Oceanic coastline and super-universality of percolation clusters

Abstract

New fractal subset of a rough surface, the ``oceanic coastline&#39;&#39;, is defined. For random Gaussian surfaces with negative Hurst exponent $H<0$, ``oceanic coastlines&#39;&#39; are mapped to the percolation clusters of the (correlated) percolation problem. In the case of rough self-affine surfaces ($H \ge 0$), the fractal dimension of the ``oceanic coastline&#39;&#39; $d_c$ is calculated numerically as a function of the roughness exponent $H$ (using a novel technique of minimizing finite-size effects). For H=0, the result $d_c \approx 1.896$ coincides with the analytic value for the percolation problem (91/48), suggesting a super-universality of $d_c$ for correlated percolation problem.