Cluster size distribution in Bernoulli site percolation on a Poisson disc process
Bernoulli site percolation on a Poisson disc process, for different lattice sizes. Open clusters are colored according to their size.
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 various shades of light blue, white and red The increase of p slows down when it reaches 1/2. The histogram shows the distribution of cluster sizes. The model has some similarity with more studied continuum percolation models, such as the disc model and the Boolean model.