Seep
Porous ground, light at one edge. Each channel in the ground is open or shut by chance, and the light can only travel open channels: what you see is never the ground itself, only how far the connection reaches. As the ground slowly opens, the light presses deeper, and at exactly one half, no sooner, it can cross. Press anywhere to open the ground under your hand. Opening ground is not light; the light still has to find it.
Kesten, 1980. Below it the light always dies at a finite depth; above it, it crosses. Measured here: spanning curves at three sizes cross at 0.5007.
Conformal field theory predicts the exact chance of crossing a 2:1 rectangle at threshold. Twenty thousand lattices that never heard of conformal invariance agreed to three decimals.
The thing that crosses is not a flood but a fractal of dimension 91/48: mostly hole, connected anyway. Cluster sizes fall as a power law with exponent 187/91 (measured 2.03, target 2.05).
what this is
This is bond percolation on the square lattice, the simplest mathematical model of a porous medium, and the canonical model of a phase transition you can watch. Every channel between neighbouring sites is open with probability p, independently. The question the system asks is not how many channels are open but whether the open ones connect.
The answer is discontinuous in character. For p below one half, all connected regions are finite: the light entering from the left edge wets a fringe and stops, and waiting does not help: patience does not accumulate into crossing. At p equal to one half, exactly, an infinite connected cluster first appears. The threshold is not a measured constant but a theorem, proved by Harry Kesten in 1980 after two decades of physicists narrowing in on it numerically.
The page ramps p slowly through that threshold and back, then draws a new ground and breathes again. Brightness obeys one law: only what is connected to the left edge is lit. The settled interior cools to ember gray; the advancing front is the bright thing; when the connection first arrives at the far edge, the path it took flashes once and lets go. When the ground recedes below threshold the light does not dim. It retreats, because connection is not a quantity but a fact.
the gates
Five numbers were fixed in the project notes before any code existed, with tolerances and the direction an honest error would lean: the threshold at exactly one half; Cardy's conformal-field-theory crossing probability for a 2:1 rectangle, 0.175647; the spanning cluster's fractal dimension 91/48; the cluster-size exponent 187/91; and the correlation-length exponent 4/3. All five gates ran headless against the same engine this page renders from, and all five passed first try: the crossing point at 0.5007, Cardy's value hit to three decimals across twenty thousand lattices. The one honest wrinkle: the two exponents that missed their exact values inside tolerance both missed low, opposite to the direction the pre-registration declared. The declarations were wrong about my errors and the gates caught that too, which is what they are for.
The pointer opens ground; it does not paint light. If you open a path while the ground is nearly ready, you can be the one channel the crossing needed, and watch the flash take a route through your hand.