Modular and hierarchical structures are ubiquitous in the brain. Two distinct hypotheses for such morphogenesis involve genetic specification (e.g. chemoaffinity and positional information) or spontaneous structure emergence from symmetry breaking (e.g. pattern formation). Indeed, there is rich evidence supporting both hypotheses in different systems, and more recently evidence that both processes might interact, for instance with genetic specification providing initial but relatively low-information positional guidance or growth rules, and emergent self-organization actually generating the structures. In this talk, I will consider the emergence of two systems in the brain: the visual processing hierarchy with topographic and spatial structure, and the set of functionally discrete and independent velocity-integrating grid cell networks organized spatially along an anatomical gradient. I will describe how simple growth and competition rules driven by spontaneous activity can lead to the genesis of structured sensory processing hierarchies, and how genetically specified smooth gradients with purely local recurrent interactions on two scales can lead to global module emergence. These models make numerous predictions about connectivity and gene expression in the brain. If time permits, I will discuss how biological principles can be abstracted to drive modularity in artificial neural networks. In sum, simple growth rules, competitive local interactions and smooth gradients can produce rich emergent order on multiple scales in the form of maps, modules, and hierarchies, with resulting predictions that bridge scales from genes to connectivity to function.

Replaced by Center for Living Systems student-organized special lecture.