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- Title
SPACE-FILLING CURVES OF SELF-SIMILAR SETS (III): SKELETONS.
- Authors
RAO, HUI; ZHANG, SHU-QIN
- Abstract
Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. In a previous paper by Dai and the authors [Space-filling curves of self-similar sets (II): Edge-to-trail substitution rule, Nonlinearity32(5) (2019) 1772–1809] it was shown that for all the 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.
- Subjects
CURVES; ALGORITHMS; TOPOLOGICAL spaces
- Publication
Fractals, 2020, Vol 28, Issue 2, pN.PAG
- ISSN
0218-348X
- Publication type
Article
- DOI
10.1142/S0218348X20500280