Percolation

To produce an example of such a percolation, start with a square lattice of side length L and some number p, 0 <= p <= 1.

Generate a random number in [0,1] for each cell of the lattice, and say a cell is empty if the random number is less than p.

Here we see patterns generated in this way for p = 0.1, p = 0.2, ..., p = 0.9.

The empty cells are black, the filled cells white.

Imagining the dark cells are empty and the light are filled with a solid, it is easy to see that a fluid injected anywhere along the left side of p = 0.4 cannot flow to the right side.

For p = 0.7 there are channels through which fluid can flow from left to right.

Return to percolation.