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Geodesic Distances On Sierpinski-Like Sponges And Their Skeleton Networks

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ying Lu & Qingcheng Zeng & Jiajun Xu & Lifeng Xi, 2024. "Geodesic Distances On Sierpinski-Like Sponges And Their Skeleton Networks," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(01), pages 1-8.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:01:n:s0218348x24500063
    DOI: 10.1142/S0218348X24500063
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