%
%  Code to perform simple iteration and show cobweb plot for a mapping
%
%   x_{n+1} = f(x_n)   n=0,1,2,...
%
clear
clf
                               
a=input(' Enter parameter a: '); % constant for logistic map
xstart=input(' Enter the left-hand plot limit: ');
xend=input(' Enter the right-hand plot limit: ');

x=xstart:0.001:xend;
plot(x,func(x,a),'r',x,x,'r')
axis([xstart xend xstart xend]) % scale picture
axis('square');                         % ensure plot is  square 
hold on

x(1)=input(' Enter x_0: ');
nmax=input(' Enter the number of iterations: ');

format long
fprintf('\n    n       iterate \n')     % Print table header

for n=1:nmax
  x(n+1)=func(x(n),a);
  fprintf('  %3.0f     %10.6f \n', n,x(n+1))               %Print iterate
  if (n>1) plot( [x(n) x(n)], [x(n) x(n+1)],'b'); end      %vertical line
  plot( [x(n) x(n+1)], [x(n+1) x(n+1)],'b--')              %horizontal line
  pause
end