you may recall this tantalising article about accurately repeating patterns in the Book of Kells
Wanting to know more about this technique I contacted the professor, who kindly forwarded me his paper. I then asked my technically-minded father to translate this into layman's speak! This explanation is found, further below.
My own personal bit here .... However, what I am absolutely intrigued by is - if indeed the monks used this technique (free-fusion stereocomparison), could they or would they have intentionally created artwork intended for 3D viewing? There is mention (The Book of Kells by B. Meehan, page 88) 'The Book of Kells employs the unusual colouristic technique, shared only with the 8th century Lichfield Gospels, of adding a thin translucent wash of one colour on top of another. A relief effect was frequently achieved through the layering of as many as three pigments on top of a ground layer. It is regrettable that this complex 3D effect was largely lost when the leaves (pages) were wetted for flattening in the 19th century.'
On page 89 of this same book, there is a description/quote about The Book of Kells from 1185 AD: "...If you look at them (the drawings) carelessly and casually and not too closely, you may judge them to be mere daubs rather than careful compositions. You will see nothing subtle where everything is subtle. But if you take the trouble to look very closely, and penetrate with your eyes to the secrets of the artistry, you will notice such intricacies ... that you will not hesitate to declare that all these things must have been the result of the work, not of men, but of angels." - Giraldus Cambrensis.
A layman's explanation of the precise copying technique:
Professor Cisne is simply proposing a (quite plausible) theory on how the artists working on the Book of Kells managed to replicate repeated patterns with such astonishing accuracy centuries before the invention of optical magnifying devices. The technique he thinks they were using is called stereomicrography and it is simply a means of using the eye/brain combination to convert small lateral (side ways) drafting errors into apparently large (perceived) depth errors so that the errors leap out at you.
You remember back in the eighties when the so-called Magic Eye books were popular. These were collections of drawings that, when looked at in a particular way produced a startling 3-dimensional effect. ( http://www.vision3d.com/sghidden.html )
The thing is you have to train yourself to focus your eyes on infinity whilst you are looking at the drawings at a viewing distance of about normal reading distance, about 300mm. The ancient monks may have stumbled on the technique by staring idly into space through the page they were working on instead of concentrating diligently on God's work.
I have attached a couple of quick sketches which should illustrate the illusion for you. When you get the technique right you will see three images of the squares side by side: you concentrate on the centre one which will appear as a pyramid on the top line and as a empty or receding pyramid on the bottom line. You will notice that all I have done is to shift the centre of the square 1mm to the right in the top left square and 1mm to the left in the bottom left square. That 1mm error translates in a depth perception of about 12mm. It is possible to increase that "magnification" even further if you tailor the image pitch to be slightly different from a harmonic of the distance between the pupils of the observer's eyes.
You may also notice that it is possible to achieve the reverse effect of depth perception by crossing your eyes when viewing the drawings ie the bottom drawing becomes the pyramid and the top one the hollow pyramid. It is a bit more difficult to hold your eyes steady when doing it this way. If the patterns exactly match one another there is no depth perception. Very slight irregularities however will stand out which, of course, is the point of the professor's theory.
You will need to print the diagrams out or view them on screen at A4 size to get the desired effect (the sides of the squares should be 20mm). I have used a horizontal pitch of 25mm which will probably be OK for your eye spacing assuming it is pretty close to mine. You can experiment for yourself with slightly different pitches to see the effect.
If you are into Celtic and zoomorphic knotwork, it is not hard to see that you could produce patterns which would produce a 3 dimensional interwoven effect be slightly offsetting to the right and left in one of the images and joining the offset points smoothly. If you are going to experiment with this sort of thing I would start with straight lines since curves are going to involve a great deal of practice and technique. Remember that the small offsets which will produce this effect have to be along the x axis. The y axis could be used in the case of aliens from the planet Zork who have one eye above the other.
A further note about my posting yesterday (above). I've had another read through the paper Professor Cisne forwarded me. Actually, yes, he does touch on the possibility of the technique being used to create stereoscopic (3D viewable) images by the celitc artists, but doesn't come right out and say that it was definitely done on purpose in celtic manuscripts (like the Book of Kells).
His paper focuses mainly on proving the technique was known and used by celtic artists, in creating repeating patterns to truly microscopic detail, using only your eyes and a template set to the side of your work, for the copying and checking of the accuracy of it, and this could also be why scribes of the era are shown with pen and knife in hand, for they would often be correcting the tiny detailed artwork. He also mentions the technique could explain the miracles of speedy proof-reading by the famed scribe, Saint Columba.
If you want to read his original paper, the professor may forward it to up to 50 people in total, but rather than everyone hassling him I'd suggest its best to subscribe and download the paper from here: