During brain development, billions of axons navigate over multiple spatial scales to reach specific targets, and so form functional circuits. However, the limited information capacity of the zygotic genome puts a strong constraint on how, and which, axonal routes can be encoded. We propose and validate a mechanism of development that can provide an efficient encoding of this global wiring task. The key principle is that successive mitoses of the neural stem cells induce a hierarchical organization of gene expression patterns in global high dimensional expression space. Provided that mitotic daughters do not stray too far from one another, this hierarchy of gene expression is embedded (with some loss) in 3-dimensional brain space. However, it is sufficiently well embedded to provide a multi-scale map over the final neuronal progeny of development. Thus, a traversal of the gene expression hierarchy has in many instances a dual traversal of brain space and so offers systematic sequences of expression profiles able to guide a growth cone from its source neuron to a collection of remote target neurons. We explain this principle mathematically, and confirm its operation through simulation. Furthermore, we have analyzed gene expression data of developing and adult mouse brains, published by the Allen Institute for Brain Science, and found them consistent with our simulations: gene expression indeed partitions the brain into a global spatial hierarchy of nested contiguous regions that is stable over pre- and postnatal time. We use this experimental data to demonstrate that our axonal guidance algorithm is able to robustly extend arbors over long distances to specific targets, and that these connections result in a qualitatively plausible connectome.