I pulled these two seedlings out for a photo op. Earlier this year, both were single fans like the one on the left. Then the one on the right developed two central growing points, as if it were naturally dividing. I watched a long time and finally the scape emerged between them. About the same time the scape appeared, two more growing points started up on the outer sides of the fan(s). Right now there are two taller ones and two smaller ones with the scape in the middle. (Previewing shows you have to enlarge the photo to see it all).
When I moved them today, I saw growth coming up on the one that looks like a single fan, but it's still hidden down between two leaves. I expect a scape on that plant in a while. It seems like this kind of increase is a type of division that accompanies a scape. When the scape is gone, that fan growth is a whole new fan. I'm not real sure about the two new smaller ones. I haven't seen that a lot. Doesn't seem likely they would be associated with scapes, so I'm thinking fans only. Going from a single fan to four fans by summer isn't too bad, though.