Geodesics of Higher-Dimensional Sierpinski Gasket

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY（2019）

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摘要

It is of great interest to analyze geodesics in fractals. We investigate the structure of geodesics in n-dimensional Sierpinski gasket F-n for n >= 3, and prove that there are at most eight geodesics between any pair of points in F-n. Moreover, we obtain that there exists a unique geodesic for almost every pair of points in F-n.

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关键词

Fractal,Geodesic Distance,Sierpinski Gasket,Self-Similar Measure

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