Constrained percolation in two dimensions


The effect of implanting square lattice sites of zero occupation probability at the center of a finite but large square lattice for site percolation was investigated. The introduction of symmetrical forbidden site lattices of different sizes inside 40x40 and 60x60 lattices yield percolation threshold values increasing with the size of the forbidden lattice. It was shown that topology in two dimensions dictates the value of the percolation threshold.