Most examples of self-organized spatial patterns in ecosystems are based on Alan Turing's activator-inhibitor principle, where pattern formation is driven by spatial variation in biological growth conditions. I will highlight a new mechanism of pattern formation in ecosystems that is based on the individual movement of animals, and is akin to the physical principle for phase separation, known to explain pattern formation in alloys such as steel or bronze. Using models and experiments, I will argue that both processes can occur simultaneously, and interact to determine the resilience of ecosystems to disturbances and changing environmental conditions.