  We study a heretofore ignored class of spiral patterns for oscillatory media
as characterized by the complex Landau-Ginzburg model. These spirals emerge
from modulating the growth rate as a function of $r$, thereby turning off the
instability. These spirals are uniquely determined by matching to those outer
conditions, lifting a degeneracy in the set of steady-state solutions of the
original equations. Unlike the well-studied spiral which acts a wave source,
has a simple core structure and is insensitive to the details of the boundary
on which no-flux conditions are imposed, these new spirals are wave sinks, have
non-monotonic wavefront curvature near the core, and can be patterned by the
form of the spatial boundary. We predict that these anomalous spirals could be
produced in nonlinear optics experiments via spatially modulating the gain of
the medium.
