Examples of percolation processes include the penetration of liquids through a stationary porous phase, infiltration of the liquid phase along the grain boundaries of a polycrystal, the formation of polymer gels, as well as ferromagnetism and electric conductivity of impurity semiconductors.

Percolation occurs when the concentration of a filler or pores reaches a certain critical level (percolation threshold) following the build-up of a continuous network (connections) of filler particles (clusters) from one side of a material specimen to another.

Percolation is easy to demonstrate on the example of electric current passing through a two-dimensional square lattice consisting of conducting and non-conducting elements. Two opposite sides of the lattice have metal terminals soldered to them that are connected to a power source. At a certain critical concentration of conducting elements arranged randomly the circuit closes (see fig.).

Stanislav Smirnov from St. Petersburg was awarded the Fields Medal (a mathematics equivalent of the Nobel Prize) in 2010 “for the proof of conformal invariance of percolation and the planar Ising model in statistical physics”.