balls in place when p=0.63
Physicists make models.
Lets try p=1.0 - is there percolation?
Lets try p=0 - is there percolation?
What is the smallest p that works for our square grid???
- Put the balls on a lattice grid
Put either a metal or a glass ball in each square of a grid
- Balls are ``connected'' to a ball above, below, right and left
- We want the sample to have top to bottom and right to left connections to conduct electricity - diagonal does not work in the standard model
- A ball would be metal with probability p between 0 and 1.0 and p_c
is the critical value above which the sample is conducting
- We find this on a computer by calculating a random number between 0 and 1.0 for each square.
We test if some p is the right one by checking which sites have metal balls by
if our random number is less than the trial p if it is
we put a metal ball there. If not a glass ball would go there.