This is such an interesting subject matter. What if it were possible for things to dream that we don't think have a "bio" logical makeup? Let us think about the state we need to be in before we get to dreams. We take it for granted and call it, "asleep." I remember Mike Tyson, saying, "What if you are reincarnated as a rock?"
First off, if you were a rock in your first life, then you became reincarnated as a rock, certainly, you would be a chip off the old block. At face value, or stone value, that is what one may think. However, there are a lot of different kinds of rocks. Furthermore, all these different kinds of rocks have different properties. Also, when we have our most expansive dreams, it is often said that we were sleeping like a rock. What if rocks are dreaming the fuck out of this existence?
I find it ironic that people describe dreams in terms of creatures that have little or no time to dream, e.g.: birds and butterflies. As soon as those creatures decide to fall asleep, they will fall like a rock out of the sky. Other creatures that don't live in flight are often not considered dreamlike. A rock need take the constant effort to keep itself afloat in the sky to survive, so therefor, it has plenty of time to dream.
If one were to separate their typical psychology from human psychology, then they would see that rocks have life, too....instead of just sleeping like one and wanting to be a butterfly or a bird at the same time. It is a bit of double think, isn't it?