At what porosity does the water first reach the bottom? The blue front spreads one patch per tick through connected pores and stops where dark rock seals off every channel.
Try this Set porosity to 58 and press Reset (porosity is only read at setup). Run it several times; the water reaches the bottom in a little under half the runs. At 55 it almost never does, and at 62 it almost always does.
About this model Where it ends up
Site percolation, the problem Broadbent and Hammersley named in 1957: open a random fraction of the sites in a grid and ask whether they connect one side to the other. On this 121 × 89 grid, water entering from the top goes from rarely to almost always reaching the bottom between porosity 55 and 62, near the square-lattice threshold of 59.27%.
Setup makes each patch a pore with probability porosity/100 (read only at setup), leaves the rest as rock, and wets the pores in the top row. Each tick updates all patches from the previous state: a pore with a wet neighbor to its north, south, east or west becomes wet, so water also moves sideways and upward. The run stops the tick after the wet count stops changing. bottom-reached counts the wet patches in the bottom row; wet-fraction is the share of open pores that got wet.
This is the same process as the Fire model on the same grid, turned on its side. Fire has to cross the long side and water the short one, so water gets through at slightly lower densities (half the runs at about 58%, against about 60% for fire).
