%%%user input
r       =1;
numiter =1000;
startx  =rand;

%%%change at your own risk!!!
x0      =0:0.01:1;
y0      =r*x0.*(1-x0);

x       =zeros(1,2*numiter);
y       =zeros(1,2*numiter);

initx   =startx;
for n=1:numiter
    x(2*n-1)    =initx;
    y(2*n-1)    =r*x(2*n-1)*(1-x(2*n-1));
    x(2*n)      =y(2*n-1);
    y(2*n)      =y(2*n-1);
    initx       =x(2*n);
end

X       =x(2:2:2*numiter);
tol     =0.000001;
idxX    =find(abs(X(1:numiter-1)-X(numiter))<tol,1,'last');
if(~isempty(idxX));
    lenper  =numiter-idxX;
else
    lenper  =inf;
end

if(ishandle(1))
    clf(1);
end
figure(1);
plot(x0,y0,'b-',x,y,'k-',[0 r/4],[0 r/4],'r-');
set(gca,'FontSize',16,'FontWeight','bold');
title(['x_{start} = ' num2str(startx)]);
legend(['f(x) = ' num2str(r) 'x(1-x)'],'x_{n+1}=f(x_n)','y=x','Location','Best');

if(ishandle(2))
    clf(2);
end
figure(2);
plot(1:numiter,X,'k.');
set(gca,'FontSize',16,'FontWeight','bold');
title(['period = ' num2str(lenper)]);
xlabel('n');
ylabel('x_n');
set(gca,'YLim',[0 1]);