Entropy calculation atoms simulation

[ChrisVer]

I have the following program that simulates a stochastic system of 400 particles. What I want to do now is separate the 200x200 grid into 2x2 smaller grids, out of which I will calculate each probability:
P_i= \frac{\sum_{\text{atoms}}}{4}
and from which in each step I'll be able to determine the entropy...
However I don't see how I can make the division to sub-grids... any help?
In the second part of code quote I show what I've tried to implement..but I don't think it works.

import sys
from pylab import *
from random import randintion() #allow animation
figure(figsize=(10,10)) #setup graph window

#Setup the problem
atoms = ones([400,2])*100                  #define all droplet coords to be at point 100,100
line, = plot(atoms[:,0], atoms[:,1], 'ro')
xlim(0,200)
ylim(0,200)
draw()
wait= raw_input("Press return to continue")

#time steps to take input
N= int(sys.argv[1])
#loop over steps
for i in range(N):

    #Go through all atoms
    for j in range(400):

         #move each atom
         atoms[j,0] += randint(-1,1)
         atoms[j,1] += randint(-1,1)
        #check boundary
         x,y = (atoms[j,0], atoms[j,1])
         if x==200: atoms[j,0] = 198
        elif x==0: atoms[j,0] = 2
         if y ==200: atoms[j,1] = 198
        elif y==0: atoms[j,1] =2

    #see how things look now
    line.set_xdata(atoms[:,0])
    line.set_ydata(atoms[:,1])
    draw()

wait= raw_input("Press Return to exit")

xs= atoms[:,0]
ys= atoms[:,1]
P=zeros([100,100])
for i in range(0,200,2):
    for j in range(0,200,2):
            P[i/2,j/2] = xs[i]+xs[i+1] +ys[j] + ys[j+1]
P=P/4.
Entropy=0.0
for i in range(100):
    for j in range(100):
        if P[i,j]!=0: Entropy+= P[i,j]*log(P[i,j])
        else: Entropy+=0.0

 

[Mark44]

What I would do is start with a smaller matrix, say 4 x 4, and see what needs to be done to split it up into four 2 x 2 matrices. The upper left submatrix with consist of P[0, 0], P[0, 1], P[1, 0], and P[1, 1]. See if you can figure out what the entries would be for the upper right. lower left, and lower right submatrices. You might be able to extend the idea to splitting your 200 x 200 matrix into 10,000 2x2 submatrices.