  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 ($H \ge 0$), the
fractal dimension of the ``oceanic coastline'' $d_c$ 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.
