Bernoulli bond percolation on a honeycomb lattice

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Bernoulli bond percolation on a honeycomb lattice

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Nils Berglund

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Bernoulli bond percolation on a honeycomb lattice, for different lattice sizes.

The parameter p increasing from 0 to 1 is the probability that a bond is open. Closed bonds are shown in dark purple, and open ones in yellow when they are connected to the left boundary, and pink otherwise. The increase of p slows down when it reaches the critical value, which is equal to 1 - 2*sin(Pi/18), or about 0.652703645. The graph shows the rsize of the percolation cluster (the set of open bonds connected to the left boundary), divided by the number of open bonds, as a function of p.

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