Although the density and speed of integrated circuits has grown exponentially during the last decades, so too have costs of fabrication and test facilities. Current computational methods depend on completely reliable hardware, a constraint that greatly increases the degree of fabrication precision required to avoid failure of individual components, and also increases the amount of post-fabrication testing required to confirm correct function. Nature has solved these production problems. The neocortex, is a cellular computer that generates intelligent behavior. But more than this, it constructs and configures itself by replication of a few precursor cells. Each derived cell is equipped with a set of related rules inherited from its functional parents, and by each cell implementing these locally, the overall cell mass is able to achieve global coherent action. Harnessing these principles for artificial fabrication would revolutionize computer technology. Here we propose some first steps towards understanding these developmental construction mechanisms. We will demonstrate, by a fusion of experimental neuroscience, detailed physical simulation, and theoretical analysis, the principles by which a population of real or artificial neurons can grow and assemble themselves into functioning circuits. We will apply these principles by engineering some first self-constructing applications, in which a designed genetic code is inserted into a precursor cell, and so initiates a developmental process of cell division, cell migration, neurite growth, and synaptogenesis. The final global organization of self-constructed neural networks appears to be an attractor in which component neurons are able to satisfy their own local organizational objectives. Thus, unlike existing artificial processing systems, we expect our self-constructed networks to respond to damage or environmental changes by significant self-repair and axonal re-wiring.