Turing and animal coat patterns

The present article describes a beautiful contribution of Alan Turing to our understanding of how animal coat patterns form. The question that Turing posed was the following. A collection of identical cells (or processors for that matter), all running the exact same program, and all communicating with each other in the exact same way, should always be in the same state. Yet they produce nonhomogeneous periodic patterns, like those seen on animal coats. How does this happen? Turing gave an elegant explanation for this phenomenon, namely that differences between the cells due to small amounts of random noise can actually be amplified into structured periodic patterns. We attempt to describe his core conceptual contribution below.