GEODESIC DISTANCES ON SIERPINSKI-LIKE SPONGES AND THEIR SKELETON NETWORKS

Ying Lu (), Qingcheng Zeng (), Jiajun Xu () and Lifeng Xi
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Ying Lu: School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P. R. China
Qingcheng Zeng: School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P. R. China
Jiajun Xu: School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P. R. China
Lifeng Xi: School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 01, 1-8

Abstract: In this paper, we investigate the equivalence of connectedness for the Sierpinski-like sponge and skeleton networks, and find out the relation between the geodesic distance on the sponge and renormalized shortest path distance on the skeleton networks. Furthermore, under some assumption on the IFS, we obtain the comparability of the Manhattan distance and the geodesic distance on the sponge.

Keywords: Fractal; Fractal Network; Sierpinski-Like Sponge; Geodesic Distance; Manhattan Distance (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500063

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