Cluster size distribution in Bernoulli site percolation on a cubic lattice

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Cluster size distribution in Bernoulli site percolation on a cubic lattice

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Nils Berglund

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Clusters and cluster size distribution in 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. The animation shows only open lattice cubes, where cubes in the same cluster have the same color. The histogramm shows the distribution of cluster sizes. The critical value of p is close to 0.311604.

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