Space-Filling Curves of Self-Similar Sets (III): Skeletons
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In: Fractals, Vol. 28.2020, No. 2, 2050028, 12.03.2020.
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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 -