Percolation Cluster

Site percolation on a square lattice: each site is occupied independently with probability p, and a spanning cluster connects the left and right boundaries. The infinite square-lattice threshold is p_c≈0.5927; one finite grid can span below it or fail above it. The sweep repeats seeded finite grids at each p and shows a nominal 95% Wilson interval around the observed spanning fraction. It is not a threshold estimate or a simultaneous confidence band.