Continuum Percolation of Anisotropically-Distributed Disks

Many problems of practical significance can be mapped onto a model of continuum percolation with circular disks, including overlapping images of fluorescent molecules in superresolution localization microscopy. In many such problems the positions of the disks are correlated or anisotopically distributed, e.g. in fluorescent labeling of the cytoskeleton. We have adapted the commonly-used Newman-Ziff algorithm to determine the percoclation thresholds of such systems, studying the percolation threshold as a function of the degree of anisotropy in the system, and comparing with percolation thresholds in systems of ellipses with uncorrelated positions but varying degrees of eccentricity.