@Carl Love thank you! 

@mehdi jafari thank you that's great.

@Kitonum actually is there a way to generalise this to a function so you just say  F(Matrix(3,3,[1,2,3,4,5,6,7,8,9]) returns the plotting as you described?  that would be extremely helpful.

@Kitonum thanks for this!   just out of curiosity, would you know if there is an inbuilt procedure on maple to plot the rows of a 3x3 matrix or would you have to do it the same way as this?

@Preben Alsholm @Carl Love

Is there anyway to prove this function F converges pointwise?  I've never done a proof of any sorts on Maple. 

N:=10 ; #global variable
F:=(x,y)->signum(abs(x-N/2)+abs(y-N/2)-N/4); 
Average := proc(F, f0::Matrix) local f, i, j;
  f := copy(f0);
  for i to N do 
    for j to N do
      if F(i, j) < 0 then
        f[i, j] := (f0[i - 1, j] + f0[i + 1, j] + f0[i, j + 1] + f0[i, j - 1])/4 ;
      end if
    end do
   end do;
   f
end proc;
f0:=Matrix(N,F); 
Average(F,f0); 
f0;  

@Carl Love yeah i see what you mean, it could be that we're just missing out on something simple to prove it.  This just has me confused.

@Carl Love what would it be with your specifications?

@Carl Love  thanks for the feedback.  I think you're right.  If you check out the link Im pretty sure its the same A as from that.  Sorry for the confusion.

@Carl Love thanks so much, im trying to play around with this now, could you give me just a basic example of it working?

thanks for the help so far but im still deeply confused, here is some more stuff that we did that was supposed to help but it didnt really :(

The procedure Q below does some preformating for the plot.

with(LinearAlgebra) :
Q:=proc(A,L,N) local i, V, RV;
V := Transpose(Matrix(L));
RV := [A, V];
for i to N do RV := [op(RV), A . (RV[-1])] end do;
return RV
end proc

we might also want to use map for instance to convert the matrices in the output of Q to
lists. This would be done by map(x->convert(x,list), Q(A,L,N)) ;

@YasH  neither can I sadly.  any ideas at all?