function feigenbaum(stt,fin,stps,myfl);
%(r parameter,start x,how many transients to ignore,no of iterations, list values=1 no=0)
%myfl=1 also plots Lyapunov exponent
% examples r=3+65/90+.018 gives period 5 r=3+65/90+.02 period 10 inside the period 5 window 
%3.6055 period 10 in the period 10 window.
%example feigenbaum(3,4,1000,0)

clf; %clear the current figure
iters=300;
lambda=zeros(stps);
xi=zeros(1,iters*stps); %make xi, yi vectors 1 by iters*steps
yi=xi;
wb = waitbar(0,'Please wait...'); %make a wait bar so we cna see how long it will run
stp=0;
for r=stt:(fin-stt)/stps:fin % step through all the r values
    x=.1;
    curpos=floor(stp*iters); % set a position in xi and yi for the current iterations
    stp=stp+1;
    for i=1:iters
        x=myfn(r,x); %iterate away the transients
        if myfl
            lambda(stp)=lambda(stp)+log(abs(myder(r,x)));
        end
     end
    for i=1:iters
        x=myfn(r,x); % now iterate a set of x and y values ready for a scatter plot
        if myfl
            lambda(stp)=lambda(stp)+log(abs(myder(r,x)));
        end
        xi(curpos+i)=x;
        yi(curpos+i)=r;
    end
    waitbar((r-stt)/(fin-stt),wb) %update the wait bar
end    
close(wb); %close the wait bar
if myfl
    lambda=lambda/iters;
end
hold on
%scatter(yi,xi,'r','MarkerSize',1); %do the scatter plot
plot(yi,xi,'ok','MarkerSize',1); %do the scatter plot
if myfl
    plot(linspace(stt,fin,stps),lambda,'r');
end
hold off
function myval=myfn(r,x) %here is the function
myval=r.*x.*(1-x);
%myval=r*x^2-r*x+1;
%myval=r*exp(x);
function myd=myder(r,x) %here is the derivative
myd=r-2*r*x;