Math is awesome! I’m guessing some of you disagree, so let me try to change your mind with the help of this article I just read. The article, called “Uncoiling the Spiral: Maths and Hallucinations,” describes the work of several different researchers and how they are able to mathematically model hallucinations (obviously). The author first describes Klüver’s four form constants of hallucinations: funnel, spiral, honeycomb, and cobweb (pictured above). These hallucinations, which consist of spirals, circles, and rays that radiate from the center, correspond to stripes of neural activity in the V1 region (the first area of the visual cortex to process visual information) inclined at certain angles. Basically, in a horrendous simplification, geometric patterns formed in the visual cortex by neural activity directly translate to the visualized hallucination pattern.
The aspect I found really interesting was that Paul Bressloff and his colleagues have been able to build upon other mathematical models of biological phenomena to nearly replicate these hallucinations. They modified mathematical modeling of coat pattern formation in animals developed by Alan Turing (How the Leopard Got Its Spots), incorporating additional complexities as they went along, to produce a simulated hallucination that is nearly identical to a ‘natural’ hallucination (see below).
Although I didn’t grasp all the details of the math, I am still amazed by how much math is able to explain in nature!
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Jack Cowan presented a video lecture about these studies and subject back in 2006.