In 2001, Paul Bressloff of the University of Utah, together with four colleagues from elsewhere, made a mathematical assault on the — until then — lack of understanding of what happens in a so-called “geometric hallucination”. Here’s Bresloff:
Here’s the study:
“Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex,” P. C. Bressloff, J. D. Cowan, M. Golubitsky, P. J. Thomas and M. Wiener, Phil. Trans. Roy. Soc. B, 40 :299-330 (2001). [Artistic recreations of the hallucinations are reproduced here, right.] The paper begins by saying:
“This paper is concerned with a striking visual experience: that of seeing geometric visual hallucinations…. This paper describes a mathematical investigation of their origin based on the assumption that the patterns of connection between retina and striate cortex (henceforth referred to as V1) — the retinocortical mapöand of neuronal circuits in V1, both local and lateral, determine their geometry.”
Such hallucinations had been classified, much earlier, by psychologist Heinrich Klüver. The paper cites Klüver’s 1966 book Mescal and Mechanisms of Hallucinations (which was a reprint of things that Klüver had published decades earlier):
Halucinatory images were classified by Kluver into four groups caled form constants comprising (i) gratings, lattices, fretworks, ¢ligrees, honeycombs and chequer-boards, (ii) cobwebs, (iii) tunnels, funnels, alleys, cones and vessels, and (iv) spirals.
(Thanks to investigator J. Muegge for bringing this to our attention.)