Nature is certainly not invariant under changes of scale. Phenomena and laws are characterized by parameters that determine their physical dimensions. However, while the complexity of some many-body systems may stem from a profusion of distinct scales, rich structures (such as fractals) exist even when there is no more than one essential scale associated with *discrete* scale invariance. I will discuss how intrinsically quantum-mechanical structures with unique properties, sometimes labeled "Efimov physics", emerge in nuclear and some closely related atomic systems from a contact three-body force.