Donkeys

While I was in Israel, one of the locals said something interesting. He said that many of the paths in use were created by donkeys, and had often been there for thousands of years. The reason he gave for this was that donkeys allegedly always take the easiest route from A to B, even over difficult terrain. That got me thinking.

It should be reasonably easy to set up a situation with a donkey and a mathematically well-defined surface, and to see whether it does indeed take something very close to the minimum energy route from A to B, and what sort of distance this holds over. Does it work as far as the eye can see? How does it cope with variable terrain types - e.g. mud, solid grass, rocks? Does it follow the sort of route that would be predicted by a proper mathematical minimum energy route, or does it follow a local energy minimization, or even just a picking a vaguely easy route for the next 20m that leads in the right sort of direction?

I'm sure there's a PhD project in there somewhere, for a mathematician who likes donkeys...