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

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Space-Filling Curves of Self-Similar Sets (III): Skeletons. / Rao, Hui; Zhang, Shuqin.
in: Fractals, Jahrgang 28.2020, Nr. 2, 2050028, 12.03.2020.

Publikationen: Beitrag in FachzeitschriftArtikelForschung(peer-reviewed)

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Rao H, Zhang S. Space-Filling Curves of Self-Similar Sets (III): Skeletons. Fractals. 2020 Mär 12;28.2020(2):2050028. doi: 10.1142/S0218348X20500280

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@article{49efe434819549d0aea4c7a286ead2f6,
title = "Space-Filling Curves of Self-Similar Sets (III): Skeletons",
abstract = "Skeleton is a new notion designed for constructing space-filling curves of self-similarsets. In a previous paper by Dai and the authors [1], it was shown that for all connectedself-similar sets with a skeleton satisfying the open set condition, space-filling curves can beconstructed. In this paper, we give a criterion of existence of skeletons by using the so-calledneighbor graph of a self-similar set. In particular, we show that a connected self-similar setsatisfying the finite type condition always possesses skeletons: an algorithm is obtained here.",
keywords = "Self-similar se, Skeleton, Finite type condition, Space-filling curves, Self-Similar Set, Finite Type Condition, Space-Filling Curves",
author = "Hui Rao and Shuqin Zhang",
note = "Publisher Copyright: {\textcopyright} 2020 World Scientific Publishing Company.",
year = "2020",
month = mar,
day = "12",
doi = "10.1142/S0218348X20500280",
language = "English",
volume = "28.2020",
journal = "Fractals",
issn = "0218-348X",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "2",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Space-Filling Curves of Self-Similar Sets (III): Skeletons

AU - Rao, Hui

AU - Zhang, Shuqin

N1 - Publisher Copyright: © 2020 World Scientific Publishing Company.

PY - 2020/3/12

Y1 - 2020/3/12

N2 - Skeleton is a new notion designed for constructing space-filling curves of self-similarsets. In a previous paper by Dai and the authors [1], it was shown that for all connectedself-similar sets with a skeleton satisfying the open set condition, space-filling curves can beconstructed. In this paper, we give a criterion of existence of skeletons by using the so-calledneighbor graph of a self-similar set. In particular, we show that a connected self-similar setsatisfying the finite type condition always possesses skeletons: an algorithm is obtained here.

AB - Skeleton is a new notion designed for constructing space-filling curves of self-similarsets. In a previous paper by Dai and the authors [1], it was shown that for all connectedself-similar sets with a skeleton satisfying the open set condition, space-filling curves can beconstructed. In this paper, we give a criterion of existence of skeletons by using the so-calledneighbor graph of a self-similar set. In particular, we show that a connected self-similar setsatisfying the finite type condition always possesses skeletons: an algorithm is obtained here.

KW - Self-similar se

KW - Skeleton

KW - Finite type condition

KW - Space-filling curves

KW - Self-Similar Set

KW - Finite Type Condition

KW - Space-Filling Curves

UR - http://www.scopus.com/inward/record.url?scp=85082106230&partnerID=8YFLogxK

U2 - 10.1142/S0218348X20500280

DO - 10.1142/S0218348X20500280

M3 - Article

VL - 28.2020

JO - Fractals

JF - Fractals

SN - 0218-348X

IS - 2

M1 - 2050028

ER -