%
% Cobwebbing for Xm+1 = f(Xn)
%
%       X[m+1] = rX[m](1-X[m])
%
% Since X[m+1] is the population probability, it should be 
%             0<= X <=1,
% which means
%             0<= r <=4.
%
% Jae-Hun Jung

r = input('0<= r <=4, r = ? ');

x = linspace(0, 1);
fx = r*(1-x).*x;
plot(x,fx), pause

hold on
plot(x,x,'-m'),
pause

x0 = input('0<= x0 <=1, initial population = ? '); 
for i = 1:100
    x1 = r*(1-x0)*x0;
    z = [x0 x0]; w = [x0 x1];
    plot(z,w,'Or-'), pause
    z = [x0 x1]; w = [x1 x1];
    plot(z,w,'Oc-'),pause
    x0 = x1;
end