Abstract
A new fractal subset of random surfaces, the "oceanic coastline", is defined. For 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 via Monte Carlo simulations as a function of the exponent H. 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 the correlated percolation problem.