RU Herculis is another Mira with strongly varying cycle-to-cycle behavior. It has a high amplitude, approaching nine magnitudes from peak to trough on some cycles, although six magnitudes is more typical. As is often the case with large-amplitude stars, the light curves are strongly asymmetric, with rapid rises and slower declines. RU Her often shows a shoulder on the rising branch of the light curve as well.
RU Her is known to show surface asymmetry from optical interferometric observations, something it shares with most -- and perhaps all -- Mira variables. The cause of asymmetries in Miras isn't known, but these asymmetries have potential to tell us something about the workings of the star, and the eventual course of its evolution. The asymmetries appear in the infrared (e.g. Ragland et al. 2006), suggesting they're at the level of the photosphere; in the case of RU Her at least, they're not seen in microwave maser emission that occurs farther out from the surface (see Cotton et al, 2010 ApJS 188, 506).