  Typically discussed in the context of optics, caustics are envelopes of
classical trajectories (rays) where the density of states diverges, resulting
in pronounced observable features such as bright points, curves, and extended
networks of patterns. Here, we generate caustics in the matter waves of an atom
laser, providing a striking experimental example of catastrophe theory applied
to atom optics in an accelerated (gravitational) reference frame. We showcase
caustics formed by individual attractive and repulsive potentials, and present
an example of a network generated by multiple potentials. Exploiting internal
atomic states, we demonstrate fluid-flow tracing as another tool of this
flexible experimental platform. The effective gravity experienced by the atoms
can be tuned with magnetic gradients, forming caustics analogous to those
produced by gravitational lensing. From a more applied point of view, atom
optics affords perspectives for metrology, atom interferometry, and
nanofabrication. Caustics in this context may lead to quantum innovations as
they are an inherently robust way of manipulating matter waves.
