Computational reflection uses software architectures that are capable of self-modification at runtime. These systems have implementations between two extremes: procedural reflection, in which unlimited self-modification is available at the expense of infinite recursion; and declarative reflection, which uses pre-defined metrics to drive the self-modification and is hence limited in scope. Biological processes also exploit the concept of reflection, where natural selection drives the process of modification. The concept of a 'program' in computing has an analogy with an individual member of a species. The process of life is discretised into a series of autonomous systems, each of which creates modified versions of itself as offspring. This paper unifies the concept of computational reflection with biological systems via a new analysis of von Neumann's Universal Constructor. The result is a bio-reflective architecture that is capable of unconstrained self-modification without the problems of infinite recursion that exist in the computational counterparts. The new architecture is a blueprint for applications in Artificial Life studies, Evolutionary Algorithms, and Artificial Intelligence.