{"title":"The boundary of Rauzy fractal and discrete tilings","authors":"Hyosang Kang , Woojin Choi , Jeonghoon Rhee , Youchan Oh","doi":"10.1016/j.csfx.2025.100126","DOIUrl":null,"url":null,"abstract":"<div><div>We present two methods of constructing the Rauzy fractal by partitioning all points within it into disjoint sets, refer to as layers. We show how these layered structures of the Rauzy fractal can plot the boundary of the fractal effectively. By generalizing the self-replicating pattern of this structure, we demonstrate a new way of discrete tilings of two-dimensional plane.</div></div>","PeriodicalId":37147,"journal":{"name":"Chaos, Solitons and Fractals: X","volume":"14 ","pages":"Article 100126"},"PeriodicalIF":0.0000,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos, Solitons and Fractals: X","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2590054425000016","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/2/1 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
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Abstract
We present two methods of constructing the Rauzy fractal by partitioning all points within it into disjoint sets, refer to as layers. We show how these layered structures of the Rauzy fractal can plot the boundary of the fractal effectively. By generalizing the self-replicating pattern of this structure, we demonstrate a new way of discrete tilings of two-dimensional plane.
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