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arXiv · 0902.1615

Perturbation of self-similar sets and some regular configurations and comparison of fractals

Junyang Yu
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Abstract

We consider several distances between two sets of points, which are modifications of the Hausdorff metric, and apply them to describe some fractals such as $δ$-quasi-self-similar sets, and some other geometric notions in Euclidean space, such as tilings with quasi-prototiles and patterns with quasi-motifs. For the $δ$-quasi-self-similar sets satisfying the open set condition we obtain the same result as a classical theorem due to P. A. P. Moran. In this paper we try to gaze on fractals in an aspect of their "form" and suggest a few of related questions. Finally, we attempt to inquire an issue -- what nature and behavior do non-crystalline solids that approximate to crystals show?

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Junyang Yu. 2009-02-10. Perturbation of self-similar sets and some regular configurations and comparison of fractals. https://arxiv.org/abs/0902.1615

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