We have constructed a computational platform suitable for examining emergence of shape homeostasis in simple three-dimensional cellular systems. An embryo phenotype results from a developmental process starting with a single cell and its genome. When coupled to an evolutionary search, this platform can evolve embryos with particular stable shapes and high capacity for self-repair, even though repair is not genetically encoded or part of the fitness criteria. With respect to the genome, embryo shape and self-repair are emergent properties that arise from complex interactions among cells and cellular components via signaling and gene regulatory networks, during development or during repair. This report analyzes these networks and the underlying mechanisms that control embryo growth, organization, stability, and robustness to injury.