That may not even be Damascus. It could be a pattern put on the gun to make it look Damascus. In those days, the Damascus gun had a better reputation than the fluid steel barrels of the day...
It's real damascus... I just had the barrels "reblacked" by one of the most well known damascus barrel guys in the US (he actually did the whole restoration). I think it would be equally as impressive to put some sort of even and repeatable "coating" on a set of barrels in 1889 and have it still be visible this many years later.
Here is a good before picture showing the years of slow rusting that hid the underneath pattern after a light sanding...
I am somewhat hesitant to admit that I had no idea about the barrels when I bought the gun... just pure dumb luck... was looking for an cheap and nice hammer gun to consider restoring and playing with myself.
DF, there are lots of Pieper guns out there...one of the first to "mass produce" guns... they made single shot rim-fires, pistols, shotguns, and rifle/shotgun combos. However, you won't find very many with that damascus on them (or this grade of wood)...
I've done quite a good bit of research on the subject and have only found one other known gun with this damascus. There are likely a few others but at this point can't imagine there are too many.
Pieper is most famous for the breech block barrel design. The chamber area of this gun are fluid steel but the barrels are obviously the damascus pattern...
The barrels are engraved "Grand Prize Paris Exhibition 1889"