The visible part of plane self-similar sets
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Given a compact subset F of R2, the visible part VθF of F from direction θ is the set of x in F such that the half-line from x in direction θ intersects F only at x. It is suggested that if dimH F ≥ 1 then dimH VθF = 1 for almost all θ , where dimH denotes Hausdorff dimension. We conrm this when F is a self-similar set satisfying the convex open set condition and such that the orthogonal projection of F onto every line is an interval. In particular the underlying similarities may involve arbitrary rotations and F need not be connected.
Falconer , K J & Fraser , J M 2013 , ' The visible part of plane self-similar sets ' , Proceedings of the American Mathematical Society , vol. 141 , no. 1 , pp. 269-278 . https://doi.org/10.1090/S0002-9939-2012-11312-7
Proceedings of the American Mathematical Society
© Copyright 2012 American Mathematical Society. First published in Proceedings of the American Mathematical Society 2012, published by the American Mathematical Society)