This paper explores a formal model of autopoiesis as presented by Maturana, Uribe and Varela, and analyzes this model and its implications through the lens of the notions of eigenforms (fixed points) and the intricacies of Goedelian coding. The paper discusses the connection between autopoiesis and eigenforms and a variety of different perspectives and examples. The paper puts forward original philosophical reflections and generalizations about its various conclusions concerning specific examples, with the aim of contributing to a unified way of understanding (formal models of) living systems within the context of natural sciences, and to see the role of such systems and the formation of information from the point of view of analogs of biological construction. To this end, we pay attention to models for fixed points, self-reference and self-replication in formal systems and in the description of biological systems.