Erik M. Rauch, Mark M. Millonas, and Dante R. Chialvo, Pattern formation and functionality in swarm models, Physics Letters A 207: 185-193 (1995).
The self-organization of patterns of flow in social insect swarms is a beautiful example of how intelligent and efficient behavior of the whole can be achieved even in the absence of any particular intelligence or forethought of the individuals. Indeed, such patterns can have functionality even without the awareness of the individual entities themselves. Our model concerns the generic behavior of a kind of stochastic particle-field system in which the motion of the "particles" both changes the field and is affected by the field.
An example of numerical simulations of the model: The emergence of a system of trails over time. Red represents the ants, different shades of yellow the pheromone strengths. (This is a color version of Figure 1.)