I'm going to guess it is Herniaria glabra. I see it is noted as a biennial/perennial. That probably means it technically is a perennial but very short-lived and so best treated as a biennial.

No idea about growing or self-seeding.

FataMorgana

Thanks; I was hoping someone might have had experience with it. A single plant has covered a 15" diameter patch, is about 2" tall with tiny bright green leaves. It is very attractive, I must get some seeds for next year. coing