Though migraine causes great suffering for millions of people, there has been much success, in the last decade or two, in understanding what goes on during attacks, and how to prevent or minimize them. But we still have only a very primitive understanding of what, to my mind, are among the most intriguing phenomena of migraine — the geometric hallucinations it so often evokes. What we can say, in general terms, is that these hallucinations reflect the minute anatomical organization, the cytoarchitecture, of the primary visual cortex, including its columnar structure — and the ways in which the activity of millions of nerve cells organizes itself to produce complex and ever-changing patterns. We can actually see, through such hallucinations, something of the dynamics of a large population of living nerve cells and, in particular, the role of what mathematicians term deterministic chaos in allowing complex patterns of activity to emerge throughout the visual cortex. This activity operates at a basic cellular level, far beneath the level of personal experience. They are archetypes, in a way, universals of human experience.