Hi Dan,
You are right, no doubt.
I was trying to explain that Roo had shown to me, on this post (http://igkt.net/sm/index.php?topic=1545), that my necklace problem could in fact be expressed as a "double loop" problem. In that sense, the necklace problem was a recent application of a double loop (even though the picture didn't show a double loop in the OP sense).
I was lazy to take another picture, but you pushed me to it. Thank you, this will make for a more technically-correct post.
Here then is the necklace problem mentioned earlier, solved with a two-loop butterfly.
(http://asiteaboutnothing.net/knots/i_forum_necklace_alpine.jpg)
Since then, others on the thread have offered more eye-pleasing solutions. Wondering if you'd have any other ideas. :)
Wishing you a fun day,
Andy
ps: for the archives, here is a close-up of the grapevine variation on the necklace.
(http://asiteaboutnothing.net/knots/i_forum_necklace-grapevine.jpg)