Sounds like a good idea... TARTANS !
From what I have seen, the design on a tartan is to big to wrap around a pen tube and remain identifiable. That is, some of the design will be left out.
Thinking (ouch!) about it, I was wondering if a pic could be taken of the tartan, which could be a kilt or whatever. Then this can be printed in color at a scale that fits the tube.
Two ways to handle the print:
1. Wrap the print around the tube itself, and then encapsulate it with resin. You can then shape the barrels any way you want.
After the barrels are sanded to a gloss, the clear resin will act as a magnifier, and the print will appear to be at the surface of the barrel.
2. Turn the barrels to a diameter a hair smaller than finished size, and sand to about 400. Take the barrels off the lathe and mandrel. Glue the tartan print around the barrel, making sure the print sticks out a hair from the end of the barrel, and LET DRY completely. Let dry well no matter what kind of glue you use! Overnight would be advisable. Best glues are the ones used for decoupage, and white carpenter's glue, like Elmer's.
After the glue on the barrel has dried completely, put the barrels on a dowel of suitable size. Spray a coat of the glaze, and let dry completely. Build up the glaze by applying 2 or 3 additional coats, letting dry in between. The coating will be glossy but somewhat uneven. DO NOT SAND between coats !!
Now sand carefully to even out the ends of the barrels with the tube, and remount the barrels on the mandrel and lathe. Use a fine grit sandpaper (600) or MM to level the glaze. You can tell it is leveled when the high gloss disappears. Be gentle, the coating is thick, but you don't want to sand it thru. All you want to do is get rid of any uneveness in the surface. Now gently sand with MM to 12000.
BARREL SIZE: Talking about the thickness of a hair! If you wrap a .004 printed paper around a barrel, the barrel will be .008 thicker. To this add the thickness of the glue, and the glaze, a few thousands thick depending on how much you put on. About 1/64" undersize is probably OK, but a caliper would help here.
GLAZE: What I have used is Krylon Triple-Thick Crystal Clear Glaze. It comes in a 12 oz spray can for about $3. I bought mine at the Wally store. Very economical. This is an acrylic product, and the finish is colorless, and very TOUGH.
I have used this glaze in a number of situations where nothing else is practical. It builds up a thicker coat than the Krylon Crystal Clear. For example, I have applied decals to barrels, and then coated with the glaze as a protection.
This glaze cannot be distinguised from a CA finish, but can be applied in situations where CA cannot be used or is impractical.
This is from my personal experience, which I like to share. I offer it as a suggestion only. Your mileage might vary. All other disclaimers apply.
ADDED: This might also work for other pics, ribbons, etc.