  Classical variable stars called RR Lyrae stars have pulsating outer envelopes
comprised of excited atoms. Here we demonstrate that the qualitative and
quantitative properties of RR Lyrae variables and one subclass of their atomic
scale constituents: singly-excited helium atoms undergoing transitions between
Rydberg states, share a remarkable degree of self-similarity. In terms of
masses, radii, oscillation periods, morphologies and kinematics the stellar and
atomic analogues obey a simple set of discrete self-similar scaling equations.
The concept of stellar/atomic self-similarity may prove useful in the search
for a deeper understanding of both stellar and atomic systems.
