What could be the reasons for the tips of my nipples turning a purple color?

Circulation. Are the changes only in the nipples? Is there any bleeding? Is it both sides? Can be certain why they turn purple - is it temperature related - only the cold. Unless you voted in iraq a blue finger can be circulation related. People can have raynaud's where their fingers, toes, etc turn white in the cold but you are just seeing circualtion changes. Do the nipples feel cold when turn purple.
Purple nipples. This is basically a normal, transient change due to changes in the blood vessel beneath the nipples. The nipples are an erotic organ and get extra blood flow with arousal; after that the nipples can get congested, and congesiton of the veins will cause a blue or purplish color. I don't think you need to be concern. I am assuming you are not talking about purplish-black discoloration from a bruise.