Jay Bonner’s new book on Islamic geometric patterns is as dense and thick (595 pages) as the thorniest of textbooks, but the hundreds of illustrations and the immersion in this topic are simply fascinating. The first chapter of Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction (Springer International Publishing AG) offers 150 pages about the history and evolution of the geometric arts among the Umayyads, the Buyids, the Ghaznavids, the Great Seljuks, and more than a dozen other clans, dynasties, and empires. Photographs show domes, mosaics, stucco panels, a pierced-stone window, Quranic frontispieces, and other features covered with intricate and often colorful grid-form geometrics, many of which incorporate stars and floral designs.

Bonner gives a free lecture on the evening of Friday, Sept. 29, at St. John’s College. The title is “The Beauty and Complexity of Islamic Geometric Patterns: Historical Development and Traditional Design Methodology.” “This is a thousand-year-old tradition,” Bonner said. “It started in earnest in the 10th century, when it took on a distinctive Islamic quality. Khurasan was a hotbed of innovation. For a 300-year period, the art form grew into maturity and became highly complex — for example, having multiple star forms within the same structure.” The regularity of these grid-based patterns can appear almost soothing, but some are downright kinetic or even visually confounding in the way of M.C. Escher — and indeed, Sir Roger Penrose says Escher was inspired by symmetrical patterns at the Alhambra Palace in Granada, Spain. Penrose wrote the foreword for Bonner’s tome. “He’s one of the premier physicists of our time, but he also came up with some geometric concepts that astonished the world in the 1970s,” Bonner said.

The book’s last chapter, “Computer Algorithms for Star Pattern Construction,” was contributed by Canadian computer scientist Craig S. Kaplan. Bonner’s appreciation for geometric designs is grounded in art, but he acknowledges the validity of a more numbers-oriented perspective. “There is a historic interplay between the artists and the mathematicians, the geometers, that were active in the royal court. There is debate in the field of Islamic art history over the degree to which the founding of this tradition was reliant on mathematicians.”

It would be impossible to treat the ideas in Islamic Geometric Patterns without diving into the world of tessellations (grids of repeated shapes) and the “poly-gonal technique.” In his preface, the author cites the long-ago discovery by Muslim geometric artists “that geometric patterns could be extracted from underlying polygonal tessellations, herein referred to as the polygonal technique.” He has become a proponent of this design methodology as the one “most responsible for the tremendous diversity and complexity that are hallmarks of this form of art.”This preference stands against the “point-joining” method that is most often cited by other writers as primarily responsible for the wealth of Islamic geometric patterns.

In the polygonal technique, an artist uses an underlying tessellation (also known as the underlying grid or the generative tessellation) as a pattern for creating the final pattern. Its simplest form is a grid of hexagons. And, exactly like scaffolding in building construction, the underlying tessellation is removed after the pattern is finished. (The generation process is very complicated, and it is an advantage that the patterns are captivating even if you don’t know precisely how they were made.) Bonner had an early firsthand experience with the generative tessellation when he was a student at the Royal College of Art in London. “I was at the British Museum examining an Egyptian Quranic frontispiece and I had oblique light from a window, and when the light raked across the page, it created the subtlest shadow that showed the underlying tessellation, which was painted over.”

The two primary manifestations of this geometric tradition are in architecture and the book arts — Quranic frontispieces and tooled leather bindings. It was also used in the applied arts; these patterns can be seen on furniture, pottery, and jewelry. Bonner identified three main streams in this ornamental tradition: calligraphic, geometric, and floral. “When you think of Islamic calligraphy, you think of a very flowing, rhythmic, dynamic structure, but this is also strictly governed by geometry,” he said. In many of the patterns used in architecture and books, the shapes are defined by thick, “elbowy” lines that resemble the ancient Kufic variety of Arabic script. In the first chapter of the book, Bonner writes that calligraphy is thought of as the pinnacle of art in Muslim cultures. Calligraphers copying the Quran had twin goals in beauty and legibility, regarding the task as art practice and spiritual discipline as well as being pragmatic.

Non-Muslims are usually most familiar with Islamic geometric patterns in architectural applications, and those have mostly been three-dimensional. “There was a certain amount of fresco in the Islamic world, but painting was not quite so important, except in illuminated manuscripts,” Bonner said. “In the architectural media, most of the patterns are done in stone and wood and ceramic and sometimes in metal.” They may appear as ornamental friezes and windows or as pierced-stone grillwork and screens. In these, the pattern must be tight enough to be structurally strong and keep birds out, but loose enough to admit light.

A good example of a floral pattern shows in a Bonner-designed panel that was used on a new minbar, or freestanding stairway ending in a speaking platform, for the Masjid al-Haram (Grand Mosque) courtyard in Mecca, Saudi Arabia. Bonner studied this discipline at the Royal College of Art, where he received his master’s degree. In 1990, he and his family moved to Santa Fe, and he established Bonner Design. He has worked for decades as an architectural ornamentalist, designing features for buildings in Mecca, Medina, and other locations in the Middle East.

It is commonly believed that this art form exists mainly because of an Islamic proscription against depicting figures. “It involves anything with a heartbeat; the floral tradition is used, but it tends to be highly stylized,” Bonner said. “But I argue that the depiction of animal and human figures was never a strong enough tradition to allow for ongoing development; it was episodic. There are certainly religious strictures, but the geometric tradition is based on convention more than any specific text.”

Bonner’s book represents a significant advancement in the analysis and classification of Islamic geometric patterns. To create a symmetrical tessellation, the basic units of a grid — what Bonner terms the “fundamental domain” — can be multiplied through four means: rotation, reflection (as if in a mirror), translation (the object is moved in the plane without changing shape or size), or glide reflection (a combination of reflection and translation). An example of Bonner’s classification is his division of these patterns into two main streams: systematic and nonsystematic patterns. “The systematic uses a finite set of tiles that can combine in innumerable ways, and I’ve identified five historical systems. One uses regular polygons, two use fourfold systems, one is fivefold, and one is sevenfold.”

The book explains that threefold symmetry “is characterized by hexagons or six-pointed stars located on the vertices of either a triangular or a hexagonal repeat unit.” In fourfold symmetry, “it’s eight-pointed stars, octagons, or squares placed on the vertices of a square repeat unit.” Fivefold and sevenfold systems similarly relate to geometrical versions of five and seven.

Bonner said “nonsystematic” patterns still use an underlying grid, but the individual cells are original to that grid. “You can’t take them out as independent elements and recombine them.” One of the book’s examples of nonsystematic patterns comes from the Seljuk Sultanate of Rum, which Bonner said produced “amongst the greatest pattern-makers. This one has a fantastic pattern with nine-, ten-, eleven-, and twelve-pointed stars.”

Look at the book’s photograph of a pierced marble jali screen on a tomb dating to India’s Mughal Empire. The caption tells us the screen’s pattern exhibits “fourfold system B” and is an evidence of the primacy of the polygonal technique. It’s also a beauty, with eight-pointed stars inside octagons as well as irregular pentagons. This example is also important because it’s one of the few where the finished product includes the generative tessellation, and it is not only visible, it’s the boldest feature in the pattern.

While the book’s first and last chapters are respectively illustrated with photographs and with figures made by Kaplan, all 500 of the drawings in the intervening chapters are by Bonner. He uses AutoCAD, Rhino3D, and Adobe Illustrator. “Most of the images you see in the book are historic examples, but in order to illustrate certain principles, sometimes I have thrown my own patterns in. I love the kind of interface between what is rather regimented in this way of extracting patterns from underlying tessellations, the overlap between that and the ability to bring one’s own creative sensibilities to it.”

When Islam was exported beyond the traditional Islamic world, were there noteworthy developments in geometric patterning? “The surprising transferral was from Spain to the New World,” Bonner said. “There are fantastic mudejar buildings in South America and in Mexico that are pretty elaborately decorated with these patterns.” For the 1912 Scottish Rite Center in Santa Fe, the Los Angeles architectural firm Hunt & Burns referenced the Moorish Alhambra “in order to connect Santa Fe, New Mexico, with Santa Fe, Spain, where the Moors surrendered to Spanish rule in 1492,” according to the Society of Architectural Historians’ online encyclopedia (SAH Archipedia). The connection is obvious in the horseshoe-arched doorway and windows, but the building’s dramatic interior also boasts polychromatic and gold plaster friezes based on ornamentation at the Alhambra, as well as wood grilles carved in geometric patterns.

Although Bonner is not a Muslim, his work has been well received by the faithful. “I have given lectures and workshops in North Africa and Turkey, and I never had anything but respect and appreciation shown me. Most of my work is in Saudi Arabia, and they mostly want floral patterns. They’re a little wary of geometric patterns, that someone will come along and say something. This actually happened in an airport. It involved a big wall of tiles with 12-pointed stars and someone came along when it was in construction and said, ‘It’s pretty, but 12 means Shia Islam and we’re Sunnis.’ This is crazy, because Sunnis have used 12-pointed stars and the Star of David forever. But nowadays if it looks like the cross, it’s branded as Christian; if it’s a six-pointed star, it gets branded as the Star of David and Israel. Who knows, maybe the next thing will be eight.”

Bonner’s predilection for these patterns goes way back. “I spent a lot of time making geometric forms when I was a boy. I don’t know why. It just appealed to me. I’d start with a five-pointed star and I’d extend the points and connect them with other lines and make radial designs. When I look back at them, they were very similar to Islamic structures. It was only as a teenager that I saw a book of Islamic architecture and it had designs that resonated with me in terms of the aesthetics and what I love, but also, in some cases I saw designs that I had already made and thought were original to me.”

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