Ann, could it possibly be Oriental Poppy? Are the leaves hairy at all? It also looks like not all of them have the red stems down at the bottom, or do they just not show up?
They do self-sow generously, and for years I was thinning them out, in my daughter's garden in Utah. Not all have pointy, ferny leaves either, some are rounded at the ends like your plant. You could dig one up and see if it has fleshy, white rhizomes under there . . ?
