dark purple stuff is most likely coraline algae. It's good, but if it's blocking your view, you can easily remove it. If you have a glass tank, you can just take a razor blade to it.
The green grass is most likely hair algae, which indicates a nitrate/phosphate problem, as those are what the algae eats and lives off of. If you do not have a test kit for these things, you should purchase them, and test your water. Then, go from there. You normally get phosphates from either tap water, or food that contains phosphate. If you're using tap water, you need to stop immediately! Even with conditioner, tap water is bad. The conditioner only neutralizes the minerals and whatnot in tap water, but it doesn't remove them. This is the #1 cause of algae problems in aquariums. You should start using RO water (reverse osmosis) asap!