Feedback / loop node in DaVinci Resolve?

Hi there. I'm looking for a compositing package that has a "loop" or "feedback" node (it may have a different name) This type of node "persists" from frame-to-frame. As input, it's fed the last frame, then the software performs some small transform, etc leading to slowly "mutating" loops. It's different from a typical compositing, where you work with the current frame only. Does anyone know if daVinci Resolve has something likes this?

Duplicate node?

Duplicate node?

How do you loop with duplicate node?

Problem with looping parts of graph inside directed acyclic graphs, which nodegraph is, comes from the ”directed” and ”acyclic” parts, meaning data flows in one direction only. Unfortunately I don’t know enough about internals of Fusion to say how much it applies in practice and whether it would be possible in some out of the box manner.