Unit visualizations are a family of visualizations where every data item is represented by a unique visual mark-a visual unit-during visual encoding. For certain datasets and tasks, unit visualizations can provide more information, better match the user's mental model, and enable novel interactions compared to traditional aggregated visualizations. Current visualization grammars cannot fully describe the unit visualization family. In this paper, we characterize the design space of unit visualizations to derive a grammar that can express them. The resulting grammar is called ATOM, and is based on passing data through a series of layout operations that divide the output of previous operations recursively until the size and position of every data point can be determined. We evaluate the expressive power of the grammar by both using it to describe existing unit visualizations, as well as to suggest new unit visualizations.