西尔平斯基网络的最短路径距离和哈斯道夫维度

Fractals Pub Date : 2024-03-26 DOI:10.1142/s0218348x24500567

JIAQI FAN, JIAJUN XU, LIFENG XI

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摘要

本文将研究西尔平斯基网络的几何结构，西尔平斯基网络是连通自相似西尔平斯基地毯的骨架网络。在一些合适的条件下，我们发现重归一化最短路径距离与平面曼哈顿距离相当，并得到了 Sierpinski 网络的豪斯多夫维。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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SHORTEST PATH DISTANCE AND HAUSDORFF DIMENSION OF SIERPINSKI NETWORKS

In this paper, we will study the geometric structure on the Sierpinski networks which are skeleton networks of a connected self-similar Sierpinski carpet. Under some suitable condition, we figure out that the renormalized shortest path distance is comparable to the planar Manhattan distance, and obtain the Hausdorff dimension of Sierpinski networks.

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Fractals

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