2D site percolation

What you are seeing: a square lattice where each site is independently "occupied" with probability $p$. As $p$ rises past a critical value, a single giant connected cluster appears that spans the lattice from top to bottom (the percolating cluster). Below the critical $p$, only small isolated islands.

Critical probability $p_c = 0.59274621\ldots$. Drag the slider through $p_c$ and watch the landscape change from "small puddles" to "one continent". The largest-cluster fraction is shown live; if a spanning cluster exists its sites are highlighted in yellow.