Self-replication is central to all life, and yet how it dynamically emerges in physical, non-equilibrium systems remains poorly understood. Von Neumann's pioneering work in the 1940s and subsequent developments suggest a natural hypothesis: that any physical system capable of Turing-universal computation can support self-replicating objects. In this work, we challenge this hypothesis by clarifying what computational universality means for physical systems and constructing a cellular automaton th...