%0 Journal Article
%T Intersections of moving fractal sets
%A Indrek Mandre
%A Jaan Kalda
%J Physics
%D 2013
%I arXiv
%R 10.1209/0295-5075/103/10012
%X Intersection of a random fractal or self-affine set with a linear manifold or another fractal set is studied, assuming that one of the sets is in a translational motion with respect to the other. It is shown that the mass of such an intersection is a self-affine function of the relative position of the two sets. The corresponding Hurst exponent h is a function of the scaling exponents of the intersecting sets. A generic expression for h is provided, and its proof is offered for two cases --- intersection of a self-affine curve with a line, and of two fractal sets. The analytical results are tested using Monte-Carlo simulations.
%U http://arxiv.org/abs/1307.4242v1