function fixedpt
%fixedpt.m produces the step diagram corresponding to fixed point
%iteration.

a=3.6;  %try a=3.5 versus a=3.6
x=zeros(1,51);
x(1)=0.5;
for k=1:50
    x(k+1)=3.6*(x(k)-x(k).^2);
end
x=[x;x];
x=x(:)';
plot(x(1:end-1),x(2:end),'b')

hold on
xf=linspace(0,1,200);
plot(xf,3.6*(xf-xf.^2),'k',[0 1],[0 1],'r')