%0 Journal Article
%T The visible part of plane self-similar sets
%A Kenneth J. Falconer
%A Jonathan M. Fraser
%J Mathematics
%D 2010
%I arXiv
%X Given a compact subset $F$ of $\mathbb{R}^2$, the visible part $V_\theta F$ of $F$ from direction $\theta$ is the set of $x$ in $F$ such that the half-line from $x$ in direction $\theta$ intersects $F$ only at $x$. It is suggested that if $\dim_H F \geq 1$ then $\dim_H V_\theta F = 1$ for almost all $\theta$, where $\dim_H$ denotes Hausdorff dimension. We confirm 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.
%U http://arxiv.org/abs/1004.5067v1