% scaledwalks.m shows rescaled walks with varying numbers of steps

clf;                          % clear the figure

M = [50 1000 100 5000 200 25000]; % number of steps to take in the six windows

N = max(M);                     % the largest number of steps  
t = (0:1:N)';                   % t is the column vector [0 1 2 3 ... N]
S = [0; cumsum(2*(rand(N,1)>0.5)-1)];
                                % S is the running sum of +/-1 variables

for i=1:6,
  subplot(3,2,i)

  N = M(i);
  t = (0:N)';

  plot(t/N,S(1:N+1)/sqrt(N));            % plot the path
  axis([0 1 -2 2]);
  title(['First ' int2str(N) ' steps'])
end