Period 88 pi-based oscillator (Paul Callahan). I found this while doing a search of perturbations of the pi heptomino in order to find a stable reflector. Three eaters rotate a pi by 180 degrees in 44 generations. Three more, placed in the same way with respect to the new pi, rotate it back.

Note that the pi rotation proceeds very chaotically, at least at my level of intuition. The pi often appears spontaneously in simulations starting with random cell populations. Its reappearance here seems a lucky coincidence, possible only because it is so common. This also demonstrates the power of exhaustive search; it is hard to imagine finding such a reaction by hand.