Plants don't turn purple. The purple pigment is already in the plant, you just can't see it because the chlorophyll hiding the color. As soon as the plant stops producing chlorophyll you will start to see the underlying colors. You can kind of see the colors as the plant is growing. For example my Pre 98 Bubba Kush is almost black as it grows. It turns a wonderful deep purple at finish. On the other hand my Agent Orange is a light green and turns yellow during the flush. I had a Green Love Potion strain that ended up a beautiful deep red.
Basically to see the colors you have to get rid of the chlorophyll. Obviously you don't want to do this while it's growing! If you grow outdoors your plants will eventually turn on their own due to nutrient lock-out because of the lower temps. Indoors all you have to do is flush your plants.
Back in my collage days one of my favorite labs was the one about plant pigments. We went out and got a bunch of leaves and ground them up. We added water and used a test strip to suck up the mixture. As the water climbed up the paper it left bands of color depending on the weight of the pigments. So you end up with bands of purple, red, yellow and green. Cool shit!