I think to look for Arabic in the patterns would not result in a typical barrel or blade. To look at a culture's sense of art and decoration as it was carried from one media to another makes a lot of sense. "We" have been decorating hunting weapons for thousands of years. The British engraving of the 1800's was flowing from the Victorian "culture". It is what appealed to them. In the same way, the blades and barrels of the Ottoman empire were decorated in a manner that flowed from their culture.
I remember Oscar once referenced Leo S. Figiel, "On Damascus Steel". So at the time, I purchased a copy. I read through it and put it away. I recently picked it up again. Figiel spends the majority of the book dealing with blades. Only the last chapter really digs into barrel making. A lot of the examples are styles of mechanical damascus that were never copied in western Europe. ( I do wish I had written down all the sources Oscar mentioned.... )
Put succinctly, neither crucible nor mechanical damascus were a European invention. The technology did not suddenly appear and then just disappear. There is a lot of history and cultural intercourse occurring to produce even simple damascus shotgun barrels.
In understanding how it all came about, the contribution of each culture along the way and how it eventually ended, we learn.
Some people are only interested to know where those damascus barrels on their what ever shotgun came from. That is fine. A subset of all this has been to identify Belgian makers and understand the commerce that occurred. As tariffs were raised in the US, the Belgians responded with product that met the need and the price. The flip of this seems to be that some English firms went out of business because they could not compete with the Belgian labor rates (still working this piece).
A bit of trivia...Liege was under siege in the 1300's. It eventually fell. It is the 1st known use of hand canons during a siege. Liege was important because of it's long tradition as a center for bladed weapons.
I know how often I have dismissed the damascus blade as a dead end when researching damascus barrels. But I think, in a small way, I am beginning to understand why Oscar considered Figiel important. The blade evolved from crucible (or bloom) to mechanical damascus. The damascus blade was a necessary step to the damascus barrel.
Pete
