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

TL;DR

This paper explores the structure of site percolation models on 3D lattices with various neighborhoods, proposing modifications of invasion percolation algorithms and providing an R package for their implementation.

Contribution

It introduces iso- and anisotropic invasion percolation algorithms for 3D lattices with different neighborhoods, and develops an R package for their application.

Findings

Algorithms for anisotropic invasion percolation are proposed.

The algorithms encompass various neighborhood shapes.

An R package SPSL implements these algorithms.

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.