% BIFDIAG Biffurcation diagram for logistic map.

%   Francisco J. Beron-Vera
%   $Revision: 1.0 $  $Date: 2006/09/05 11:52:25 $

clear

f=@(x,r) r*x.*(1-x);

x=linspace(0,1,250)';
r=linspace(0,4,500);

y=[];
for s=r
   z=x;
   for I=1:250
      z=f(z,s);
   end
   y=[y z];
end

plot(r,y,'k.','MarkerS',.1)
xlabel('$r$','Interpreter','LaTeX')
ylabel('$x = f(x)$','Interpreter','LaTeX')
title('$f(x) = r x (1-x)$','Interpreter','LaTeX')