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 -