Cluster size distribution in Bernoulli site percolation on a lattice of triangles

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Cluster size distribution in Bernoulli site percolation on a lattice of triangles

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Bernoulli site percolation on a lattice of equilateral triangles (whose centers form a hexagonal lattice), for different lattice sizes. Open clusters are colored according to their size.

The parameter p increasing from 0 to 1 is the probability that a triangle is open. Closed triangles are shown in dark blue, and open ones in colors ranging from light blue to yellow. The increase of p slows down when it reaches the critical value, which is approximately equal to 0.69704. The histogram shows the distribution of cluster sizes.

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