% Random walk in 2 dimensions in a city with n*n blocks
% Goal: find average number of steps to get out the city
%       if the initial position is random
itests = 1000;       % number of tests
rng('shuffle');      % seed random number generator
ncity=0;
fprintf('   Random Walk 2 \n')
fprintf('    L     Steps \n')
fileID = fopen('random2.txt','w');      %writing to a file
tic

while ncity < 100
   ncity = ncity+2;
   stotal = 0;
   for it=1:itests 
    x = randi([0 ncity],1,1);  %initial random position along x
    y = randi([0 ncity],1,1);  %initial random position along y
    nsteps = 0;
    out = 0;
    while (out == 0)
        nsteps = nsteps+1;
        iway = randi([0 3],1,1);
        switch iway
            case 0
            x = x + 1;
            case 1
            x = x - 1;
            case 2
            y = y + 1;
            case 3
            y = y - 1;
        end  %switch
        if x < 0 || x > ncity || y < 0 || y > ncity % if out of city
            out=1;
        end
    end %while
    stotal = stotal + nsteps;
end %for
%  average number of steps
asteps = double(stotal)/double(itests);
fprintf('%5i     %5.2f\n', ncity, asteps)  
fprintf(fileID,'%5i     %5.2f\n', ncity, asteps);
end %while

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