The emergence of large-scale brain networks, and their continual refinement, represent crucial developmental processes that can drive individual differences in cognition and which are associated with multiple neurodevelopmental conditions. But how does this organization arise, and what mechanisms govern the diversity of these developmental processes? There are many existing descriptive theories, but to date none are computationally formalized. We provide a mathematical framework that specifies the growth of a brain network over developmental time. Within this framework macroscopic brain organization, complete with spatial embedding of its organization, is an emergent property of a generative wiring equation that optimizes its connectivity by renegotiating its biological costs and topological values continuously over development. The rules that govern these iterative wiring properties are controlled by a set of tightly framed parameters, with subtle differences in these parameters steering network growth towards different neurodiverse outcomes. Regional expression of genes associated with the developmental simulations converge on biological processes and cellular components predominantly involved in synaptic signaling, neuronal projection, catabolic intracellular processes and protein transport. Together, this provides a unifying computational framework for conceptualizing the mechanisms and diversity of childhood brain development, capable of integrating different levels of analysis – from genes to cognition. (Pre-print: https://www.biorxiv.org/content/10.1101/2020.08.13.249391v1)