  The misalignment mechanism for axion-like particles (ALPs) is a leading
explanation for dark matter. In this work we investigate ALPs with non-periodic
potentials, which allow for large misalignment of the field from the minimum
and make it possible for ALPs to match the relic density of dark matter in a
large part of the parameter space. Such potentials give rise to
self-interactions which can trigger an exponential growth of fluctuations in
the ALP field via parametric resonance, leading to the fragmentation of the
field. The fluctuations later collapse to halos that can be dense enough to
produce observable gravitational effects. These effects would provide a probe
of dark matter even if it does not couple to the Standard Model (or too
feebly). We determine the relevant regions of parameter space in the (ALP mass,
decay constant)-plane and compare predictions in different axion fragmentation
models. These proceedings are a short version of arXiv:2305.03756
