Geodesics of right isosceles Sierpiński gaskets and their relatives

Xiaohan Li, Xiangyu Liang and Yumei Xue

Chaos, Solitons & Fractals, 2025, vol. 192, issue C

Abstract: In this paper, we calculate the number of geodesics in the Sierpiński gasket with right isosceles triangle boundary using code representation and derive the geodesics of specific Sierpiński relatives. We find that the geodesics in the Sierpiński gasket with right isosceles triangle boundary are 1, 2, 3, 4 and 5, similar to those in the gasket with an equilateral triangle boundary, except for the instances where it can take these values. These results contribute to the characterization of the topologies of Sierpiński relatives.

Keywords: Fractal; Sierpiński gasket; Sierpiński relatives; Iterated function systems; Geodesics (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077924014899

DOI: 10.1016/j.chaos.2024.115937

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