How to Map an O'Neill Cylinder?

[wormspeaker]

You mean other than just make a rectangular image and map it to the inside of a cylinder?

Yes. Just making a rectangular map just doesn't seem to do it justice. Particularly since what you can see in the sky at any point in the cylinder would be just as important as what was around you on the ground.

Maybe something like below. (If they had 4 land masses instead of 3. It's hard to do anything but 90 degree angles in MS Paint.)