Cluster growth for Bernoulli site percolation on a cubic lattice
The connected component of one face for Bernoulli site percolation on a cubic lattice, for increasing parameter p and different lattice sizes.
All cubes of the lattice are independently open with probability p, and closed with probability 1-p, except the cubes of one face, which are all open. The animation shows only the connected component of open lattice cubes containg the face of open cubes. The colour of the cubes depends on their distance to the open face. The graph shows the ratio between the number or cubes in the connected component, and the number of open cubes.