Heinrich Klüver (1897-1979) was an experimental psychologist at University of Chicago who did groundbreaking work in the emerging field of visual hallucination from the late 1920s through the 1970s. He conducted a range of self-experiments using peyote in a lab setting, recording as much subjective and objective data as he could while high.
Image by Psion005 @ deviantart. Used with permission.
He noted that this work might be useful for anthropologists and art historians looking at primitive art and cave paintings, where these patterns have sometimes been depicted. Subsequent neurologists have identified the hexagonal shape of structures in the primary visual cortex as a likely source for these patterns, when combined with "stripes" of neural activity (inhibition and excitation) that can occur under certain conditions, including sensory deprivation, pressing hard on both eyes, and when taking hallucinogens. These effects were even observed in some blind people.
This is related to the mathematics of periodicity I mentioned in the article on Hans Jenny and cymatics.
Jack Cowan, also of University of Chicago, has continued this interesting work and has helped develop mathematical formulas that model how these structures in the cortex generate these images. Basically, the visual cortex sends out waves in periodic bursts that ebb and flow, resulting in the amazing geometric patterns many people experience.
For details, here's Dr. Cowan lecturing on the topic:
Geometric Visual Hallucination (Jack Cowan)