Does anyone know what this flower it?

drannhh is correct. It will take much longer with seeds. They may also need statification to germinate the seeds.

I think you will more luck propagating it from the root. Please see the link I posted above.

It only lasted a couple of days but hopefully it spread some seeds and I'll have more next year! They are so beautiful and I love the color!

That picture looks like the flowers on my orchid! I hope the little flowers come up next year, I was delighted when I saw the first one! It was in my yard when I was mowing and I went around it. When I was done, I got scissors and trimmed the grass around it so that I wouldn't destroy it.

Yes, I expect the beautiful flower will come up again and again as it is a perennial (meaning that it grows back from its root stock as opposed to seeding) and here is a page you might enjoy that discusses propagating them: http://www.plantingflowerbulbs.com/anemone-flowers.htm This will help in case you want to transplant your anemone, as the type of "root" it has, whether rhizome or tuber or fibrous root makes a difference in how to handle it. Anemones are one of the most beautiful easy to grow plants around and are considered by some to be invasive, in the sense of a pest, but I cannot agree with that at all, because I just love them, the more the better! Thanks for the BR :-)

It did remind me, by the color, of my violet plant inside the house but it looked so soft and velvety I love this flower!