% logistic map
%
 nn = 300;                        % number of iterations
%
 y(1) = .5;                      % initial conditions
%
 r = 3.73;                       % parameter value
% iterations
 for jj=1:nn
 y(jj+1) = r.*y(jj).*(1-y(jj));  % logistic map - no noise
% y(jj+1) = r.*y(jj).*(1-y(jj)) +.01.*randn(1);  % logistic map - small noise
%
 v(2.*jj-1) = y(jj);             % save values for plotting below
 u(2.*jj-1) = y(jj+1);
 v(2.*jj) = y(jj+1);
 u(2.*jj) = y(jj+1);
 end;
%
%                Plotting
x = 0:.01:1;
y = r.*x.*(1-x);                % curve which describes the map
%
 plot(x,x)                       % plot diagonal y_n+1 - y_n
 hold on
 plot(x,y)                       % plot  nonlinear function ry(1-y)
 plot(v,u,'r')                   % plot data points from the iteration
 hold off