The bad-idea and it's sample
Never mind what the end idea is - I wanted something completely reversible, and it had to have a supplementary weft.
This sounds like overshot (daldräll), so I started with the traditional cat's paw pattern. After adding another "block" and a "turned" tieup, I had this:
Could perhaps be interesting?
Then I made one (of probably several) bad decisions: what if I put it into the fan reed?
Now, the fan reed has 26 dents per fan, so I had to reduce the repeat to 26 profile ends (each representing 2 warp ends). Then I had this:
Still recognizable... perhaps. The treadling can be reduced in various ways, and is perhaps better left until the actual weaving. But wait: I have to have an idea of when/how often to change the reed position... some possible variations:
Now, no doubt you all wonder why I didn't abandon the idea right here? Looking back, I wonder, too. (But is was only some 180 ends, and perhaps it would be interesting, and...)
The end product is (was, for this try, anyway) to be relatively low-contrast, but for the sample I used what was nearest at hand: a narrow white cotton warp and a blue-green already-wound quill, also cotton. (Maybe, but only maybe, it would have looked better with lower contrast...)
I'm sure you all agree that this sample has no future...
(Next try will, perhaps, be a biggish waffle weave. If I can figure out a way to use a discontinuous weft.)
Bonus: with a bigger scale (which of course makes it a dräll rather than an overshot - thus min 24 shafts, preferably 32 or 40), and a natural linen on a white warp, I still think the pattern is "good enough":