delay that actually changes how you play

ok so i've been going deep on delay lately and the thing that keeps coming up is how certain units don't just sit behind your playing, they push back at you. like the eventide stuff in particular, the DDL-500 style approach where the repeats feel almost alive? you start chasing the tail of your own notes and suddenly you're playing differently than you intended. that's the kind of character i'm talking about. curious what pedals you all feel have that quality, where the delay isn't just an effect but more like a conversation partner.