x0=0.7;
a=4;
n=100;
f = @(x) a.*x.*(1-x);
x=[x0,x0];
pert=0.000001;
xx=[x0+pert,x0+pert];
for k=1:n 
    x=[x,f(x(end)),f(x(end))];
    xx=[xx,f(xx(end)),f(xx(end))];
 end;
figure(1)
plot(1:n+1,x(2*(1:n+1)),'r-',1:n+1,xx(2*(1:n+1)),'b-',1:n+1,(sin(2.^(0:n).*asin(sqrt(x0)))).^2,'g-')
figure(2)
axis equal
plot(x,x,'g-',x(1:2*n+1),[0,x(3:2*(n+1))],'r-',xx(1:2*n+1),[0,xx(3:2*(n+1))],'b-',[0:0.01:1],f(0:0.01:1))