  We consider the patterns formed by small rod-like objects advected by a
random flow in two dimensions. An exact solution indicates that their direction
field is non-singular. However, we find from simulations that the direction
field of the rods does appear to exhibit singularities. First, ` scar lines'
emerge where the rods abruptly change direction by $\pi$. Later, these scar
lines become so narrow that they ` heal over' and disappear, but their ends
remain as point singularities, which are of the same type as those seen in
fingerprints. We give a theoretical explanation for these observations.
