Math and Hallucinations

Is there something in our brains that make humans see the same geometric patterns during drug use, illness, or near-death experiences? Even pressing on our eyes can induce the same spirals other people see. Research by professor of Mathematical and Computational Neuroscience Paul Bressloff and his colleagues at Oxford shows that these patterns are formed in the first visual field of the brain, or V1.
An object or scene in the visual world is projected as a two-dimensional image on the retina of each eye, so what we see can also be treated as flat sheet: the visual field. Every point on this sheet can be pin-pointed by two coordinates, just like a point on a map, or a point on the flat model of V1. The alternating regions of light and dark that make up a geometric hallucination are caused by alternating regions of high and low neural activity in V1 — regions where the neurons are firing very rapidly and regions where they are not firing rapidly.

A closer look at the types of specialized neurons in the V1 field and how they interact with each other explains the geometric patterns.
Bressloff and his colleagues used a generalised version of the equations from the original model to let the system evolve. The result was a model that is not only more accurate in terms of the anatomy of V1, but can also generate geometric patterns in the visual field that the original model was unable to produce. These include lattice tunnels, honeycombs and cobwebs that are better characterised in terms of the orientation of contours within them, than in terms of contrasting regions of light and dark.

That's about as simple as I can make it in a short blurb; the entire article explains it better. Yes, there is math involved. Link -via Metafilter

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