This paper introduces dynamic composite physicalizations, a new class of physical visualizations that use collections of self-propelled objects to represent data. Dynamic composite physicalizations can be used both to give physical form to well-known interactive visualization techniques, and to explore new visualizations and interaction paradigms. We first propose a design space characterizing composite physicalizations based on previous work in the fields of Information Visualization and Human Computer Interaction. We illustrate dynamic composite physicalizations in two scenarios demonstrating potential benefits for collaboration and decision making, as well as new opportunities for physical interaction. We then describe our implementation using wheeled micro-robots capable of locating themselves and sensing user input, before discussing limitations and opportunities for future work.