  We establish how active stress globally affects the morphology of
disclination lines of a three dimensional active nematic liquid crystal under
chaotic flow. Thanks to a defect detection algorithm based on the local nematic
orientation, we show that activity selects a crossover length scale in between
the size of small defect loops and the one of long and tangled defect lines of
fractal dimension $2$. This length scale crossover is consistent with the
scaling of the average separation between defects as a function of activity.
Moreover, on the basis of numerical simulation in a 3D periodic geometry, we
show the presence of a network of regular defect loops, contractible onto the
$3$-torus, always coexisting with wrapping defect lines. While the length of
regular defects scales linearly with the emerging active length scale, it
verifies an inverse quadratic dependence for wrapping defects. The shorter the
active length scale, the more the defect lines wrap around the periodic
boundaries, resulting in extremely long and buckled structures.
