In an electric field, work must be done to move a charged particle from one point to another. |
If |
The potential is related to the strength of the electric field around
|
Like simple DLA, the dielectric breakdown model is constructed on a grid
of square cells |
Select a large circle, S, on the grid. |
Assign to the
potential f the value 1 at each cell on this circle, and the value 0 to the cell
|
The boundary conditions of the problem are that the potential keeps these values at these locations. |
Consistent with these conditions, the value of
the potential is determined at each cell of the grid (by a discrete version of Laplace's
equation - details are not necessary here) and then for each of the four cells
|
p(a,b) = f(c(a,b))t( |
One of these four points is selected at random, with probabilities given by
the |
Together with the point |
Compute the potential again with boundary conditions
|
Compute the growth probability for each of the 6 cells adjacent to the cluster and add another cell randomly, according to these probabilities. |
Continuing in this way grows a DBM cluster. |
Return to DLA.