Saturday, 30 October 2010

Just Fallen Short

Quasi-periodicity in 15th century Islamic Art and whether it actually has been developed as a concept is still a matter of a somewhat controversial debate. There are three sites in the city of Esfahan which have been studied in this regard in considerable detail, two rather small patterns on a spandrel and a portal on the Darb-i Imam shrine in the Dardasht quarter of the old city (1453) and a huge pattern on the western iwan of the Great Mosque. Several authors have, in the meantime, tried to overlie Penrose patterns of kites and darts or thick and thin rhombuses in order to prove that medieval artisans were able to apply what had been described by Roger Penrose only five centuries later. See, for example, Lu and Steinhardt (2007), their response to some additional work by Makovicky (2007), or Cromwell (2008) here, here, and here.

However, while a certain desire for subdivision and self-similarity can easily be traced on the respective buildings, it is not perfect, in particular not at the Darb-i Imam’s spandrel and portal, and the Great Mosque’s western iwan (probably 17th century). The higher level of girih- or proto-tiles is composed of decagons and bowties in each case only. I have pointed some time ago to a possible solution for creating in fact a perfect subdivision if one had considered a special arrangement of girihs in the upper right corner of the spandrel of the Darb-i Imam, which is composed of decagons, bowties and, in fact, the elongated hexagon, or bobbin, which can be found all-over. The picture below indicates the higher level pattern originally found on the spandrel (left) and a suggested pattern (right) which takes into account a small portion of the lower level pattern in the upper right corner. See more information here.


On the western iwan of Esfahan’s Great, or Friday, Mosque, the highest level is composed of alternating half decagons while the spaces in-between are filled with half bowties. Both decagons and bowties follow mainly the suggested subdivision rule. However, the pattern is distinct as it introduces, at the intermediate level, a rhombus, which is otherwise missing in the subdivision. If one adds colors (picture below, left), it becomes clear that the artisans just fell short in creating a true Penrose pattern.

Certainly, it would have been possible to assemble the five-point star (purple in the left picture) by a bobbin and two bowties instead. How it would look then can be seen in the right picture above (by Benjamin R. Schleich from his dissertation, which can be found here). A nice animated gif, instantly explaining the concept of subdivision and self-similarity, can be found here.


The picture below shows the western iwan, or sofe-shāgird, the iwan of the student (sic!). Sofe-e ustadh (the iwan of the master) faces it, it is the eastern iwan.

That medieval artisans just fell short of creating something that would really have amazed us 500 years later may be regarded as indirect proof that they had not really penetrated the mathematical concept. But if they actually had, why would that have been more interesting? Medieval artisans were keen to produce, with the help of eminent mathematicians, interesting ornaments and designs on mosques and buildings, not mathematical breakthroughs. They achieved a ‘dazzling’ appearance anyway; I have pointed to that several times here on this blog, see here and here. By removing color as a common element, for instance in the case of the Gonbad-e Qabud in Maraghah (1196), they even created something what would absorb and dazzle scientists even eight centuries later.

That has made a lasting impact, hasn’t it?

First published at Freelance.

Sunday, 3 October 2010

Intricate Patterns

Mathematic breakthroughs in the 10th and 11th centuries in Baghdad and, for instance, Esfahan may have resulted during the 15th century in an explosion of Islamic Art and Architecture. In particular the use of so called girih tiles, that is a set of polygonal prototiles with well-defined decorating lines may have allowed medieval artists in Iran and Central Asia to create decagonal tessellations with, in few cases, Penrose-similar patterns. Between the mid-14th and early 16th centuries, the Timurids ruled over much of the Islamic world. The highly sophisticated and strictly geometric (‘Islamic’) patterns on glazed tiles covering buildings and monuments became later more and more floral. Exquisite examples of this changing style can be seen in Esfahan's Grand Mosque and Darb-i Imam, Mashhad’s Gohar Shad mosque, or the Friday Mosque in Yazd.
The Timurids were repelled in Iran by the rulers of the Safavid dynasty (1501–1736 CE) who established the Shi’a branch of Islam as state religion. Many historians regard specific achievements during these centuries as the true apogee in Islamic Art and Architecture. One marvelous example is the Naqsh-e Jahan in Esfahan. Geometric, calligraphic and floral designs cover both religious and secular buildings while ancient roots of the Iranian society, in particular the Achaemenid style of intricately carved wooden ceilings and slender pillars are well preserved in certain palaces, reminding of the grandeur of ancient Persepolis.



Another area where the specific designs of the Safavid period can still be studied is few surviving carpets of that time. Two years ago, Christie’s Auction House has sold an Esfahani silk carpet of about 1600 for an, at that time, record amount of $4,450,500. I was wondering at that time, how many of these inalienable carpets are still hoarded by wealthy Tehran bazaaris in their vast storages.
Well, some of these masterpieces have only survived in paintings of the European Renaissance period (14th to 16th centuries). Famous examples include paintings of Hans Holbein the Younger (ca. 1498-1543) and Lorenzo Lotto (1480-1556). Saudiaramco World has dedicated an article in its recent issue to “Threads on Canvas”, i.e., mainly Anatolian carpets displayed on famous Renaissance paintings (by Tom Verde). Some of the carpet designs are even called after Holbein, and others may have been identified on still existing pieces. In particular Holbein’s portrait of merchant Georg Giese, or Gisze as the painting was entitled by the artist, (1532) is a fascinating masterpiece illustrating much of the life circumstances of the confident young man, for example his engagement (the carnations in a fragile vase placed too close to the edge of the table) and wealth, symbolized by the carpet on the table. The strapwork border and even the design of the central field can actually be seen in an Anatolian carpet in the Philadelphia Museum of Art.


Another example by Holbein is the famous Ambassadors (1533) which may strike the viewer by its surrealistic anamorphic skull in the lower third of the painting, which is only discernible as such when the picture is viewed at an acute angle. It is what nowadays would be called a gimmick, both to shock, or at least surprise, the viewer and impress him or her for the superior mastering of the complicated technique. Again, the table is covered by an Anatolian carpet with a ‘large-pattern Holbein’ design. A similar existing example can be found in the Museum für Islamische Kunst in Berlin, Germany.



© Preussischer Kulturbesitz/Bridgeman Art Library; Philadelphia Museum of Art; Saudiaramco World.

More about carpets of the Ottoman era in general and Holbein carpets in particular may be found here.

First published at Freelance.