Rectifiable curves in Sierpinski carpets
Estibalitz Durand-CartagenaJeremy Tyson
28A8030L9911B57fractalrectifiable curveFarey fraction
We characterize the slopes of nontrivial line segments contained in self-similar and non-self-similar Sierpi\'nski carpets. The set of slopes is related to Farey sequences and the dynamics of punctured square toral billiards. Our results provide a first step towards a description of the rectifiable curves contained in such carpets.
Indiana University Mathematics Journal
2011
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10.1512/iumj.2011.60.4382
10.1512/iumj.2011.60.4382
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Indiana Univ. Math. J. 60 (2011) 285 - 310
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