Look at Figure 2. It is a table of 25x25 lattices of different values of p. As the probability increases, right around p = 0.6 an interesting phenomenon occurs. For the first time, it becomes possible to trace a path from one side of the grid to another while staying in one cluster. That is, a cluster exists that extends top to bottom, left to right. This is referred to as an infinite cluster. This is actually from where the term percolation theory comes. The cluster has percolated through the medium in much the same way that water percolates through a porous medium like coffee grounds in your coffee pot.

Much of percolation theory is dedicated to studying phenomena near the critical value of p, which is labeled pc (c for critical.) These phenomena are collectively called critical phenomena and the theory use to describe them is called scaling theory.

Figure 2