  We study dynamics of the classicalization phenomenon suggested in
arXiv:1010.1415, according to which a class of non-renormalizable theories
self-unitarizes at high-energies via creation of classical configurations
(classicalons). We study this phenomenon in an explicit model of
derivatively-self-coupled scalar that serves as a prototype for a
Nambu-Goldstone-St\"uckelberg field. We prepare the initial state in form of a
collapsing wave-packet of a small occupation number but of very high energy,
and observe that the classical configuration indeed develops. Our results
confirm the previous estimates, showing that because of self-sourcing the
wave-packet forms a classicalon configuration with radius that increases with
center of mass energy. Thanks to self-sourcing by energy, unlike solitons, the
production of classicalons dominates the high-energy scattering. In order to
confront classicalizing and non-classicalizing theories, we use a language in
which the scattering cross section can be universally understood as a geometric
cross section set by a classical radius down to which waves can propagate
freely. The difference is, that in non-classicalizing examples this radius
shrinks with increasing energy, whereas in classicalizing theories expands and
becomes macroscopic. We study analogous scattering in a Galileon system and
discover that classicalization is less efficient there. We thus observe, that
classicalization is source-sensitive and that Goldstones pass the first test.
