What is this groundcover? Tell me more about it!?

Sorry I don't have a photo to upload at the moment. I will update later if I don't get an answer.

This plant was growing on our property when me moved here, so I'm assuming it's native, but I suppose a previous owner could have introduced it. It is a low-growing groundcover with delicate green fern-like foliage. In the summer it has little lavender puffball flowers on slender straight stalks about 2-4 inches tall. (Similar to a dandelion or mimosa flower except lavender). I have never seen them in a nursery to buy, but I wouldn't call myself an expert gardener by any means.

I would love to transplant this elsewhere because it makes such a pretty carpet-like groundcover and is so low-maintenance, so any info you can share would be appreciated!