Hi anteater, nice to me you. And a big welcome to NGA.
That is correct, when they bloom and set seed the seed will not be the same as the parent plant. If you don't want seedlings coming up everywhere just cut the bloom stalks off when the flowers are finished. They are a great source of food for all the different bees, ect.
If you decide to make your own cross between your cultivars you can save the seed and plant them in smaller containers in early spring.
Nice webbing on your 'Arctic White'.
What part of the country do you live in?
