In 1926, Heinrich Klüver systematically studied the effects of mescaline (peyote) on the subjective experiences of its users. In addition to producing hallucinations characterized by bright, "highly saturated" colors and vivid imagery, Klüver noticed that mescaline produced recurring geometric patterns in different users. He called these patterns 'form constants' and categorized four types: lattices (including honeycombs, checkerboards, and triangles), cobwebs, tunnels, and spirals.
In 1988 David Lewis-Williams and T.A. Dowson incorporated the form constant into their Three Stages of Trance model, the geometric shapes comprising the visuals observed in the model's first stage.
Klüver's form constants have appeared in other drug-induced and naturally-occurring hallucinations, suggesting a similar physiological process underlying hallucinations with different triggers. Klüver's form constants also appear in near-death experiences and sensory experiences of those with synesthesia. Other triggers include psychological stress, threshold consciousness (hypnagogia), insulin hypoglycemia, the delirium of fever, epilepsy, psychotic episodes, advanced syphilis, sensory deprivation, photostimulation, electrical stimulation, crystal gazing, migraine headaches, dizziness and a variety of drug-induced intoxications. These shapes may appear on their own or with eyes shut in the form of phosphenes, especially when exerting pressure against the closed eyelid.
It is believed that the reason why these form constants appear has to do with the way the visual system is organized, and in particular in the mapping between patterns on the retina and the columnar organization of primary visual cortex. Concentric circles in the retina are mapped into parallel lines in visual cortex. Spirals, tunnels, lattices and cobwebs map into lines in different directions. This means that if activation spreads in straight lines within the visual cortex, the experience is equivalent to looking at actual form constants.
Author Michael Moorcock once observed in print that the shapes he had seen during his migraine headaches resembled exactly the form of fractals. The diversity of conditions that provoke such patterns suggests that form constants reflect some fundamental property of visual perception.
Cultural significance 
The practice of the ancient art of divination may suggest a deliberate practice of cultivating form constant imagery and using intuition and/or imagination to derive some meaning from transient visual phenomena.
Psychedelic art, inspired at least in part by psychedelic substances, frequently includes repetitive abstract forms and patterns such as tessellation, Moiré patterns or patterns similar to those created by paper marbling, and, in later years, fractals. The op art genre of visual art created art using bold imagery very like that of form constants.
See also 
- Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J.; Weiner, Matthew C. (March 2002). "What Geometric Visual Hallucinations Tell Us About the Visual Cortex" (fee required). Neural Computation (The MIT Press) 14 (3): 473–491. doi:10.1162/089976602317250861. PMID 11860679. Retrieved 2009-04-21.
- Text from "Hallucinogens and Creativity" page by Susan Opar
- "Spontaneous pattern formation in large scale brain activity: what visual migraines and hallucinations tell us about the brain"; online video of lecture by Jack Cowan
- "Spontaneous pattern formation in the primary visual cortex"