Percolation

Each bond of the lattice is open with chance p, on its own; every p uses the same random numbers, so as you drag p up, bonds only ever open and clusters only ever merge. The largest cluster is gold. Below one half the open bonds form scattered islands; near one half the largest cluster grows abruptly over a narrow range of p and reaches from the top edge to the bottom, and the corner says it spans. Turn the water on and it seeps down from the top row along open bonds: below one half it soon stops; past one half it gets all the way down, and the corner records how many steps that took. Switch to the close-up and, near the threshold, the clusters are full of holes of every size.