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Here in the Smokies we have a large variety of trilliums that come in reds, white, yellow, and "painted". I have had a lot of fun learning the different types, especially the white ones because there are several different white ones and you really have to pay attention to get the id correct. The variegated wake robin trillium in my yard actually took me 2 years to identify (and asking an expert) because its a very unusual variety and not found in a book that I know of; they are usually red or white, and the painted trillium are the only other ones I know of with that color splash.

I'm going to have to pay a lot more attention to the trilliums when they flower this year to see if there are different varieties here.

Look at several things: whether the flower is sitting above or hanging below the leaves, what the center looks like (both the stamens and the very center), and what the petals look like (thin/thick, straight/wavy, etc). I am betting if you have one kind you have several, and if you think about it let me know what you discover!