How to grow green freshwater algae?

I don't think the algae grows on the rock, it kind of just sticks to it. Put in some fertaliser and nutrients (aparentlty cat food works) ewww........) on the surface of the water in direct sunlight, wait a week and alacazam! you have created alage! Otherwise, go to a park with a waterproof bag and scoop out some, nobody will care! and dump it in your water and it will spread out in its own time.

You just need to ensure that the rock remains damp and but not fully submerged in water and the algae would grow!