  Isolated many-body systems far from equilibrium may exhibit scaling dynamics
with universal exponents indicating the proximity of the time-evolution to a
non-thermal fixed point. We find universal dynamics connected with the
occurrence of extreme wave excitations in the mutually coupled magnetic
components of a spinor gas which propagate in an effectively random potential.
The frequency of these rogue waves is affected by the time-varying spatial
correlation length of the potential, giving rise to an additional exponent
$\delta_\mathrm{c} \simeq 1/3$ for temporal scaling, which is different from
the exponent $\beta_V \simeq 1/4$ characterizing the scaling of the correlation
length $\ell_V \sim t^{\,\beta_V}$ in time. As a result of the caustics, i.e.,
focusing events, real-time instanton defects appear in the Larmor phase of the
spin-1 system as vortices in space and time. The temporal correlations
governing the instanton occurrence frequency scale as $t^{\,
\delta_\mathrm{I}}$. This suggests that the universality class of a non-thermal
fixed point could be characterized by different, mutually related exponents
defining the evolution in time and space, respectively. Our results have a
strong relevance for understanding pattern coarsening from first principles and
potential implications for dynamics ranging from the early universe to
geophysical dynamics and micro physics.
