Difference percolation on a square lattice

Simulations of percolation processes on random site square lattices are performed implementing a different occupation algorithm for both ordinary percolation (OP) and invasion percolation (IP) problems. The main feature of the occupation process is the fact that it is performed in a locally restricted way by inspecting the difference between the measure assigned to neighboring sites. This restriction carries an intrinsic change in the distribution of invaded sites with a different percolation threshold and the same universality class. Conclusions are drawn concerning physical problems of propagation phenomena with local barriers where these simulations prove the possibility of controlling the wide spread of the invasor.