  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. Despite the apparent complexity of such patterns, they
are based on just a small number of fundamental forms described by the theory
of catastrophe optics. Here, we demonstrate caustics in the matter waves of an
atom laser, extending catastrophe optics to catastrophe atom optics. We
showcase the generic forms of fold and cusp caustics, and exploit internal
state manipulation to trace the flow of atoms. Atom optics affords new
perspectives for fundamental science, metrology, atom interferometry and
nano-fabrication techniques. Exploring the role of caustics in this context may
lead to innovation as the generation of caustics is inherently robust, and
leads to a variety of pronounced and sharply delineated features.
