1. Modelling collective animal behaviour David J. T. Sumpter Department of Mathematics Uppsala University

2. Moving together Aggregation in space. Moving in the same direction. Complex patterns.

3. Self-propelled particle models current positioncurrent velocity position and velocity of neighbours stochastic effect future position future velocity

4. Aggregation model in one dimension current positioncurrent velocity position and velocity of neighbours stochastic effect future position future velocity e is a random number selected uniformly at random from a range

5. Aggregation model in one dimension

6. Cockroach aggregation Cockroaches Model

7. Radakov’s fish

8. Alignment model in one dimension current positioncurrent velocity position and velocity of neighbours stochastic effect future position future velocity e is a random number selected uniformly at random from a range

9. Position: Velocity: Time SpaceTime Average direction Alignment model in one dimension

10. Position: Velocity: Time SpaceTime Average direction Alignment model in one dimension

11. Position: Velocity: Time SpaceTime Average direction Alignment model in one dimension

12. Transition from disorder to order measures order in the system. η is degree of randomness, ρ is density (number of particles over size of world).

13. Transition from disorder to order measures order in the system. η is degree of randomness, ρ is density (number of particles over size of world).

14. Transition from disorder to order measures order in the system. η is degree of randomness, ρ is density (number of particles over size of world).

15. Alignment model in two dimensions current positioncurrent velocity position and velocity of neighbours stochastic effect future position future velocity where the θ j are the directions of i’s neighbours and ε is chosen uniformly at random from a range.

16. Alignment model in two dimensions

19. Attraction, alignment and repulsion in three dimensions

23. Collective Animal Behaviour www.collective-behavior.com

24. Collective Animal Behaviour www.collective-behavior.com

25. Collective Animal Behaviour www.collective-behavior.com

26. Collective Animal Behaviour www.collective-behavior.com

27. Collective Animal Behaviour www.collective-behavior.com