One example is the mutually-syncrhonizing behavior of multiple TCP streams traversing a network. The general traffic structure is chaotic, but the "regular" pulsations of mutual self-synchrony are readily apparant when the traffic is examined in detail. Order naturally arises out of chaos in a seeming local reversal of entropy.
Another example of chaotic repeatability is the two-pole, three-flexure coupled pendulum effect which occurs in certain gas molecules when excited by RF energy near nuclear magnetic resonance of the end atoms of the molecules. Of particular interest is the wave function of the intermolecular quantum coupling which appears as induced densities approach the triple-point.
Our last example is the chaotic recurrence of people who seem determined to take the contents of this page seriously, an event whose period is decreasing of late, but which is no less entertaining.
Have a nice day, or rant, which ever you prefer.