Anti-aligning interaction between active particles induces a finite wavelength instability: The dancing hexagons

By considering a simple model for self-propelled particle interaction, we show that anti-aligning forces induce a finite wavelength instability. Consequently, the system exhibits pattern formation. The formed pattern involves, let us say, a choreographic movement of the active entities. At the level of particle density, the system oscillates between a stripe pattern and a hexagonal one. The underlying dynamics of these density oscillations consists of two counterpropagating and purely hexagonal traveling waves. They are assembling and disassembling a global hexagonal structure and a striped lineup of particles. This self-assembling process becomes quite erratic for long-time simulations, seeming aperiodic.