10 December 2011

Islamic art and "Magic Eye" images

From a book by Oliver Sacks about the physiology and psychology of perception:
David Brewster, a nineteenth-century scientist… observed a related form of stereo illusion. Gazing at wallpaper with small repetitive motifs, he observed that sometimes, with the proper convergence or divergence of gaze, the patterns might quiver or shift and then jump into startling stereoscopic relief, seeming to float in front of or behind the wallpaper.

it seems likely that such “autostereograms” have been experienced for millennia, with the repetitive patterns of Islamic art, Celtic art, and the art of many other cultures. Medieval manuscripts such as the Book of Kells or the Lindisfarne Gospels, for example, contain exquisitely intricate designs done so exactly that whole pages can be seen, with the unaided eye, in stereoscopic relief. (John Cisne, a paleobiologist at Cornell, has suggested that such stereograms may have been “something of a trade secret among the educated elite of the seventh- and eighth-century British Isles.”)

In the past decade or two, elaborate autostereograms have been widely popularized in Magic Eye books.
--Oliver Sacks, The Mind’s Eye, pp. 137-8.
Those unfamiliar with "Magic Eye" books can read about them at Wikipedia.  The embedded image is "Geometric arabesque tiling on the underside of the dome of the Tomb of Hafez in Shiraz."  For extensive research on Islamic design, visit the Catnaps.org website compiled by TYWKIWDBI reader John Lockerbie.

Addendum:   Those seriously interested in this subject matter should look at the two links submitted by reader Dan Noland: a comparison of Islamic design patterns with the molecular arrangement of quasicrystals,  and another discussing Medieval Islamic architecture, quasicrystals, and Penrose tilings.

Addendum #2:  Here is some additional insight from Mr. Lockerbie:
The asymmetry of the design is interesting in that, as suggested, there may be at least two possibilities, perhaps at least three. Firstly, there is the probability that a number of artisans worked on the ceiling, directed by a master craftsman. Each may have deliberately attempted to work in slightly different and personal interpretations within the overall piece maintaining its form and balance. Secondly, the individual fitting of the tiles may have required small adjustments to the work in order to take up discrepancies both in the tiles as well as in the ground on which they are set.
Thirdly, and a very commonly presented argument in the Islamic world, is that no designed work should be perfect: each must demonstrate an irregularity as to do otherwise would be to show yourself in competition with Allah. 

If the latter is correct, then it's possible that the first two reasons might be actively subsumed within its argument.

Incidentally, the most unusual eccentricity of the design to my eye is the lack of geometrical coherence of the central yellow-based pattern around the central hole. With sixteen-point geometry establishing the surrounding star pattern, I would have anticipated something far better aligned to its points.
That last observation re the asymmetry is quite compelling; I hadn't even noticed that part of the design until he pointed it out.  Interesting.


  1. Hmmm. I have never been able to conjure up the images that others claim to see. :(


  2. I used to get this effect with the regular pattern of perforations in the head-lining of our 1964 Ford Cortina.

  3. Lurker111, I couldn't see magic eye images for the longest time either. No one ever told me that the background patterns are still supposed to be IN focus while you see the 3D image. I had always figured that since you're not focusing where you normally would, the original picture would be blurry. Also, I don't know if it's just me, but it's easier to see the 3D if I take off my corrective lenses. It still takes me a while to work at seeing the 3D images, but now I can see most of them.

    p.s. Oliver Sacks is awesome

  4. gorgeous image... and interesting to see the word "arabesque" in something that has nothing to do with dance.
    Did you notice in the embedded image that the diamond shapes just outside the central part are all different from each other? I wonder what (if any) significance that might have?

  5. I hadn't noticed, Jen, but it's true. And the rest of the pattern isn't strictly repetitive either. There must be an interesting reason for the variability.

  6. Skipweasel beat me to it. I used to enjoy getting the stereoscopic effect from looking at the headliner in my old '59 Chevy Apache pickup! It was just the right distance and repetition to make it pop into depth stereo, even by chance sometimes.

  7. haha yes as kids, me and my cousin discovered this on patterned wallpaper.

    Interestingly, he would do it cross-eyed, while I would go wall-eyed- so we would see opposite effects.

    But magic-eye images require wall-eyedness, so I have always had a preternatural ability to instantly view them.

    Also makes viewing autostereograms without a device possible, and solving "find the 6 differences" puzzles instant.

    Any way to monetize this ability?

  8. There is indeed an interesting reason for their variability. Islamic tilings are frequently Quasicrystaline in nature.

  9. Also an interesting paper on the subject entitled : "Medieval Islamic Architecture, Quasicrystals, and
    Penrose and Girih Tiles: Questions from the Classroom" [pdf].

  10. Excellent. Anyone following this thread who has an interest in art should check out Dan's links - particularly the second one.

  11. What Abbie, David and skipweasel said. I used to stare at the ceiling of our Plymouth Valiant until the dots popped out of the dotted fabric. And then I'd have to touch them to make them pop back. I can imagine my mom looking in the rear view mirror wondering why her daughter was pawing at the roof of the car....

  12. I've never had the ?pleasure of riding in a Plymouth Valiant that I can remember. I've tried searching the web for a photo of the pattern you've described, without any success.

  13. I have a computer monitor that can do 2D to 3D conversion. Out of curiousity I decided to see how it responded to this image. Interestingly, although on the rest of the site it makes text and images hover above the page, whenever this picture was on screen it didn't use any 3D effect anywhere on the screen. I would love to know what this tells us about the algorithms it is using. Further research is required...


  14. Squibfish, does that conversion capabiity have a practical use for your work or something?

  15. The headliner pattern we are remembering is a simple array of offset perforation dots common in headliner fabric of that era. It's probably the most simple stereo pattern possible.
    Search for perforated headliner. Here's one example I found. Some of these images are good enough I can get the 3D effect directly from the photos.


  16. Ahhh! Thank you, David. I recognize that pattern - it's the pattern on Dr. Scholl's Air-Pillo insoles I put inside my shoes!

    I don't have time right now, but maybe next time I'm on a long plane flight, I'll take off my shoe and stare at the bottom of it and see what happens...

  17. Ha! New purpose for shoe gazing! We're just doing some inner-soul work, etc., etc.

  18. Stan,

    Isn't that what got Richard Reid in trouble?


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