Formation of clusters of localized states in a gas discharge system via a self-completion scenario

Formation of extended structures composed of localized states via the self-completion scenario is observed. The localized states are actually current filaments in a dc driven planar semiconductor-discharge system. The structure grows from a solitary localized state in the subcritical domain, where the homogeneous state is stable. It is proved that compact hexagonal clusters form due to the attractive interaction between distant filaments. A semiphenomenological model of the activator-inhibitor type is proposed which suggests that the Turing mechanism triggers the phenomenon.