Percolation on a Triangular Lattice Under Anisotropic Conditions

The properties of percolation of objects of various shapes on a two-dimensional triangular lattice is studied by means of Monte Carlo simulations. Depositing objects of various shapes and sizes are made by directed self-avoiding walks on the lattice. Anisotropy is introduced by positing unequal probabilities for orientation of depositing objects along different directions of the lattice. This probability is equal p or (1−p)/2, depending on whether the randomly chosen orientation is horizontal or not, respectively. It is found that the percolation threshold θp increases with the degree of anisotropy, having the maximum values for fully oriented objects.