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

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