Are US Congressional districts required to be connected?

With all the talk of gerrymandering of late, I was looking up North Carolina's past election maps. And man, the 2016 map which caused the court case looks downright normal compared to some of the ones they've had in the past.

But something caught my eye in the 1993-1998 map. I was under the impression that congressional districts were required to be connected sets, which is why so many districts on that map have narrow corridors connecting them. But I just don't see how districts 1, 3, and 7, or districts 6 and 12, can possibly all be connected.

So I guess I have two related questions

• Are congressional districts required to be connected? If not, how often have disconnected districts appeared?
• Are districts in the 1993-1998 map actually disconnected, or is there some geometric wizardry going on at scales that image doesn't resolve?

For this purpose, connection through territorial waters is acceptable, so places like Hawaii or Michigan's upper peninsula that are divided by water don't count.