  I demonstrate that the concept of a non-equilibrium attractor can be extended
beyond the lowest-order moments typically considered in hydrodynamic
treatments. Using a previously obtained exact solution to the relaxation-time
approximation Boltzmann equation for a transversally homogeneous and
boost-invariant system subject to Bjorken flow, I derive an equation obeyed by
all moments of the one-particle distribution function. Using numerical
solutions, I show that, similar to the pressure anisotropy, all moments of the
distribution function exhibit attractor-like behavior wherein all initial
conditions converge to a universal solution after a short time with the
exception of moments which are sensitive to modes with zero longitudinal
momentum and high transverse momentum. In addition, I compute the exact
solution for the distribution function itself on very fine lattices in momentum
space and demonstrate that (a) an attractor for the full distribution function
exists and (b) solutions with generic initial conditions relax to this
solution, first at low momentum and later at high momentum.
