If a wood nymph is near a tree, or a water nymph is near a fountain, they won’t wander very far from it. Specifically, their AI would tell them to consider any space more than X distance from a fountain to be invalid.

They also don’t teleport away from fountains, unless they’re scared or carrying stolen items. When they do teleport, their destination is biased towards any trees or fountains that are on the level, respectively.

Water nymphs may create a pool on their spot when killed. Items they stole from the player fall into it, of course.

Wood nymphs may create a tree on their spot when killed, and mountain nymphs may leave a boulder.

Wood nymphs, or players polymorphed into wood nymphs, can walk through trees as if they weren’t there.

Kicking a tree may generate one or more angry wood nymphs.