  We provide a one-to-one map between the spin correlations and certain
three-dimensional shapes, analogous to the map between single spins and Bloch
vectors, and demonstrate its utility. Much as one can reason geometrically
about dynamics using a Bloch vector -- e.g. a magnetic field causes it to
precess and dissipation causes it to shrink -- one can reason similarly about
the shapes we use to visualize correlations. This visualization demonstrates
its usefulness by unveiling the hidden structure in the correlations. For
example, seemingly complex correlation dynamics can be described as simple
motions of the shapes. We demonstrate the simplicity of the dynamics, which is
obscured in conventional analyses, by analyzing several physical systems of
relevance to cold atoms.
