Trilliums, as their name implies, are plants with three petals and three leaves. On occasion, a genetic mutation creates a trillium flower with multiple petals. These are known as "double blooms" and are prized by some gardeners. I saw the one pictured above growing in the wild at the Kalamazoo Nature Center in May 2010.
Growing a few feet away was this four-petaled trillium, with four leaves-- another genetic rarity. Some people call this a "quadrillium." I don't know if these mutations had a common cause, perhaps coming from the same parent plant.
While these individual plants have unusual appearances, they are still Trillium Grandiflorium (Large Flowered Trillium). I'm curious to see if they bloom again this Spring.
I teach economics at Kalamazoo College. My wife is also an economist. We were on sabbatical in Europe for the 2014-15 academic year. (Salamanca, Spain, followed by Oxford, UK.) We were in Uruguay for the 2006-7 academic year.