In a complex system, interactions between individuals can lead to the emergence of overall behavior. A vivid example is the sheep model, which reflects the richness and complexity of herd behavior through simple rules and interactions.

The basic idea of the sheep model is to simulate the movement and behavior of individuals (sheep) under certain rules. In this model, each sheep has its own goal, which is usually to follow the other sheep around it and maintain a certain distance to avoid isolation. This simple act of following and avoiding collision can produce coordinated and orderly group movement. When one sheep starts to move, the surrounding sheep are affected and move with it, thus forming a mobile herd.

This phenomenon can be used to explain many phenomena in nature, such as the migration of groups, the swimming of schools of fish or the flight of flocks of birds. Although the behavior of each sheep is relatively simple, when a large number of individuals are together, the system as a whole exhibits complex dynamic characteristics, such as the emergence of collective movement, clustering, dispersion, and turning. In this way, we can observe neat formation, smooth movement, and response to external stimuli.

The application of sheep model is not limited to the biological field, but also can be extended to other scientific research and practical applications. For example, in the flow of traffic, how drivers affect each other, causing traffic congestion or smooth driving; How individuals influence group decisions through information dissemination in social networks. Behind these phenomena, there is a similar mechanism to the sheep model.