One of the time-honored traditions of Cub Scout campouts is little kids putting bugs in cages to see what happens. On one such occasion I witnessed, A mantis and a firefly were placed together in a cylindrical wire container. The mantis faced downward on one side of the cage, and the firefly was on the bottom. After wandering around for a while, the firefly traveled up the side right in front of the mantis. When the mantis struck, it merely knocked the firefly down to the bottom before it immediately followed the exact same path. The same thing repeated two more times before the mantis successfully caught and ate the firefly.
Also, this thread reminded me of the Lévy flight foraging hypothesis. Not specifically related, but I wonder if there have been similar attempts to model insect foraging and problem-solving movements mathematically.