SOME TOPOLOGICAL PROPERTIES AND APPLICATIONS OF EQUILATERAL SIERPIŃSKI RELATIVES

Xiaohan Li (), Xiangyu Liang (), Cheng Zeng and Yumei Xue ()
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Xiaohan Li: School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China
Xiangyu Liang: School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China
Cheng Zeng: ��School of Mathematics and Information Science, Shandong Technology and Business University, Yantai, Shandong Province 264003, P. R. China
Yumei Xue: School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 06, 1-12

Abstract: In this paper, we extend the results for connectivity and convex hulls of Sierpiński relatives whose convex hulls have right isosceles triangle boundaries to the relatives corresponding to equilateral triangle version. Furthermore, we use a particular subclass of the relatives called trapezoid-shaped relatives to build new hexagonal fractals, which helps to visualize and distinguish the subgroups of symmetries of the hexagon. These results contribute to identify the topologies of Sierpiński relatives.

Keywords: Sierpiński Gasket; Sierpiński Relatives; Iterated Function Systems; Connectivity; Convex Hulls; Dihedral Groups (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24501226

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