Statistical physics
Percolation
Bond percolation on a pixel lattice. Each edge has a fixed random sample; it opens when that value is ≤ p. Scroll to zoom into sites as squares.
Scroll to zoom · drag to pan · double-click or 0 to reset · R resample · arrows nudge p
What you’re seeing
This is bond percolation. Every pixel is a site; connectivity is through edges, each with a fixed Uniform[0,1] sample. An edge is open when its sample is ≤ p. Sliding p only re-thresholds — no new randomness until you resample.
Clusters are painted in random RGB. When p rises and clusters merge, the larger piece keeps its color. When p falls and a cluster splits, the larger fragment keeps the color (undo restores the absorbed color).
Frames for every p step bake quietly in the background so playback stays smooth. The lattice is one site per canvas pixel. On the infinite square lattice, pc = 1/2 exactly for bonds.