: | 1. College of Mathematics and Statistics, Chongqing University, 401331 Chongqing, China;2. Institut für Mathematik, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany |
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Abstract: | In this paper, we study two classes of planar self-similar fractals with a shifting parameter ε. The first one is a class of self-similar tiles by shifting x-coordinates of some digits. We give a detailed discussion on the disk-likeness (i.e., the property of being a topological disk) in terms of ε. We also prove that determines a quasi-periodic tiling if and only if ε is rational. The second one is a class of self-similar sets by shifting diagonal digits. We give a necessary and sufficient condition for to be connected. |
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Keywords: | Self-similar tile Connectedness Disk-likeness Quasi-periodic tiling |
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