Space-Filling Curves of Self-Similar Sets (III): Skeletons

Hui Rao, Shuqin Zhang

Research output: Contribution to journalArticleResearchpeer-review


Skeleton is a new notion designed for constructing space-filling curves of self-similar
sets. In a previous paper by Dai and the authors [1], it was shown that for all connected
self-similar sets with a skeleton satisfying the open set condition, space-filling curves can be
constructed. 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.
Original languageEnglish
Article number2050028
Issue number2
Publication statusPublished - 12 Mar 2020

Bibliographical note

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  • Self-similar se
  • Skeleton
  • Finite type condition
  • Space-filling curves
  • Self-Similar Set
  • Finite Type Condition
  • Space-Filling Curves

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