Intersections of moving fractal sets
Institute of Cybernetics at the Tallinn University of Technology - Akadeemia tee 21, 12618, Tallinn, Estonia, EU
Received: 15 May 2013
Accepted: 2 July 2013
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.
PACS: 05.45.Df – Fractals / 05.40.Jc – Brownian motion / 05.45.Tp – Time series analysis
© EPLA, 2013