  Motivated by the formation of fingerprint patterns we consider a class of
interacting particle models with anisotropic, repulsive-attractive interaction
forces whose orientations depend on an underlying tensor field. This class of
models can be regarded as a generalization of a gradient flow of a nonlocal
interaction potential which has a local repulsion and a long-range attraction
structure. In addition, the underlying tensor field introduces an anisotropy
leading to complex patterns which do not occur in isotropic models. Central to
this pattern formation are straight line patterns. For a given spatially
homogeneous tensor field, we show that there exists a preferred direction of
straight lines, i.e.\ straight vertical lines can be stable for sufficiently
many particles, while many other rotations of the straight lines are unstable
steady states, both for a sufficiently large number of particles and in the
continuum limit. For straight vertical lines we consider specific force
coefficients for the stability analysis of steady states, show that stability
can be achieved for exponentially decaying force coefficients for a
sufficiently large number of particles and relate these results to the
K\"ucken-Champod model for simulating fingerprint patterns. The mathematical
analysis of the steady states is completed with numerical results.
