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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 Downloads: 176588 Total View: 1991930
Frequency: quarterly ISSN Print: 2576-0645 CODEN: JAMCEZ
Email: jamc@hillpublisher.com
Article Open Access http://dx.doi.org/10.26855/jamc.2024.03.003

A Study of Sierpinski Fractals Based on Regular Polygons and Circles

Xuening Tang1, Dongxing Yu2,*, Jinhai Yan3

1University of Amsterdam, Amsterdam, the Netherlands.

2School of Education, Sanda University, Shanghai, China.

3Division of Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, China.

*Corresponding author:Dongxing Yu

Published: April 25,2024

Abstract

This paper studied the properties of Sierpinski fractals based on regular polygons and circles. Dilation is adopted as the basic principle to generate “perfect Sierpinski polygons” and “perfect Sierpinski circles”—defined as having neither overlap nor detachment among sub-shapes. The ideal contraction ratios for some regular polygons to become perfect Sierpinski polygons are calculated using trigonometry. A general formula is further derived by making a connection between perfect Sierpinski polygons and Sierpinski circles. A brief exploration is conducted of the Sierpinski circle model, from which some interesting properties are revealed, like the segregation of shapes. Based on these properties, a general formula to calculate the radius of the nth layer of sub-circles within one stage of iteration is derived. Lastly, the connection between the two Sierpinski models is discussed based on the limitations and implications of this study. Future researchers are recommended to dive deeper into the properties of Sierpinski travel and its relationship with other Sierpinski models.

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How to cite this paper

A Study of Sierpinski Fractals Based on Regular Polygons and Circles

How to cite this paper: Xuening Tang, Dongxing Yu, Jinhai Yan. (2024) A Study of Sierpinski Fractals Based on Regular Polygons and CirclesJournal of Applied Mathematics and Computation8(1), 16-27.

DOI: http://dx.doi.org/10.26855/jamc.2024.03.003