[dekhn]

I don't visualize anything while programming, most of the time, but once when I was learning how to do recursion, an entire program popped into my head while I was falling asleep, I could see it floating there in front of me.

This happens when I get really OCD about things. I start to visualize fully-formed solutions to problerms. For a while I thought this was a superpower, but after experiencing it a few times, I noticed that when I got OCD, I couldn't be around other people, and my physical health dropped noticeably as I ignored food. I suspect a number of well-known mathematicians experience this.