Pattern formation

Active systems like flocks of animals, self-propelled micro-organisms or the cytoskeleton constitute an intriguing class of non-equilibrium systems. Locally generated internal forces together with interactions between the constituents are the cause for remarkable self-organisation processes which lead to structures as diverse as cohesive flocks of birds, swarming microorganisms or aster-like structures in cytoskeletal systems. Besides their active nature those systems show further similarities like the inherent polarity of the constituents, a density-dependent transition to ordered phases or huge density fluctuations.

These similarities suggest universal organizing principles underlying pattern formation in these systems; an idea followed by theoretical models on all levels of description: Micro- or mesoscopic models directly map local forces and interactions via only a few and preferably simple interaction rules, while macroscopic approaches rely on the systems’ generic symmetries.