Tiger lilies are an escaped ornamental. But these are not normal ones, which have 6 petal-like parts, but rather mutant ones (probably a known cultivar; I've seen similar ones elsewhere) in which the petals are tripled, so they have 18. Doubling/tripling/etc of petals is a common phenomenon -- sometimes seen in wild-type flowers, but very common in ornamental cultivars. Roses were all bred from wild roses that have 5 petals. There's a lot known now about the genes that govern flower pattern formation. What we have here is what's called a homeotic mutation -- a transformation of one part into another. In this case it's a transformation of stamens (and probably 1 other whorl) into petals. What's really cool is that it's an incomplete transformation, so you can often still see the filament of the stamen embedded in the petal, and a fully-functional pollen-bearing anther growing at its tip. Here's a closeup. There are numerous genes that are known to be involved in pattern formation in flowers. Many of them are transcription factors -- "master control genes" that bind to DNA and turn on or off other genes.