  We use various electrode layouts to tailor the profile of the electric field
in a two-dimensional (2D) dielectric-barrier-discharge system, thereby creating
spatial templates for the lateral distribution of discharge filaments. Our
discussion focuses on the formation of patterns and the interactions between
filaments in several template configurations. Hexagonal and square lattice
templates produce patterns reminiscent of the surface phases of adatoms on
crystal surfaces. For the square lattice, a lateral displacement between
opposing lattice electrodes modifies the pattern-forming behavior of the
system. In a stripe-electrode arrangement, each discharge filament terminates
in two dissimilar footprints, and the resulting pattern exhibits smectic
behavior. A circular ring template establishes periodic boundary conditions and
produces a new pattern in which adjacent filament footprints differ in shape.
Finally, electrodes featuring isolated and twinned pins are used to investigate
the pairing and clustering of filaments. We find that under certain conditions,
filament pairs may stabilize at either of two characteristic bonding distances.
We also study the range of distances over which a filament will either prevent
the ignition of or annihilate nearby filaments.
