Two Random walker, self avoiding Help

Consider a 20 by 20 two-dimensional lattice with x and y coordinates varying from 1 to 20. My program needs to simulate two people moving on this lattice in a self-avoiding random walk with periodic boundary conditions. One person starts at position (5,15) and the other starts at (15,5). “Self-avoiding” means that once a node has been visited by one of the walkers, it can never be visited again by either walker.

Help in making this self avoiding and adding another walker??

 if true
    %Random walk in 2D, periodic boundaries
xmax = 20; %grid size
ymax = 20; %grid size
nsteps = 400; %number of steps in the simulation
x = round(xmax/2);
y = round(ymax/2);
plot(x,y,'bo')
ht = title('Steps taken = 0');
h = [];
axis([0.8 xmax+0.2 0.8 ymax+0.2])
hold on
for i = 1:nsteps
   d = randi(4); %direction (north(1), west(2), south(3), east(4))
   dx = 0;
   dy = 0;
   switch d
      case 1
         dy = 1;
      case 2
         dx = -1;
      case 3
         dy = -1;
      case 4
         dx = 1;
   end
   nx = x + dx;
   ny = y + dy;

   %Now apply periodic boundary conditions
   if nx<1
      x = x + xmax;
      nx = nx + xmax;
   elseif nx>xmax;
      x = x - xmax;
      nx = nx - xmax;
   end
   if ny<1
      y = y + ymax;
      ny = ny + ymax;
   elseif ny>ymax;
      y = y - ymax;
      ny = ny - ymax;
   end
   %Draw a line from the current position to the next position
   if ~isempty(h)
       set(h,'MarkerEdgeColor','b')
   end
   line([x nx],[y ny])
   h = plot(nx,ny,'r*');
   set(ht,'String',['Steps taken = ' num2str(i)])
   x = nx;
   y = ny;
   pause(0.1) %the pause that refreshes
end
hold off
  end

[Asatur Khurshudyan]

Have you been able to add the second walker?

Answer 1

[Guillaume]

Can't you just record all the visited points in a 20x20 logical matrix.

[Jessica Benidict]

how?

[Guillaume]

%... (initialisation)
visited = zeros(xmax, ymax); %turn to 1 when visited
for i = 1:nsteps
   cangothatway = [ ~visited(x, mod(y, ymax)+1)  %can go north?
                    ~visited(mod(x-2, xmax)+1, y) %can go west?
                    ~visited(x, mod(y-2, ymax)+1) %can go south?
                    ~visited(mod(x, xmax)+1, y)];  %can go east?
   availabledir = find(cangothatway);
   if isempty(availabledir)
      %reached a dead end!
      break;
   end
   dirindex = randi(numel(availabledir));
   d = availabledir(dirindex);
   %... (calculate next position, draw line, etc.)
   visited(x, y) = 1;
end

[Image Analyst]

Or, using logical data type.

visited = false(xmax, ymax); % Turn true when visited
...
visited(x, y) = true;