%   1  2  3  4  5
%   6  7  8  9 10
%  11 12 13 14 15
%  16 17 18 19 20
%  21 22 23 24 25
% Setup of the matrix:
corner = ...
[.6 .2 0 0 0;
.2 .4 .2 0 0;
0 .2 .4 .2 0;
0 0 .2 .4 .2;
0 0 0 .2 .6];
side = diag([.2 .2 .2 .2 .2]);
mid = ...
[.4 .2 0 0 0;
.2 .2 .2 0 0;
0 .2 .2 .2 0;
0 0 .2 .2 .2;
0 0 0 .2 .4];
z = zeros(5);
A = [
corner,side,z,z,z;
side,mid,side,z,z;
z,side,mid,side,z;
z,z,side,mid,side;
z,z,z,side,corner];

%setup start distribution:
startpos = [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]';


result = NaN(5);
result(:) = A^15 * startpos;
bar3(result)
axis([-.5,5.5,-.5,5.5,0.038,0.042]);
result(13)