P3D Escher, stereo, impossibility

[abram klooswyk <abram.klooswyk@xxxxxx>]

Recently Steve Berezin announced on S3d that he offers Escher 
3D Viewer cards, (S3d 1035,25 Feb 2000) see comment in next 
posting.

The Dutch graphic artist M.C. Escher (1898 - 1972) never made 
stereodrawings himself, which I always have found somewhat 
disappointing. He probably could have done it better than most 
artists who did try stereowork. He knew about stereophoto- 
graphy, he admired the stereopictures his son Arthur send him 
from Indonesia in 1959. Bruno Ernst (see below) also had given 
him a pseudoscope, in 1956. 

A large part of Escher's work is strictly two-dimensional, 
covering the plane with intriguing patterns was one of his  
lasting themes. These tiling studies (tessellations) in part 
were inspired by the Arab tilings in the Alhambra (Spain), 
mathematical infinity studies were another inspiration. 
Among the famous studies from this series are circle limits 
and square limits studies. The huge woodcut Metamorphose II 
(1939-1940) is also in this series (192 x 3895 cm, about 6 x 
128 feet, a later version was enlarged to a width of 223 feet, 
made for a Postoffice in the Hague).

But other themes in his work obviously are so involved with 
space imaging that stereo could be expected, IMHO. This is 
especially the case where 3D structures emerge from the 
plane, as in Reptiles (1943) and Drawing (1948, also known as 
Drawing Hands, two hands drawing each other). These prints 
seem to scream for 3D conversion, which now has been done. 
Stereoscopy really adds value to them, and is not just a 
gimmick, in my opinion.

Escher also has made some famous "impossible" prints: "Cube 
with Bands", "Belvédère", "Ascending and Descending" and
"Waterfall".  
Impossible figures paradoxically _can_ be done in stereo,
but the impossibility mostly becomes more evident.
It is often believed that Roger Penrose invented the 
impossible triangle in 1958, but in fact it was first 
conceived by the Swedish artist Oscar Reutersvärd in 1934,
who also drew the first endless staircases in 1950.
(Several impossible pictures and paintings have been made 
in past centuries, but not often to show the mathematical 
impossibility.)

Bruno Ernst, a Dutch mathematician and teacher, has written 
books on Escher as well as on impossible figures. His real 
name is J.A.F. de Rijk  [Hans], he is a member of the Dutch 
stereoclub and as written many articles in the Club Bulletin. 
He has a many-sided mind and has written many books on varies 
subjects, using a number of pen names.
In 1986 he was among the organizers of an exhibition of 
impossible figures in Utrecht, the Netherlands.

There I have met Oscar Reutersvärd, who  told me that he had 
made stereo versions of impossible drawings from 1959 on, also 
as anaglyphs. Arthur Girling, a former editor of the ISU 
bulletin "Stereoscopy" had made several stereodrawings of 
impossible figures in later years, after he had seen 
Reutersvärd's figures on Swedish stamps. 
I had brought three of Arthurs drawings as framed anaglyphs 
(18 x 18 inches) for the exhibition, which Reutersvärd liked 
very much. Girling used "solid" figures, like the impossible 
triangle, Reutersvärd so far had only tried figures of the 
so-called "impossible tuning fork" type. 

Sandro del Prete, the Swiss artist, recently (at the Lindau 
ISU Congress) showed a stunning example of this last type of 
stereo pictures: a temple in which the columns, and the spaces 
between columns, change their roles when you look from the 
base to the top, remarkably stereovision didn't break the 
illusion.

Now one of Escher's impossible drawings, the "Ascending and 
Descending" has been converted to 3D.

A different type of 3-dimensional space perception, which 
doesn't depend on binocular vision, is given by motion 
parallax. At the large Escher retrospective, celebrating his 
100th birthday, in 1998 in Rotterdam, the Netherlands, a video 
movie was shown were you flew in a space rocket through 
Escherian landscapes, and in fact around and sometimes through 
his objects, mostly at very high speed. (The viewing platform 
were the spectators stood, was made to make rocking movements 
to add to the illusion.) Motion parallax gives a remarkable 
depth effect, comparable to stereovision. The "rocket" flew 
around and through the "Belvédère", showing that the pillars 
were in fact bend... I should like to see that in stereo too.

More comment and facts on the 3D Conversions of Escher 
drawings in next posting.

Abram Klooswyk