Archive for January, 2013

Post Script to An Odd Visual Effect in a Tibetan Rug

Posted in Uncategorized on January 30, 2013 by rjohn

After, we had published and announced Part 2 in this sequence of posts, I received two additional submissions.  I am not going to announce it, but am simply publishing this postscript so as to include them.

First, Pat Weiler wrote saying  “I am pretty sure that this optical illusion has been present in other art forms prior to this use, such as tile work and mosaics.”

He sent along a “modern” but “related” further example.

stair rug

And Dave Scherbel wrote:

“…You guys are working very hard at this.  Let me propose a very simple explanation.  Please refer to the photoshopped figure below of your “head on” shot.

annotated tibetanrugstraighton copy

“There are twice as many blue squares than white ones. Forget the light/dark blue issue: when seen from a foreshortened view, they appear as just blue. The geometry is such that when you stand away from the center of the pattern but along a 45 degree view (such as the “perspective” view photograph), you see blue parallel lines extending along your line of sight. That is because the pattern creates a continuous unbroken line with a width 1/2 the diagonal of the squares.  See the parallel lines I’ve drawn on the rug with the red arrows indicating line of sight. This effect happens when viewing the upper right and lower left quadrants. 

“However, when viewing the upper left and lower right quadrants, the continuous blue lines extend basically right to left to line of sight.  See black arrow showing line of sight extending perpendicular to the continuous blue line in the upper left.  When you return to the “heads on” view, you are deprived of the any sight line of a continuous blue line with the width 1/2 the diagonal of the squares.

“Understand that foreshortening has a role to play in this also.  From the “perspective view”, each continuous blue line, parallel to your line of sight, is visually squeezed, top to bottom, making the blue lines darker and a stronger identity.  In contrast, when viewing the top and bottom quadrants, the foreshortening only effect each individual square separately, thus maintaining the spacial identity of the white squares relative to the blue line. In the parallel line view, the white squares only seem to give the continuous blue lines a saw-tooth edge look.

“Now here’s the fun part.  This only works because the rug viewed is relatively small.  Consider a very large rug, large room size, with the same sized squares.  Stand on the same 45 degree line  from the center, but further away from the center.  Now, the view will change dramatically as you look from the center to the right or left.  Looking parallel to the right side of the rug you will now be looking at the squares pattern effectively in the “heads on” view and will not experience the blue lines: in front of you you will be seeing that part of the rug as experience in your “head on” view.  Moving your view back to the left towards the center, at some point in the rotation, the lines will seem to re-appear again and you will see the center section of the rug in the “perspective” view.”

I thanked David for this, and then wrote him:

“It seems like a more detailed and extensive version of Matthew Polk’s explanation based on his “lines” replication.  But it’s clearly a useful, “visually-cued” elaboration and one based on the rug itself.

“If we treat the two blues as one, does that convert the image to a 2×2 format, and, if so, why doesn’t the effect seem to be visible in William Bateson’s 2×2 replication?”

David said:

“In response to your question, I took William’s three color diagram (white/gray/black) and converted the gray squares to black, so it’s only two “color” now.

gray to black

“As you can see …, except at a few selected 2by2 boxes in the pattern (e.g., near the center), it does not convert to 2×2: it’s something like 33×67 in a 10×10 box; 8×17 in a 5by5 box; 5×11, in a 4by4 box; and 3×1 in a 2by2 box. 

“So the ratio varies depending on the number of squares on the sides of the selected box,  but most likely is never same/same above 2×2 boxes near where the pattern changes directions.

“However, I believe it diminishes any solutions involving the blue vs light-blue squares.”

My thanks to Pat and David for these additional contributions.


R. John Howe

Part 2 of an Odd Visual Effect in a Tibetan Rug

Posted in Uncategorized on January 27, 2013 by rjohn

Readers of the first post on this subject will have seen that Daniel Miller, long a Himalayan “range ecologist,” and student of Tibetan ways and textiles, sent me a couple of images of a Tibetan rug he owns.

The first image was “head-on” and looked like this.


A second photograph of this rug, taken from an angled perspective looked like this.


Dan, who has been looking at Tibetan rugs for maybe 30 years plus, said he’d not previously seen this effect and wondered whether others of my readers might have.

So, we put these two images up in the first post on this site and asked.  There have been a variety of responses and proposals.

A large number of folks with deep experience in Tibetan textiles said they had not seen this effect in other rugs.  One experienced person said that he had seen it “lots of times.”

The explanatory proposals seem to group as follows:

1. Illusionistic effects produced by changing knot direction or pitch in different parts of the same weaving (e.g., asymmetrical open right and asymmetrical open left).

2. Illusionistic effects produced by varying such things as the width of squares or some other design area or device.

 3. Illusionistic effects produced by change in perspective.

 Several respondents suspected that this effect might have been reproduced by proposal 1.

Dan was asked to take pictures of the back of his rug to see whether that provided any hints about the likelihood that pitch of the knot might be implicated.

The question of whether this effect might be produced by the character of the weave is a legitimate one since examples of it are known.  Rugs with silk pile famously produce dramatic differences viewed from opposite ends and there are rugs known in which the character of the weave produces different effects in different parts of the rug when viewed from different perspectives. 

Matthew Polk, indicated that he knows of such an example:

“…I have seen a rug that produced an illusion due to direction of the knots. It’s a modern silk Isfahan owned by my sister and her husband. Viewed with the warps vertically the knots to the left of center face one way and to the right face the other. Viewed from one side the design on the near side is clear while the other side looks blank…”

Daniel Miller provided three additional images of his rug, including two of its back.

He reported that the knotting was “straight Tibetan weaving.”  Here are his additional photos.

bluecheck back

bluecheck back 2

bluecheck 1

That seemed to indicate that this effect is not produced by “knot direction” or “pitch” and the like.

Next, were respondents who spoke to explanation 2:  Illusionistic effects produced by varying such things as the width of squares or some other design area or device.

The Dutch scholar, Koos De Jong, who is about to publish a book on Chinese saddle covers, wrote to say that he is treating “illustionistic” effects in them.

He shared some images, the most accessible of which is from the McMullan Collection.


You can see that a kind of three dimensional effect is created by varying interior areas of the piece as well as the width of its outside borders.

Here is a 19th century U.S. hooked rug that exhibits a similar 3-D effect in the drawing of its field.


Color and shape of design elements have been used to create a three-dimensional effect.

A third example is a quilt.

Bevs First Optical Illusion Quilt

Here the height or width of the rectangular design elements have been varied to create a distorting illusion. 

Quite a few U.S. coverlets with “overshot” designs exhibit this kind of distortion.  So do some Escher designs, like the one below.


When we look again at Daniel Miller’s Tibetan piece,


we can see that although colors vary, the shape and size of the squares do not.  So, although color may be implicated in this illusionistic effect,


size and shape of its design elements are not.  We need to look further for a real explanation and our third alternative, above, illusion created primarily by change in perspective seems to the one that offers the best chance of explanation.

I sent an image of what seemed to me a similar checkerboard rug to Wendel Swan and asked him to skew it as the image above of Daniel Miller’s piece is in the second paragraph.  He did, but the distinctive visual effect we can see in Dan’s rug did not appear.

But Matthew Polk sent me the line image below, and said:

“Interesting optical illusion (ed. referring to the Tibetan rug) which I’ve not seen before. You can duplicate the effect by printing this page with the drawing below. Look at the page straight on and it’s much like your rug. However, turn the page so that you’re looking from a corner and tilt so that you’re viewing at a low angle then the quadrant pattern will appear.”


I followed Matthew’s instructions and a illusion effect like that in Dan’s rug appeared.

Matthew explained:

“The reason it works is this. When you look at the image straight on all the lines and spaces in each quadrant all have equal weight. When you view from a corner at a low angle the lines and spaces perpendicular to your view blur creating an almost monochrome effect in those two quadrants while the lines and spaces in the other two quadrants are aligned with your point of view remaining clear and distinct. This makes them suddenly jump out of the plane of view. One wonders whether the illusion was discovered accidentally then reused as a traditional design motif.”

I also received a graphic from William Bateson.  William’s version replicated the three-color variation of the Tibetan rug.


William’s viewing instruction was like Matthew’s:  Print off the image.  Lay it on a table and view it from a corner at a low angle.

I did and, again, an illusion, like that in Dan’s rug appeared.

About William’s graphic Matthewe Polk said:

“This graphic is a better representation of what’s happening in the carpet and works for the same reasons.  Sighting at a low angle from a corner the viewer sees the long lines of white squares in two quadrants whereas the white lines cross the viewing angle at 90 degrees in the other two quadrants creating a visual contrast between the quadrants.”

William, subsequently, tested whether this illusion effect could be produced with a two color checker board and found that it could not.


About the graphic above, Matthew Polk said:

“The 2×2 graphic doesn’t work because the pattern is uniform across the entire rectangle.”

Explaining his sense of the requirements of a graphic that produces the visual effect in this Tibetan rug and wondering about other possibilities William said:

“I think it is necessary that the design be symmetric about both the major and minor axes, just as are both Polk’s and the Tibetan carpet. 

“Now the question is whether other geometric design carpets–Tibetan and others–are symmetric in this way. 

“In the Tibetan case, symmetry requires that the carpet have an odd number of rows and lines of squares in order to maintain (almost) the rule that no square touch another like-colored square except at diagonal corners.  This rule is violated only around the center-most square. 

“What do other three-colored, square-patterned weavings look like?  Surely this has been discovered by cloth weavers.

“And, if Polk’s explanation works for lines and squares, how would it be manifest, if at all, in triangles or hexagons?  Surely one of the TM regulars is a topologist.”

I asked Carol Bier, who has studied, curated and published on the relationships between mathematics and textile design.  Her exhibition on “Symmetry and Pattern” at the TM a few years ago is still visible on Drexel University’s Math Forum.

Carol said: “

You’re right — it’s definitely visible and a very interesting phenomenon. It does seem to be related to perception and anamorphism, but I’m not sure it would be considered a topological effect since it is in the plane.

 Here’s a definition of anamorphism, which seems to fit (, accessed 1/17/13):

an·a·mor·phic [an-uh-mawr-fik] Show IPA


1.Optics. having or producing unequal magnifications along two axes perpendicular to each other.

In one email, as we discussed his Tibetan piece and the effects visible in it, Dan Miller said in part:

“I wonder if the weaver of this blue checkerboard Tibetan rug had any idea of the illusion effect the design would have when the rug was taken off the loom and put on the floor and viewed from a corner at a low angle? Or, was the weaver just weaving a nice carpet with a geometric design? I guess we will never know.”

I decided to contact Jeff Spurr, with whom I’d had an exchange about weaver intentionality in another context.  Jeff said in this previous exchange that he tended to see most of the effects we experience in rugs as the result of weaver intention.

But looking at the images of this rug and the things that had been said about it, he said:

“I have no basis for true judgement in regard to this particular phenomenon. There is no doubt that “tumbling blocks,” whether in a hooked rug or log cabin-style quilt, features an illusion of depth quite deliberately achieved. I am more inclined, in the case of the Tibetan rug to assume that the rather simple checkerboard was the intended design, and the added perspectival feature was incidental.”

Jeff also provided images and some words about two Borneo rattan mats (Punan ethnic group), and one African raffia textile (Kuba kingdom)] that exhibit effects related to that we see in the Tibetan rug.

“I am attaching a photo of one of the plainer Borneo mats in my collection.. It is somewhat easier if you zoom in a bit, but you will first note that the field design is a chevron; however, looked at just a bit differently -without the dramatic change in perspective demanded in the case of the Tibetan rug – and you will suddenly see it as a stepped design. Believe me, it works both ways, although the chevron design is basic.”

Spurr 1


Spurr-Mat-Punan 01

In the second example I am attaching, another principle seems to be at work. Rather than the challenges of simplicity, the complexity of this design defeats any attempt to see it in only one way, several options presenting themselves in turn.”

Spurr 2

 Spurr-Mat-Punan 03

“The third image is of a large Kuba (Congo) raffia square in an incredibly rare technique, not the usual pile with contrasting lines of embroidery, but lateral floats about one-third inch long in contrasting black and natural creating the design. I know of only one other example in this technique (in the collections of the MFA Boston). Unfortunately, the lousy photo does not effectively reveal the remarkable “op” effects characteristic of this rare type. Unlike the other cases, this is simply “there,” but utterly unexpected given what we are used to from the standard pile examples and also those that are all in standard Kuba embroidery stitch.”

Spurr 3

Spurr-KubaSquare-TypeB 1-B


This is John Howe, talking again:

If you print off Jeff’s three examples and view them from various angles you will see that Spurr 1 exhibits effects similar to those in the Tibetan rug when viewed a) directly into a short side and b) directly into a long side, with the piece positioned square with your line of vision.

When viewed from a corner at a low angle, both Spurr 2 and Spurr 3 exhibit effects similar to those in the Tibetan rug.  These effect are clearer in Spurr 3 because its design elements have more width.

Spurr 2 speaks to another aspect of related visual phenomena.  It is generally admitted that lighter colored design devices are experienced as being closer than darker ones.  But if you look at Spurr 2 from two different (and not opposing) corners you will see that the light colored devices are more prominent in one perspective and the darker colored ones are so when viewed from the other perspective.  This demonstrates that the phenomenon that Matthew Polk first described and replicated is stronger than is the effect of light vs dark coloration.

Wendel Swan sent me two images of a contemporary rug woven by the textile authority Belkis Balpinar.


Wendel said:

“…I have no doubt that she both intended and achieved optical illusions.

On the left, it seems to mound up


while on the right


the same rug seems to spiral downward.

“The effect is due to the perspective of the viewer.”

And to push such things a little further, Doug Klingensmith, a materials scientist and textiles collector in California, sent me another example, with comment.  He said:

“The effects you discuss strike me as sort of cognitive psycho-physiology – combining the nature of optical perception and the predispositions in the mind of the viewer – intentionally fooling a trained brain a-la M.C. Escher, or just accidentally triggering a neurological response with a particular pattern and angle.

“Perhaps there are studies in optical physiology that identify the way in which our eye/brain system is fooled.”

 Here are two photos that Doug provided “…of the same room with the same black lines painted on the wall –


Doug said: “…only the viewing angle is changed. I have seen some things like this in real space and it is trippy.”

As I was about to “go to press” with this Part 2 post, one experienced participant in these discussions said that 1) I had “gone on” a bit about this effect (and that is true), and 2) that he felt that the effects being discussed often do not rise to a level that merits their description as “optical illusions.”

My own thought is that, no matter how they are most properly described, there is something interesting to be seen, here, and they have been the occasion for at least moderate pondering by some pretty experienced folks, so I’m glad that Dan Miller brought his Tibetan rug and its visual effect to our attention, and find that I have enjoyed poking about for knowledgeable indications of what and why it is.

My thanks to the participants named here, and to others, who wrote me, and often provided me with additional examples, on the side, for their contributions.

Now, since we’re finished, let me pass on three sidewalk chalk drawings that Doug Klingensmith also sent me that show how quickly a conversation like this can go out of control.





R. John Howe

Related, Recently, or About to be Published, Books


Daniel Miller (ed,), “Auspicious Carpets: Tibetan Rugs and Textiles,”  Blurb, 2009, available in paper-based copy or on-line.

Rupert Smith,  “Secrets of Tibetan Weaving: The Greensmith Collection,” Karma Trinley Darchen, 2012

Koos de Jong, “Dragon and Horse*. Saddle Rugs and Other Horse Tack from China and Beyond,” (publication pending as described by de Jong below).

 *) This publication is the outcome of a sound art-historic research, by which all published saddle rugs were compared with representations of similar rugs in Chinese painting, sculpture and applied arts in order to produce a reliable typology.

The book contains two volumes, one in English with all the images, the other with just the text in Chinese. Part one, chapter 1-6, deals with the chronological development of the Chinese saddle rug, part two, chapters 7-12, with the saddle rugs per origin. Anticipated is a format of L 30,3 W 22,5 cm, ca. 250 images (ca. 150 full-colour and 100 small supportive images), 10 maps and appendixes (technical information, reading list, glossary, index, photographic archive resources and colophon); in total ca. 50.000 words and 220 pages.

 Published by myself, a total of 2000 copies will be printed and distributed by CA Design in Hong Kong. The publication is planned in March-April 2013.

It will be a strictly non-profit publication, meaning that it is completely financed by me, without any other public or private funding. Aiming at the widest possible distribution both in the Western world and China, it will be sold at cost-price.

An Odd Visual Effect in a Tibetan Rug

Posted in Uncategorized on January 10, 2013 by rjohn

Daniel Miller, the long-time Himalayan “ranger,” and editor of the volume “Auspicious Carpets,” on Tibetan weavings (that you can buy in hard copy or as a read on the internet),

writes about an odd visual effect in a Tibetan rug he owns.

Here is an image of this rug, straight on.


Now this seems unremarkable: a nice Tibetan rug with a checkerboard design.

But look at this image that Dan also sends.


Dan says in his note:

Have you ever seen a carpet do this?  

This is an older Tibetan rug I picked up in Beijing in 1998.  A simple geometric with two shades of blue.  Worn out a bit and frayed on the edges, but still a nice rug.

When you look at it from a certain angle, it does this geometric “thing” on you and transforms into something not seen before.
I had it on my floor for like 5 months in my apartment in Beijing and then, suddenly, I was sitting in a certain place and saw the change in the design of the carpet that appeared when you see it from the right angle.  Is there a message there?  I mean I had the carpet right there every day, walking over, looking at it, and only when sitting in the proper position one day five months later did it reveal its other aspect!
Kind of cool, huh?   Perhaps some kind of Tibetan tantric textile thing……………………
Can you ask any of your “ruggie” friends if they have seen this type of “transformation” before in a geometric carpet?

At first, I thought it might be something possible to see in almost any Tibetan checkerboard rug, so I asked around a little with some folks experienced in Tibetan textiles.

Some have said they’ve not see such an effect in a Tibetan checkerboard design before.   One said that he’s seen it “lots of times,” without indicating why it might occur.
I wondered whether it might be reproducible using Photoshop manipulation.

So I sent a similar Tibetan checkerboard design to Wendel Swan and he skewed it electronically.

Negative result: he could not produce the visual effects visible in the image above, so Dan Miller’s question stands.

Has anyone reading this seen a similar effect in a Tibetan checkerboard rug (or other rug for that matter)?  And even if you have not, do you have an explanation for why it occurs in this case?

Please send responses to me, at, or to Dan Miller, at
If shareable, we will share the results with this reader population in a separate post.


As we were about to send this out Robert Piccus, who has written a much-praised book on Tibetan Rugs, sent Dan this email message:

Dear Dan,

 Happy New Year.

 Your rug is fascinating. As you say the two photos are as of two different rugs. I have never seen anything so dramatic. One of my pieces (Plate 93 in my book) has some optical illusion effect but nothing so striking. Your point whether there is some message is interesting. We sort of think of these rugs as being produced by not particularly sophisticated or mystical weavers but who knows. To my mind so much as we try there is in fact so little we (or I) really know and understand about that country (Tibet).

 Best wishes,


Anyone else?


R. John Howe