Universal behaviors have been identified in cold atoms in a broader
context than in condensed matter systems. Examples include unitary gas,
BEC-BCS crossover, quantum criticality, and atoms in reduced dimensions.
In these examples, scale invariance is frequently assumed, which leads
to a tremendous simplification of both theoretical description and
experimental characterization. Taking broccoli as an example, we show
that the information is only contained on the surface of a unit sphere
in the parameter space. Remarkably, we discuss the breakdown of "scaling
hypothesis" in a special case (unitary Bose gas), and how we can
potentially remedy the situation in complex dimensions.