function M = mash(N)
% Function to simulate random walk of Prof. Mash
% Input:
%    N = number of steps
% Output:
%    M = N x 2 matrix holding the location of Mash at each step along his
%    walk

% Initialize M
M = zeros(N,1);
% First column of M = x coordinate and is always 1, 2, 3, ... , N
M(:,1) = (1:N)';
% Start out with y position = 0
ypos = 0;

% Loop over each step
for idx = 1:N
  % Generate a random number between 0 and 1
  r  = rand(1);
  % If r < 1/3, move one m in -y direction.  If r is between 1/3 and 2/3
  % then movement in y direction. Else, move one step in +y direction
  if (r <= 1/3)
    ypos = ypos - 1;
  elseif (r > 2/3)
    ypos = ypos + 1;
  end
  M(idx,2) = ypos;
    
end