Visual physics and mathematics/Percolation

To model percolation (how a fluid passes through a porous material for example), we can randomly distribute bonds on a square network. p is the proportion of bonds among all possible links. As long as p < 1/2, the bonds do not percolate. A fluid passing through them cannot go very far. The material is not porous. But as soon as p is greater than 1/2, paths as long as desired appear:



When p = 1/2, we obtain a fractal structure. It is a structure which retains its structure when we change scale: