I have a flowering snow crab tree in my back yard and it is surrounded by a brick tree ring. This tree has a very shallow root system and I would like to plant a perennial that would expand and fill in the tree ring area. Something that can take full sun most of the day & low growing would be ideal. The problem I have is that I can't dig very large or deep holes in this area because of the shallow root system. I need a suggestion for something that I can start from seed or a small cutting.
Try creeping sedum. They like full sun and are drought-tolerant once established. However, as the tree grows, you'll need to replace with something more shade-tolerant. I wouldn't suggest Bishop's weed, lamium, or lamiastrum--they're too invasive and aggressive. How about creeping thyme? Thyme or sedum will fill in and if they get too scraggly just give 'em a haircut, they'll respond nicely.