%Example: If x_0=0.1 and f(x)=3.2x(1-x), then there is an attracting
%period-2 point.  Find them, and verify that the appropriate derivative at
%those points are less than 1 in magnitude:

f=inline('3.2*x.*(1-x)');
df=inline('3.2*(1-2*x)');
d2f=inline('(3.2^2).*(1-2*x).*(2*3.2*x.^2-2*3.2*x+1)');

x=0.1;

%Run the iterations through to get to the period-2 point first:
for j=1:100
    y=f(x);
    x=y;
end

for j=1:100
    orbit(j)=f(x);
    x=orbit(j);
end

orbit(98)-orbit(100)

d2f(orbit(99:100))
df(orbit(99:100))
df(orbit(99))*df(orbit(100))