Form Constants
Images You Don’t Have to Look At
When I began experimenting with digitally-created images, my first algorithm produced a seemingly endless series of images that were all of the same overall form: an intricate circular “wire frame.” Fig. 2 is one of my early wire frames.
Adding color to wire frames
A bare-bones wire frame isn’t particularly pleasing to the eye. To flesh out wire frames and add color, I took advantage of an algorithm that provides individual line, background, and fill colors. As far as I know, this coloring algorithm is available only in the Dyalog version of the APL programming language. It has the remarkable ability to correctly color wire frame images of almost any complexity. Fig. 3, for example, shows how it colored wire frame lines (red), filled areas (cyan), and background (black).
(Readers who are not concerned with the intricacies of computer graphics can skip the following paragraph.) If you look at even the tiniest detail in the image, you’ll see that all eight occurrences of that feature around the center are colored identically. This is surprising because the APL algorithm knows only the locations of the pointy ends of the spikes in the image. It is not given the locations of places where two lines cross. Somehow it figures out the boundaries of areas that are defined partly or completely by intersecting lines. By contrast, one commonly used fill algorithm requires that the entire figure be composed of a network of triangles (more precisely, the figure must meet the conditions of Delaunay triangulation).
Further enhancement of the wire frames
The appeal of the colored wire frames was still rather limited, so I experimented with various post-processing techniques. It turned out that I could get interesting images by applying a sequence of two GIMP/G’MIC-Qt filters to a colored wire frame: first, Artistic/Dream Smoothing and then, second, Colors/Abstraction. Figs. 4 and 5 suggest the kinds of images I can create by applying these filters to wire frames.
Fig. 4 has a radial pattern, also known as a “tunnel” or “funnel”:
Fig. 5 is a spiral, with curved “arms” radiating out from the center:
Some surprising results from psychology and brain science
While experimenting with ways to make the wire frames more interesting, I came across the work of psychologist Heinrich Klüver. Klüver used himself as a guinea pig in a study of visual hallucinations. He ingested a peyote button and carefully documented how his visual field changed under its influence. He noted four recurring patterns, which he dubbed “form constants”:
· lattices (including checkerboards, honeycombs, and triangles)
· funnels or tunnels
· spirals
· cobwebs
Many other investigators since Klüver’s time have reported similar results. The work of Jack Cowan has been especially significant. In Jennifer Ouellette’s article on Cowan in the July, 2018 issue of Quanta magazine she wrote:
“… Jack Cowan of the University of Chicago set out to reproduce those hallucinatory form constants mathematically, in the belief that they could provide clues to the brain’s circuitry. In a seminal 1979 paper, Cowan and his graduate student Bard Ermentrout reported that the electrical activity of neurons in the first layer of the visual cortex could be directly translated into the geometric shapes people typically see when under the influence of psychedelics. ‘The math of the way the cortex is wired, it produces only these kinds of patterns,’ Cowan explained recently. In that sense, what we see when we hallucinate reflects the architecture of the brain’s neural network.”
The form constants are potentially already there in your brain’s wiring — you don’t have to look at them; however, in order to perceive them, you do need to somehow suppress the neural mechanism that inhibits them during normal vision (You can’t go around hallucinating all day!) Peyote and other psychedelics can accomplish this. But Cowan wanted to generate such images mathematically. For brave readers with a strong math background I’ve put several references to research in this area at the end of this article.
An artistic approach to Form Constants
I was intrigued with the idea of algorithmically creating form constants myself, but I recognized that Cowan’s mathematical approach to generating form constants was far too difficult for me. I decided instead to use the fact that my original wire frame images fell into two of Klüver’s categories: (1) “tunnels” or “funnels,” and (2) spirals. I believed I could use image manipulation techniques to simulate psychedelic imagery with my colored wire frames. Some of the results are shown in Figs 6, 7, 8, and 9 below.
Some example images
The challenge of circular symmetry
The circular symmetry of my wire frames images is a challenge. Through repetition of the same basic form over and over these images could easily become tiresome. But the architects who designed the rose windows found in Gothic churches throughout Europe and the Hindu and Buddhist artists who created mandalas were able to produce marvelous designs within the highly constrained form of symmetrical images inside a circle. Perhaps with hard work and some imagination I could wring out of my wire frames some images that other people would find pleasing.
References
All Web sources were accessed on 6/14/2023.
https://isomerdesign.com/countyourculture/2011/03/13/form-constants-visual-cortex/
(https://www.quantamagazine.org/a-math-theory-for-why-people-hallucinate-20180730/)
Ermentrout, G.B. and Cowan, J.D., “A mathematical theory of visual hallucination patterns.” Biol. Cybernet. 34 (1979), no. 3, 137–150.
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“. Neural Computation (The MIT Press) 14 (3): 473–491.
©2023 Stuart Smith. All rights reserved.
