  The anisotropy parameter of two-dimensional equilibrium clusters of site
percolation process in long-range self-affine correlated structures are studied
numerically. We use a fractional Brownian Motion(FBM) statistic to produce both
persistent and anti-persistent long-range correlations in 2-D models. It is
seen that self affinity makes the shape of percolation clusters slightly more
isotropic. Moreover, we find that the sign of correction to scaling term is
determined by the nature of correlation. For persistent correlation the
correction to scaling term adds a negative contribution to the anisotropy of
percolation clusters, while for the anti-persistent case it is positive.
