Is the method deterministic? Unless you can modify the world, there's no reason to save it.
It's not deterministic because the order that things are generated changes based on where the player chooses to walk, and things that have already been generated place constraints on things that have not been generated yet.
That being said, since it's based on tiles, I'd assume there's a lot of room for optimizing RAM usage (and also unloading far-away areas to a file on disk if you want to get fancy).