A percolation algorithm based on cellular automata

Abstract

In many applications of percolation theory, checking the establishment of the spanning clump/cluster of overlapping particles that spans all over the field is an essential task. Given a percolation theory field modeled by two-dimensional lattice (matrix), in this paper, we present an algorithm which determines if there is a spanning clump in lattice or not. The spanning clump is the largest cluster in the field which that spans the entire network vertically, horizontally or both. Due to wide range of properties and applications of cellular automata such as simplicity and distributedness, we use them in our algorithm. The proposed algorithm is simple but yet useful and also could be run in a parallel / multicore machines. Also, the approach of the algorithm could be extended to higher dimensions.