This is the one I grow:
It has scaled, elongated little bulbs or rhizomes (not really sure which) that don't exactly have extended parts like yours, but scales broken off will easily grow into a new plant.
Many Oxalis propagate easily, and since yours does form a larger, denser clump, I'm pretty sure those extended corms are what is going on under ground as that happens. Sounds like an experiment is in order!
