Observe that if you start at any of the red states and follow what happens for six time steps, you will return precisely where you started.Because the system is deterministic, these same six states must be repeated over and over again.
This idea that these periodic states may be found "everywhere you look".This is not an easy concept to understand. You have to imagine that no matter where you place the magnifying glass and no matter what the magnification, you will find one of these states.