One of the most important characteristics observed in metabolic networks is
that they produce themselves. This intuition, already advanced by the theories
of Autopoiesis and (M,R)-systems, can be mathematically framed in a weird
looking equation, full of implications and potentialities: f(f) = f . This
equation (here referred as Ouroboros equation), arises in apparently dissimilar
contexts, like Robert Rosens synthetic view of metabolism, hyperset theory and,
importantly, untyped lambda calculus. In this paper we survey how Ouroboros
equation appeared in those contexts, with emphasis on Rosens (M,R)-systems and
Dana Scotts work on reflexive domains, and explore different approaches to
construct solutions to it. We envision that the ideas behind this equation, a
unique kind of mathematical concept, initially found in biology, would play an
important role towards the development of a true systemic theoretical biology.