  In this paper, we compute the next-nearest-neighboring site percolation
(Connections exist not only between nearest-neighboring sites, but also between
next-nearest-neighboring sites.) probabilities Pc on the two-dimensional
Sierpinski carpets, using the translational-dilation method and Monte Carlo
technique. We obtain a relation among Pc, fractal dimensionality D and
connectivity Q. For the family of carpets with central cutouts,, where, the
critical percolation probability for the next-nearest-neighboring site problem
on square lattice. As D reaches 2, which is in agreement with the critical
percolation probability on 2-d square lattices with next-nearest-neighboring
interactions.
