Return to the quadratic map \(f_\mu (x) = \mu x(1-x)\) for \(\mu >4\) . When \(\mu >4\) , \(I=[0,1]\) is no longer invariant under \(f_\mu \) . Part of I will be mapped outside I, as can be seen in Fig. 6.1. Also, from Fig. 6.1, we see that there are two subintervals \(I_0\) and \(I_1\) of I, such that \(f_\mu (I_0) = I,\qquad f_\mu (I_1) = I.\) Apply \(f^2_\mu \) to \(I_0\) and \(I_1\) respectively, we see that \(I_0\) (resp., \(I_1\) ) will have a subinterval mapped out of I. So we remove that (open) subinterval from \(I_0\) (resp., \(I_1\) ). This process can be continued indefinitely. We see that it is analogous to the process of constructing the Cantor Ternary Set \(\mathcal {C}\) .