  We analyze pattern-formation scenarios in the two-dimensional (2D) complex
Ginzburg-Landau (CGL) equation with the cubic-quintic (CQ) nonlinearity and a
cellular potential. The equation models laser cavities with built-in gratings,
which are used to stabilize 2D patterns. The pattern-building process is
initiated by kicking a localized compound mode, in the form of a dipole,
quadrupole, or vortex which is composed of four local peaks. The hopping motion
of the kicked mode through the cellular structure leads to the generation of
various extended patterns pinned by the structure. In the ring-shaped system,
the persisting freely moving dipole hits the stationary pattern from the
opposite side, giving rise to several dynamical regimes, with the pinned
multi-soliton chain playing the role of the Newton's cradle (NC).
