  We study various aspects of the scattering of generalized compact oscillons
in the signum-Gordon model in (1+1) dimensions. Using covariance of the model
we construct traveling oscillons and study their interactions and the
dependence of these interactions on the oscillons initial velocities and their
relative phases. The scattering processes transform the two incoming oscillons
into two outgoing ones and lead to the generation of extra oscillons which
appear in the form of jet-like cascades. Such cascades vanish for some values
of free parameters and the scattering processes, even though our model is
non-integrable, resemble typical scattering processes normally observed for
integrable or quase-integrable models. Occasionally, in the intermediate stage
of the process, we have seen the emission of shock waves and we have noticed
that, in general, outgoing oscillons have been more involved in their emission
than the initial ones i.e. they have a border in form of curved world-lines.
The results of our studies of the scattering of oscillons suggest that the
radiation of the signum-Gordon model has a fractal-like nature.
