  We study the out-of-equilibrium dynamics induced by a local perturbation in
fracton field theory. For the ${\mathbb Z}_4$ and ${\mathbb Z}_8$-symmetric
free fractonic theories, we compute the time dynamics of several observables
such as the two-point Green function, $\langle \phi^2 \rangle$ condensate,
energy density, and the dipole momentum. The time-dependent considerations
highlight that the free fractonic theory breaks causality and exhibits
instantaneous signal propagation, even if an additional relativistic term is
included to enforce a speed limit in the system. We show that it is related to
the fact that the Lieb-Robinson bound does not hold in the continuum limit of
the fracton field theory, and the effective bounded speed of light does not
emerge. For the theory in finite volume, we show that the fracton wave front
acquires fractal shape with non-trivial Hausdorff dimension, and argue that
this phenomenon cannot be explained by a simple self-interference effect.
