Percolation clusters

Abstract

A brief description is given of the basic concepts which arise in percolation theory. The nature of the percolation transition is illustrated by ‘snapshot’ frames from a film of a Monte Carlo simulation of a percolation process with the percolation probability varying from 0 to 1·21 p _c (where p _c is the critical probability). The largest cluster is identified in each frame, and when p is near to p _c this cluster approaches the boundaries. Finally, a short description is given of some more sophisticated percolation problems.