Seepage

Percolation on a square grid. Open each cell with probability p and neighbouring open cells join into clusters. Below about 0.593 they stay small; just above it one cluster suddenly reaches from edge to edge.

Keyboard: with the grid focused, ← and → nudge p by 0.001 (hold Shift for 0.01), T jumps to this grid's threshold, N draws a new grid, B switches between site and bond percolation, C cycles the colouring and F lights the top row or puts the fire out.

Grid
Colour
This grid
Cluster sizes

How many finite clusters there are of each size, per site, on log–log axes. At the threshold the points fall on a straight line.

this grid slope −187/91

Burning

Sets fire to every open cell on the top row; each step it spreads one link further through the open grid.

Threshold sweep

Draws many grids of the current size and type, and records for each the exact p at which a cluster first joins top to bottom.

spanning probability largest cluster share thresholds

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