The Palace Of The Alhambra

The Alhambra is the fairy-tale Moorish palace which stands on the bluff of a steep hill to the north east of the modern city of Granada in southern Spain. Granada itself lies to the north-west of the snow covered Sierra Nevada where, in winter it is possible to ski in the morning and then to swim in the Mediterranean in the afternoon.

The buildings of the Alhambra date mainly form the 14th Century and were the home of the Sultans of Granada, the last province of the Spanish peninsula to be ruled by the Moors. Flush from their achievement of Spanish unity, their Catholic Majesties King Ferdinand and Queen Isabella expelled of Boabdil, the last of the Moorish sultans from Spain in 1492. But so enchanting was the palace of the Moors that even the new Christian rulers could not bring themselves to destroy it. Across the River Darro, to the north-west is the hill of the Albaicin, a maze of narrow streets of white houses, many of the walls decorated with cascades of colourful flowers. Here live the gipsies, some of whom live in caves. If a tourist will cross their palms with silver, they will perform the flamenco for them although It will be a matter of chance whether it will be either a perfunctory or an inspired performance. Across the valley to the north east of the Alhambra is the separate summer garden of the Generalife which is another fragment of Paradise on earth, where playing fountains cool the heat of the summer.

The Alhambra (meaning "the Red Fort") is really a mountain-top walled city which includes many buildings. At the western end, keeping watch over Granada, is the ancient stronghold of the Alcazaba which now lies in ruins To the east is a former Franciscan convent which is now a parador, one of the state hotels of Spain. Towards the centre there is a large Renaissance palace built by Holy Roman Emperor Charles V which abuts against and sharply contrasts with the delicate Moorish Palace. Anywhere else, the palace of Charles V would be admired as one of the finest examples of Renaissance architecture. But clumsily set where it is, few can bring themselves to forgive Charles V for building it so close to the exquisite palace of the Moors.. Miraculously, however, the existence of the renaissance palace is not evident to a visitor within the Moorish place.

Visiting the Moorish palace, one passes through a series of contrasting halls, rooms, palaces, courtyards, gardens and rooms, including the Court of the Myrtles with its long reflecting pool fringed with myrtle bushes, the Court of the Lions with its forest of delicate pillars and its central fountain mounted on the backs of a circle of lions, the impressive Hall of the Ambassadors and not least, the sumptuously tiled royal baths where blind musicians played to the bathers from a gallery. It is not only the buildings that impress, but also their decoration. Every possible surface is covered with decoration, whether with polychromatic tiles or in richly carved stucco. Much of the decoration is in decorative forms of Arabic script with quotations from the Koran. But there are also extensive floral decorations and in the rooms adjoining the Court of the Lions stalactitic patterns hang from the ceilings.

Yet in all this richness, there are very few representations either of men or animals, for such were forbidden in Islam. The real reason for this was a desire to avoid the making of idols which might lead to their being worshipped, something contrary to the second commandment and which would offend against the strictly monotheistic religion of Islam. The Koran says very little about this, but the subsidiary Sayings of Mohamed have been construed as a prohibition against all pictures and statues whether of humans or of animals. Whatever the real intent of the restriction may have been, it has become a strong tradition in Islamic countries therefore that pictures should be avoided, not only in religious buildings, but also in secular contexts. Nevertheless, it is not an absolute bar and even in the Alhambra (a secular palace) there are some representations of animals and men.

It was this prohibition of living creatures that led to the employment of abstract patterns and quotations from the Koran. In the Alhambra they appear in great profusion and variety, ranging from simple patterns of wall tiles in contrasting colours to complex interlaced patterns, some in polychrome and others in stucco. There are many areas of simple tiling patterns, especially in the royal baths. There are also more complex patterns which are reminiscent of Celtic and Viking patterns and also Celtic knotting patterns the intricate patterns of knotting by Renaissance artists, including Leonardo da Vinci.

A visit to the Alhambra is a great delight as one meets constantly changing scenes and patterns, and is surrounded all the time by reflective pools of water, the sound of fountains and urns of coloured flowers. With the growth of air travel, the Alhambra has sadly become oppressed by visitors, but it is still possible to arrange a visit at less busy times or in the winter, when the sun still shines in Andalusia and if you can afford it and make your booking early enough It may even be possible to arrange to stay at the parador within the Alhambra itself.

M. C. ESCHER

Maurits Cornelis Escher has achieved the greatest fame as a graphic artist because of his extraordinary imagination and his applications of mathematical ideas to his art. He was born in the Netherlands in 1898 and died at the age of 73 in 1971. By 1920 or 1921 he was already showing an interest in "filling the plane" with repetitive and interlocking patterns before ever he discovered the mathematical basis for them. He created an intricate design for eight interlocking heads, which showed many of the ideas he developed in later years.

In 1922 Escher took a voyage along the coast of Spain in a freighter, an experience which appealed to him and which he repeated several times in later years. Sailing down along the east coast of Spain, he landed at Tarragona in October, 1922, from where made a brief journey to Granada in order to visit the Alhambra Palace. There for the first time he saw the intricacies of Moorish pattern and unexpectedly, he found himself very moved by them. The experience greatly stimulated his previous interest in interlocking patterns.

Escher paid another visit to Spain with his wife in May 1935, where he spent two days studying the decorative designs in the Alhambra. He made many sketches and later redrew them in his hotel room in pencil and coloured crayon. A few of the many drawings he made can be found in books of his works. From Granada Escher and his wife went on to Cordova, where he visited the great Mosque and to Seville, where he was able to study more Moorish patterns in the Alcazar or Moorish Palace..

The Islamic patterns that Escher studied were broadly of three kinds. Some were simple coloured tiling patterns, which fitted together. Sometimes they were made up of tiles with curved sides. Other patterns were complex interlaced Islamic patterns on polychrome Majolica-like tiles. Still more were intricate patterns moulded and carved in stucco. The stucco patterns are intermingled with stylised Arabic script which quotes verses from the Koran.

In June, 1937 Escher showed his drawings of tessellations to his half-brother Beer G. Escher, who was a professor of geology at the University of Leiden. Beer recognised that the drawings resembled crystal patterns, which resemble three-dimensional tessellations. He later wrote to Escher with some references to scientific articles on the subject. Escher followed up the references and discovered the mathematical world of tessellations. Among the articles were "Regular Divisions of the Plane and Point Systems" by F. Haag (1923) and "Zeitschrift fur Kristallographie" edited by the Hungarian, George Polya (1924), who was a professor at Zurich. Some of the patterns shown by Polya were copies of well-known Islamic ones. Escher's sketches from the time show his considerable interest in the patterns shown by Haag and Polya and how he was striving to develop them. It was Escher's introduction to the geometry of tessellations and was the beginning of his creative interest in them. While Escher did not thereby become a mathematician, from then on his work with tessellations was grounded in mathematical ideas. Later in the 1950s he met and became friendly with mathematicians, including the great geometer Professor H.S.M. Coxeter, of Canada. Coxeter took considerable interest in Escher's work, and bought some of his works. He became a friend of Escher, corresponded with him and suggested new ideas to him. After Escher's death, Coxeter was one of the four editors of "M.C.Escher: Art", the Proceedings of the International Congress on M. C. Escher held in Rome in March, 1985.

Escher's interest in the tessellations in the Alhambra was mainly in the simple tiling patterns. Although, in 1922, he carefully painted a watercolour copy of one of the more intricate polychrome interlaced patterns from the Alhambra, this style of interwoven tessellations seldom appears in his finished work. It might appear to have held little interest for him except that between 1938 and 1942 he experimented with carved woodblocks, which, when printed in different combinations and orientations and which resulted in surprisingly complex interwoven ribbon patters which were reminiscent of Islamic interwoven patterns. These were not published until 1986, when Escher's son, George Escher wrote an article, "Potato-Printing, A Game for Winter Evenings". But Escher's developed "simple" tiling went far beyond those of the Alhambra as he developed complex shapes, often of portrait heads, animals, birds and fishes in which he interwove widely different shapes. They had been presaged by his early "Eight Heads" of 1922.

Later Escher developed even more advanced ideas as he strove to create extraordinary three dimensional visions. He even managed to depict Infinity in his work, using what we now recognise as fractals, a concept which appears nowhere in Moorish art.

Escher left far behind him the patterns of the Alhambra and moved into a visionary world where his fertile mind joined hands with mathematical, scientific and psychological ideas to create new words of the utmost fascination and imagination. One wonders whether he would have taken an interest in paperfolding if he had known of the immense possibilities which it has and with which we have only recently become familiar.

CHRIS PALMER

This article came about because I was asked if Chris Palmer had studied Islamic tessellations. Chris Palmer was one of the first paperfolders to take an interest in this branch of origami and he has become one of the leading folders of origami tessellations which are folded, not from multiple interlocking tiles, but from a single pleated sheet. A typical one-sheet tessellation begins with the design of a regular tessellation which is marked or creased in the paper. Double creases are then folded along the lines, one valley and the other mountain and the two creases are laid flat in the form of a pleat. Where two such creases cross, a twist fold has to be made in order to enable the paper to lie flat.

Chris Palmer did, indeed study Islamic tessellations and visited the Alahambra, following in the footsteps of Maurits Escher. However, their interests in the patterns took different courses. Escher was interested in filling the plane with multiple repeating separate shapes, which fitted together and he was a graphic artist, not a paperfolder. In contrast Chris Palmer was a paperfolder who became interested tessellations folded from one sheet of paper.

I first became interested in the work of M.C.Escher and coincidentally, in tessellations and Islamic patterns as early as 1975. Mick Guy had explored the folding of multi-piece tessellations in the 1970s. Then I discovered the tessellations of the Japanese Shuzo Fujimoto, and acquired his books. Unlike previous origami tessellations, those of Fujimoto were folded from one piece of paper. If the completed folding was held up to the light, it showed a hidden pattern in light and shade.

I first met Chris Palmer at the origami convention of the Friends of the Origami Center in New York in 1995 and 1997. I found that he was folding one-piece tessellations in the manner of Fujimoto. He displayed his one-piece tessellations on the inside of windows so that the hidden pattern of his tessellations became apparent. I attended his introductory classes on folding one sheet tessellations at which I learnt the elementary principles of folding the double pleats and using a twist fold where they crossed, to enable the paper to lie flat.

I was keen to learn more about tessellations of all kinds. It came to my notice that in the autumn of 1997 Chris Palmer would be attending the convention of Centro Diffusione Origami (CDO) at San Pietro del Theme, a small spa resort near Bologna in Italy. I was also told that Paulo Taborda Barreto, the Portuguese folder who lived in Holland, who was another exponent of folded tessellations would also be attending the convention.. I had met Taborda at origami conventions twice previously, but found him to be a very elusive person. To attend a convention at which two notable exponents of origami tessellation would be present was an opportunity I could not afford to miss, so I arranged to go to Italy.

Unfortunately something prevented Taborda from attending, but I was able to meet Chris Palmer again. He showed an exhibition of his one-piece tessellations which he again hung in front of windows so that the hidden patterns could be seen. But this time they were folded not from paper, from silk cloth. Chris was naturally very protective about these and would not disclose the special techniques of folding tessellations from silk or how he fixed the creases, because he hoped to be able to sell them.

Nevertheless, Chris afforded me plenty of opportunities to talk to him about his approach to folding and he was kind enough to let me have detailed discussions with him about his tessellations. I made notes on what he said, so I retain a record of our meeting.

Chris told me that he had been a paperfolder since childhood and had later become acquainted with the work of John Montroll and Robert Lang. He had studied Islamic patterns over a long period and had also read books on the subject, including those by Keith Critchlow, J. Burgoin and others. Originally not a mathematician, he had studied aspects of mathematics relevant to tessellations and he considered that in this respect he was a mathematician. As with Escher, his interest in tessellations greatly increased as a result of a visit to the Alhambra.

One winter, Chris spent six months in Granada, staying part of the time in the town and part with various people who lived in caves above the Albaicin. During his stay Chris paid regular visits to the Alhambra Palace and studied the Islamic patterns intensively, as he said, "trying to get under the skin of them". He made sketches of both the simpler tiling patterns and also the more complex interwoven Moorish designs in stucco. He then redrew them and worked out how they were constructed. So Chris learnt about Islamic tessellations at first hand.

Chris told me that the greatest influence on him was made by Shuzo Fujimoto. He studied Fujimoto's books and refolded the patterns until he was familiar with the technique of folding them. He then developed similar patterns of his own, but was reluctant to exhibit them in case he would be considered to be plagiarising Fujimoto's own work..

Chris visited Japan in 1994 to attend the Second International Meeting of Scientific Origami, and stayed in Japan for an extra week, during which he visited the Origami Gallery. He also met Fujimoto and Toshikazu Kawasaki and other folders. He found Fujimoto to very likeable and helpful and he expressed approval of Chris's own designs. Sadly, Fujimoto was compelled to give up folding soon after this because of his failing eyesight.

Chris greatly admired Kawasaki's work, which he found intensely complex. He agreed with me when I suggested that Kawasaki's Box of Roses was a tessellation. Kawasaki presented him with an example of this fold. Chris decided to unfold it flat and in doing so he learnt a great amount in the process. He found that Kawasaki's crease pattern was a grid fold on the slew to the edges of the paper. But Kawasaki used great subtlety, sometimes folding two squares together instead of one, In this way he introduced subtle variety into the models.

Chris told me that while he admired Escher's space-filling tilings, they did not greatly excite him. He was much ore interested in those patterns which used continuous over and under patterns, like the patterns of fabrics. The pattern of interweaving could be seen in advanced Islamic patterns and he was sometimes able to modify Moorish patterns to make them suitable for his own one-piece tessellations. Chris considered that the patterns in which tiles were merely fitted together in patterns were not so important.

Chris moved from folding paper to folding cloth, mainly, but not exclusively silk. He found that this gave him a new freedom of folding and removed several obstacles which he encountered when he folded paper. He showed me a book that he had made up with his foldings of cloth. The basic crease pattern appeared on the left-hand page and the folded cloth pattern as completed on the right. Folding cloth presented new challenges. For instance, the pattern had to be stable when hung. Consequently it had to be hung the right way up as otherwise it would unfold when suspended. I asked how the creases could be made to keep in the cloth, but Chris emphasised that that was a trade secret!

Superficially similar to tessellations are Chris's "Flower Towers. A flower tower is a kind of three-dimensional tessellation which is folded from a single piece of paper. It is, however folded so that the paper falls into several layers of paper, each layer increasing in sized from the topmost layer in the centre. Paulo Taborda did some early work on this concept, although so far as I am aware, he did not publish the results of his investigations. Chris's Flower Towers are, however a very different style of tessellation from his original one-piece tessellations in the style of Shuzo Fujimoto.

Another kind style of tessellations in which Chris has been involved has been Origami "Flashers" in which he has worked with Jeremy Shafter. Chris and Jeremy became quite involved together and Jeremy published a long series of articles by Chris on his tessellations in the BARF Newsletter. (Chris later withdrew them from later reprints of the Newsletter). A flasher is a circular or polyhedral tessellation which can be made to expand and contract, as so ably demonstrated by Jeremy Shafer in his performances. Undoubtedly a flasher is a "one-piece tessellation", although it is constructed in an entirely different way from the original one-piece tessellations. It bears no more than a superficial resemblance to any tessellation in the Alhambra Palace.

Another kind of folding explored by Chris are his "Polypouches". Although they may have branched from Chris's original origami tessellations, they are (perhaps inadequately) described as "paper wrappings for polyhedra". It is preferable to regard them not as tessellations but as a separate branch of folding.

Since around 2000, developments in folding tessellations have been advancing rapidly as new folders explore a bewildering array of new ideas. Tessellations have become three-dimensional and some of the new ideas have branched out to become new categories of folding. These developments are far from the original concepts of origami tessellations of Shuzo Fujimoto and Chris Palmer and remote from anything to be seen in the Alhambra Palace. Fujimoto was the pioneer of one-piece origami tessellations and the credit must be given to him for starting the trend that led to these new developments.. Chris Palmer followed in his footsteps, but he himself has taken origami into completely new territories and he has made his own significant contributions to this burgeoning branch of origami

David Lister

4th August, 2005.