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.
