There are three important strange loops that I encountered, after I realized people are contemplating such a term, proposed and extensively discussed by Douglas Hofstadter in his books. Self-referential system is the essence of a strange loop of consciousness, see Liar, Epimenides, Barber, Russell's and Quine’s paradoxes, Gödel's incompleteness theorems, Miranker & Zuckerman theory about consciousness. Chicken or the egg dilemma is a strange loop of evolution. It can be resolved by saying that the egg evolved much earlier than the chicken, although, that egg was not the same kind of egg that appears in the dilemma, ie the one that is laid by chickens and the one chickens hatch from. But still, it's a kind of resolution, provided that we will understand one day the exact mechanism of evolution of multicellular organisms. DNA or enzymes (involved in protein synthesis and folding and in DNA replication) dilemma, and the information flow network between them, is a stran