Cabinet of emergence — specimen 07

Percolation

A grid where each cell is independently filled with probability p — no coordination between cells at all, every one flipped on its own. The question: at what p does a connected path first appear spanning from the top edge to the bottom? Site percolation on a square lattice has a known theoretical answer near p ≈ 0.593 — this specimen checks whether a real, finite grid actually finds that number, and whether the transition is as sharp as the theory predicts or blurred by the grid being finite.