  We examine the spatial field of orientations of slender fibers that are
advected by a two-dimensional fluid flow. The orientation field of these
passive directors are important in a wide range of industrial and geophysical
flows. We introduce emergent scar lines as the dominant coherent structures in
the orientation field of passive directors in chaotic flows. Previous work has
identified the existence of scar lines where the orientation rotates by {\pi}
over short distances, but the lines that were identified disappeared as time
progressed. As a result, earlier work focused on topological singularities in
the orientation field which we find to play a negligible role at long times. We
use the standard map as a simple time-periodic two-dimensional (2D) flow that
produces Lagrangian chaos. This class of flows produce persistent patterns in
passive scalar advection, and we find that a different kind of persistent
pattern develops in the passive director orientation field. We identify the
mechanism by which emergent scar lines grow to dominate these patterns at long
times in complex flows. Emergent scar lines form where the recent stretching of
the fluid element is perpendicular to earlier stretching. Thus these scar lines
can be labeled by their age, defined as the time since their stretching reached
a maximum.
