Either the light forms a finite loop or it goes out to infinity. In the
former case, the light is called localized. For * p*=1, all light
beams are known to be localized with probability 1.
The aim is to show whether the light is localized with probability 1
for different values of *p*.
Here is a simulation of 10^7 times for *p=0.8* in which the light
has not yet returned. Will it come back eventually?

The blue (I hope you're looking at this in colour) represents the forward path of the light beam and the red the backwards. The green parts are where the forward and backward paths have entered the same cell (about 50x50 lattice sites).

For detailed information about this problem, read the paper .