Hi,
Normal fibre optic wont hold the coherency of that pattern over the length, but there are optic cables that will do this. I think they are made up of a pack of tiny fibers that are arranged in a distinct pattern themselves so the pattern at one end appears at the other end. How good they are i dont know, but they are most likely used in those cable type inspection devices used for inspecting inside of small spaces where a normal camera can not go.
They might be a little expensive, i havent priced them. You'll probably also have to consider the resolution of the projected image.