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

Hui Rao, Shuqin Zhang

Publikation: Beitrag in FachzeitschriftArtikelForschungBegutachtung


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.
PublikationsstatusVeröffentlicht - 12 März 2020

Bibliographische Notiz

Funding Information:
Hui Rao is supported by NSFC-11971195 and NSFC-11431007 and the Shu-Qin Zhang is supported by Project P29910 and P27050 and by the doctoral program W1230 granted by the Austrian Science Fund (FWF).

Publisher Copyright:
© 2020 World Scientific Publishing Company.

Dieses zitieren