I've been trying to figure out how this animation was done for the past few hours. If anyone has any ideas of what effects, plugins, or software was used, I would greatly appreciate any advice.
It looks like it's done in After Effects, with some maskings, track matte on shape layers, but I can't quite figure it out.
Its a bit of a cheat. (but aren't all effects!). It just one shape (the arrow) moving in a straight line but disappearing/reappearing; either disappearing behind a diagonal matte or reappearing from behind a curved mask.
I think what really sells it is the tip of the arrow barb that is disappearing getting cut off by the emerging arrow, before the point runs behind the mask. It gives some motion to the corner turn which is happening only in your brain and not on the screen.
There is also a mask you can't see that reveals the barb as it emerges from the curved mask.
To achieve the endless loop just set up a single arrow and your masks so the arrow travels in one direction - then use the offset effect (down at the bottom in Utilities I think) and let the arrow run off one side of the screen and back on the other so that there is just a bit of space between head and tail. Then precomp all that and use it as an element and rotate it by 60 degrees and do that two more times.
The thin band of nothingness that is part of the curved mask is essential so the brain sees the negative space and associates that with a conveyor belt or roller type structure.