Oceanic coastline and super-universality of percolation clusters

Original · EN

New fractal subset of a rough surface, the ``oceanic coastline'', is defined. For random Gaussian surfaces with negative Hurst exponent H<0, ``oceanic coastlines'' are mapped to the percolation clusters of the (correlated) percolation problem. In the case of rough self-affine surfaces (H ≥ 0), the fractal dimension of the ``oceanic coastline'' dc 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 dc ≈ 1.896 coincides with the analytic value for the percolation problem (91/48), suggesting a super-universality of dc for correlated percolation problem.