If it is a new tank I wouldn't be concerned. New tanks experience diatom algae that will go away on its own eventually. without pictures it's hard to tell you what you have. Do a search for diatoms and look at pictures to compare. Diatoms will not turn into green algae and then to purple. They are all their own species. There are quite a lot of green, red, brown algaes some good some not so good. The purple algae is coraline algae and will eventually, if you're lucky, cover your rocks and could spread to your glass. This algae makes nusiance algae harder to take hold.