The structure of site percolation models on three-dimensional square lattices

Abstract: In this paper we consider the structure of site percolation models on three-dimensional square lattices with various shapes of (1,d)-neighborhood. For these models, are proposed iso- and anisotropic modifications of the invasion percolation algorithm with (1,0)- and (1,d)-neighborhoods. All the above algorithms are special cases of the anisotropic invasion percolation algorithm on the n-dimensional lattice with a (1,d)-neighborhood. This algorithm is the basis for the package SPSL, released under GNU GPL-3 using the free programming language R.