Bernoulli site percolation on a Poisson disc process
Bernoulli site percolation on a Poisson disc process, for different lattice sizes.
A Poisson disc process is first generated, and discs whose distance is smaller than a given threshold are connected. The parameter p increasing from 0 to 1 is the probability that a disc is open. Closed discs are shown in dark blue, and open ones in yellow when they are connected to the left boundary, and cyan otherwise. The increase of p slows down when it reaches 1/2. The graph shows the rsize of the percolation cluster (the set of open discs connected to the left boundary), divided by the number of open discs, as a function of p. The model has some similarity with more studied continuum percolation models, such as the disc model and the Boolean model.