  In the context of the longitudinally boost-invariant Bjorken flow with
transverse expansion, we use three different numerical methods to analyze the
emergence of attractor solutions in an ideal gas of massless particles
exhibiting constant shear viscosity to entropy density ratio $\eta / s$. The
fluid energy density is initialized using a Gaussian profile in the transverse
plane, while the ratio $\chi = \mathcal{P}_L / \mathcal{P}_T$ between the
longitudinal and transverse pressures is set at initial time $\tau_0$ to a
constant value $\chi_0$ throughout the system employing the
Romatschke-Strickland distribution. We introduce the hydrodynamization time
$\delta \tau_H = (\tau_H - \tau_0)/ \tau_0$ based on the time $\tau_H$ when the
standard deviation $\sigma(\chi)$ of a family of solutions with different
$\chi_0$ reaches a minimum value at the point of maximum convergence of the
solutions. In the $0+1{\rm D}$ setup, $\delta \tau_H$ exhibits scale
invariance, being a function only of $(\eta / s) / (\tau_0 T_0)$. With
transverse expansion, we find a similar $\delta \tau_H$ computed with respect
to the local initial temperature, $T_0(r)$. We highlight the transition between
the regimes where the longitudinal and transverse expansions dominate. We find
that the hydrodynamization time required for the attractor solution to be
reached increases with the distance from the origin, as expected based on the
properties of the $0+1{\rm D}$ system defined by the local initial conditions.
We argue that hydrodynamization is predominantly the effect of the longitudinal
expansion, being significantly influenced by the transverse dynamics only for
small systems or for large values of $\eta / s$.
