Bootstrap Percolation

Computational Physics 2007

 

 What is a Bootstrap Percolation ?

In Bootstrap Percolation (BP) we take an empty lattice and fill it with two values 1 or 0, (occupied or empty, respectively). The occupation of a single cell is determined  by an initial probability (p). After we initialize the lattice we start to erase it according to a certain rule. Here I used this rule:

If more than half the neighboring cells are occupied (in a square lattice 3 or 4 neighbors) a cell will remain full, otherwise the cell will be emptied. The lattice is periodic so the outer cell have the same numbers of neighbors as the other cells. This is known as m=3 BP.

This  process repeats itself until there is no further change in the configuration of the lattice due to the annihilation of the entire configuration (all the cells are empty), or due to a stable configuration. For m=3 BP, if there are occupied sites in the lattice the sample would be conducting or percolating.

Movie sample of Bootstrap Percolation on a 150X150 lattice with initial probability 0.945.

Movie sample of Bootstrap Percolation on a 100X100 lattice with initial probability 0.946.

Movie sample of Bootstrap Percolation on a 500X500 lattice with initial probability 0.96.

Sample of a Bootstrap Percolation on a 10x10 Square Lattice

( Number of Neighbors, m=3: Probability of occupation, p=0.8 )

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