Recent work on imaging electron gasses revealed the beautiful traces of focal caustics formed as the electrons pass over a random background potential. The new phenomenon of branching of the flow pattern was observed, as well as unexpected interference fringes. I discuss these beautiful experiments and the theory behind the observations, which is connected to nonlinear dynamics, chaos, and the correspondence principle. Amazingly, the same phenomena are apparently happening in the oceans, causing freak or rogue waves which sink many ships each year.