whatA lattice of possible bonds, each holding one fixed random number drawn once. The slider is p: a bond is open exactly when its number is below p -- sliding right only ever adds bonds, so this one seeded lattice tells one coherent story. The cluster touching both top and bottom, if any, is drawn bold.

whyThe claim: the span arrives all at once. Below threshold there are only islands -- they grow, kiss, merge, and still nothing crosses; then at one exact value (this lattice knows its own, found by bisection, always within a hair of the infinite lattice's p_c = 1/2) a single cluster suddenly spans the world. And at that moment it is a fractal -- box-counting dimension near 91/48 = 1.9, measured live -- a filigree that touches everything and fills almost nothing; past threshold it fattens toward 2. Oil fields, coffee grounds, forests before a spark: the same sudden geometry.

howBond percolation on a square lattice with union-find recomputed per slider move (milliseconds); the per-seed threshold is exact bisection over the monotone family; fractal dimension by box-counting on the bold cluster. Left alone, p ramps and pauses at the snap. One integer seeds every bond.