Prokaryotic plasmids encode partitioning (par) loci involved in segregation of DNA to daughter cells at cell division. A functional fusion protein consisting of Walker-type ParA ATPase and green fluorescent protein (Gfp) oscillates back and forth within nucleoid regions with a wave period of about 20 minutes. A model is discussed which is based on cooperative non-specific binding of ParA to the nucleoid, and local ParB initiated generation of ParA oligomer degradation products, which act autocatalytically on the degradation reaction. The model yields self-initiated spontaneous pattern formation, based on Turing's mechanism, and these patterns are destroyed by the degradation products, only to initiate a new pattern at the opposite nucleoid region. A recurrent wave thus emerges. This may be a particular example of a more general class of pattern forming mechanisms, based on protein oligomerization upon a template (membranes, DNA a.o.) with resulting enhanced NTPase function in the oligomer state, which may bring the oligomer into an unstable internal state. An effector initializes destabilization of the oligomer to yield degradation products, which act as seeds for further degradation in an autocatalytic process. We discuss this mechanism in relation to recent models for MinDE oscillations in E.coli and to microtubule degradation in mitosis. The study points to an ancestral role for the presented pattern types in generating bipolarity in prokaryotes and eukaryotes.