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arXiv · 1804.10480

Space-filling curves of self-similar sets (III): Skeletons

Hui Rao·Shu-Qin Zhang
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Abstract

Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. It is shown in [Dai, Rao and Zhang, Space-filling curves of self-similar sets (II): Edge-to-trail substitution rule,https://doi.org/10.1088/1361-6544/ab1275] that for a connected self-similar set, space-filling curves can be constructed provided that it possesses a skeleton. In this paper, we give a criterion of existence of skeletons by using the so-called neighbor graph of a self-similar set. In particular, we show that a connected self-similar set satisfying the finite type condition always possesses skeletons: an algorithm is obtained here.

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Hui Rao, Shu-Qin Zhang. 2018-04-27. Space-filling curves of self-similar sets (III): Skeletons. https://arxiv.org/abs/1804.10480

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