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Geodesics of right isosceles Sierpiński gaskets and their relatives

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  • Li, Xiaohan
  • Liang, Xiangyu
  • Xue, Yumei

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.

Suggested Citation

  • Li, Xiaohan & Liang, Xiangyu & Xue, Yumei, 2025. "Geodesics of right isosceles Sierpiński gaskets and their relatives," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077924014899
    DOI: 10.1016/j.chaos.2024.115937
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    References listed on IDEAS

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    1. Paul W K Rothemund & Nick Papadakis & Erik Winfree, 2004. "Algorithmic Self-Assembly of DNA Sierpinski Triangles," PLOS Biology, Public Library of Science, vol. 2(12), pages 1-1, December.
    2. Aslan, Nisa & Saltan, Mustafa & Demir, Bünyamin, 2019. "The intrinsic metric formula and a chaotic dynamical system on the code set of the Sierpinski tetrahedron," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 422-428.
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