function web
% web.m
% By Jeremie Korta
% December 1, 2003
% Requires web_starter file to work (unless r is put in by hand). 

global n

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% some interesting values of the parameter r

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%n = 2; r = 1; % superstable 2-cycle
%n = 3; r = fzero(@web_starter,[1,2]); % superstable 3-cycle
%n = 4; r = fzero(@web_starter,[1.1,1.4]); % superstable 4-cycle #1
n = 4; r = fzero(@web_starter,[1.9,2.0]); % superstable 4-cycle #2
%n = 5; r = fzero(@web_starter,[1.6,1.7]); % superstable 5-cycle #1
%n = 5; r = fzero(@web_starter,[1.8,1.9]); % superstable 5-cycle #2
%n = 5; r = fzero(@web_starter,[1.9,2.0]); % superstable 5-cycle #3
%n = 7; r = fzero(@web_starter,[1.5,1.6]); % superstable 7-cycle #1
%n = 7; r = fzero(@web_starter,[1.6,1.7]); % superstable 7-cycle #2
%n = 7; r = fzero(@web_starter,[1.8,1.85]); % superstable 7-cycle #3
%n = 7; r = fzero(@web_starter,[1.85,1.9]); % superstable 7-cycle #4
%n = 7; r = fzero(@web_starter,[1.9,1.95]); % superstable 7-cycle #5
%n = 7; r = fzero(@web_starter,[1.95,1.96]); % superstable 7-cycle #6
%n = 7; r = fzero(@web_starter,[1.97,1.98]); % superstable 7-cycle #7

x = [0 0];
v = [x];

figure(1)
clf

for i=1:10
    this_x = v(size(v,1),1);
    next = r-this_x^2;
    v = [v',[this_x next]',[next next]']';
end

x = linspace(-max(1,r),max(1,r),100);
plot(x,r-x.^2,'r',x,x,'r')
hold on
plot(v(:,1),v(:,2));
grid on;
axis tight
s=['Web plot of logistic map with r = ',num2str(r),' and x_0 = ', ...
            num2str(v(1,1))];
title(s)
uicontrol('Style','pushbutton','Units','normalized',...
'Position',[.75  .01  .15  .05],'String','CLOSE',...
'BackGroundColor',[.0 .0 .9],'ForeGroundColor','w',...
'Fontsize',12,'Callback','uiresume;');
uiwait;
close;





% web_starter.m
% n handles the iteration number.  n = 3 implies 3 nested functions.
% minimizing the function (done in web.m) will give the r for superstable
% n-cycle.

function x = logistic_nest(r)

global n
x = 0;
for k=1:n
    x = -x.^2+r;
end