Research on scale invariance and self similarity
Apparently fractals are self similar but not fully scale invariant. Dimensionless constants, like our apparently fine tuned and non-axiomatizable universal parameters, are scale invariant (and thus have universal effect). Many aspects of phase transitions are scale invariant.
Laurent Nottale does extensive work in scale invariance. We should ask him for a reference that distinguishes both processes in multiple domains.
Scale relativity corner "A place to talk about Scale Relativity, its foundations, tools and results."