Percolation theory was originally developed to model fluid flow through a porous medium. Since then, it's found application to -- among many other contexts -- landscape ecology.

In site percolation, each square on a checkerboard is declared occupied or empty with a given, fixed probability. One studies the resulting (distribution of) cluster sizes.

In bond percolation, each edge on a piece of graph paper is declared occupied or empty. The resulting system is qualitatively similar to, but quantitatively different from, site percolation.

Here are some models you can play with. In each, clicking on a site will highlight all nodes connected to the focal one.