Deep Southern Gardening Mystery #8

Every spring, about the time the new shoots of monkey grass emerge from the worn-out-looking dark green remnants I’ve cut down, these angular shoots come up with them. Distinct from the new growth among the monkey grass, which points directly upward, these fresh green blades tangle into distinctly angled joints and produce little globular buds, from which emerge soft-purple flowers. My neighbor has some too, and his are also among his monkey grass. But neither of us know what they are.

purple flowers in monkey grass2015-04-12 12.47.38purple flowers among monkey grass

Does anyone know what resilient little suckers are?