I got stuck up a tree on Sunday. Kinda. I was with somebody who descended and resolved it, but it was a learning-point - particularly when I usually climb alone...
I had ascended with a doubled rope, and then hauled up the tail and dropped it elsewhere to get it out of the way of my climbing partner. The way I did that was to pull up the tail incrementally and allow the taken-up bight to descend down where I wanted it to go. What happens if you do that is you end up holding the free end with the weight of all the slack rope pulling it down. The natural inclination then is to drop it. On this occasion the weight of the rope pulled the end with enough force to cause it to wrap completely around a limb much lower down, leaving it as in the image.
All seemed well until I tried to descend DdRT, when the standing end of the rope would not come up, thus preventing me from descending at all - and preventing me, therefore, from untangling the tail. To compound the problem, the single wrap meant that gravity would pull any slack out of the standing end, essentially acting as a progress-capture device, allowing me only to ascend.
Lessons learned:
This is why you should climb with a partner. Thanks Jos for descending and unwrapping my rope.
Don't drop the bight. You are probably ok to allow it to descend until you have the tail-end (though take care! The alternative is to bag the rope as you pull it up...) but then feed the tail down where you want it until all the slack follows it down and is deployed. This takes the energy out of the system, reducing the possibility of wrapping.
If you do get in this situation, anchor the working end to a limb near you and climb down SRT to unwrap the rope. If you have a throwline with you you can tie a retrievable anchor and not have to climb back up, but if not the extra climb serves you right!
Climb with a backup system. I always have a hand-jammer and foot-ascender, but I've added a gri-gri to my always-on harness-kit. With the progress-capture effect of this wrap it would have been tricky to tie a munter or super-munter for descending, and that wouldn't have been great for stopping at the wrap anyway.
Stay in school kids!