The joint action of $x\mapsto2x$ (mod 1) and $x\mapsto3x$ (mod 1) has a number of remarkable properties. Among them is that ever joint orbit is either finite or dense. Of course any minimal system has that property, but the x2,x3 system is special because it has a dense set of finite orbits that intermingle with dense orbits. In joint work with B. Kra and S. Schmieding, we abstract this property to what we call a chaotic almost minimal (CAM) system. I this talk I will discuss some properties of CAM systems, showing their similarities to and differences from the x2,x3 system.