function koch ( A, B, k )
%
%  plots a Koch curve between A and B, 
%  using k levels of recursion
%
if k == 0
  plot([A(1) B(1)],[A(2) B(2)],'-');
  hold on;
else
  L = (2*A + B)/3;                % left point
  R = (A + 2*B)/3;                % right point
  M = [0 1; -1 0];                % rotation matrix
  s = sqrt(3)/6;                  % scaling factor
  T = (A+B)/2 + s*(M*(A-B)')';    % top point
  koch(A,L,k-1);                  % left branch
  koch(L,T,k-1);                  % left mid branch
  koch(T,R,k-1);                  % right mid branch
  koch(R,B,k-1);                  % right branch
end;