  We consider the effects of spatial correlations in a two-dimensional site
percolation model. By generalizing the Newman-Ziff Monte Carlo algorithm to
include spatial correlations, percolation thresholds and fractal dimensions of
percolation clusters are obtained. For a wide range of spatial correlations,
the percolation threshold differs little from the uncorrelated result. In
contrast, the fractal dimension differs sharply from the uncorrelated result
for almost all types of correlation studied. We interpret these results in the
framework of long-range correlated percolation.
