Quasi-periodic pattern
Quasi-periodic pattern at the Gunbad-I Kabud tomb tower in Maragh

A researcher in the US reports to have found the first examples of perfect quasicrystal patterns in Islamic architecture. Her upcoming paper also describes how the designers were creating these geometric patterns from as early as the 12th century CE using nothing but rudimentary tools. It was not until the 1970s that academics began to develop mathematics that could explain these striking patterns seen in nature.

Quasicrystals are patterns that fill all of a space but do not have the translational symmetry that is characteristic of true crystals. In two dimensions this means that sliding an exact copy of the pattern over itself will never produce an exact match, though rotating the copy will often produce a match. They were first described mathematically by the British academic Roger Penrose in the guise of the famous Penrose tiles. About 10 years later Danny Schechtman of Israel's Technion University showed that the positions of atoms in a metallic alloy had a quasicrystalline structure. Since then, hundreds of different quasicrystals have been discovered in nature.

Mesmerizing patterns

Various people from both scientific and design fields have noted the similarity between quasicrystal structures and certain forms of Islamic decorative art. These mesmerizing geometric patterns, often located in places of worship, comprise repetitive patterns that reveal different features depending on whether you look at small sections or larger regions of the design.

In 2007 two physicists in the US reported that they had found an example of a 15th-century geometric pattern in Iran that showed an "almost perfect" example of Penrose tiling. These researchers concluded that the Islamic craftsmen most likely created the patterns using a set of tiles of distinct shapes, each decorated with lines that join to form the final patterns. Several other studies have also suggested that quasiperiodic patterns in Islamic architecture were constructed through local rules such as subdividing or overlapping of tiles. But none of the proposed methods has able to explain how the ancients ended up creating global long-range order in their patterns.

Now an explanation may be at hand. In this latest work, Rima Ajlouni, an architectural researcher at Texas Tech University in the US, believes that she has identified three examples of quasiperiodic patterns in Islamic architecture without any imperfections. The first pattern is a quasiperiodic cartwheel pattern that commonly used in the architecture of the Seljuk region, an empire that stretched from Turkey to Afghanistan. Ajlouni identifies specific cases in Iran at the Darb-i Imam shrine and the Friday Mosque in Isfahan. The second pattern is from the interior walls of the courtyard of the Madrasa al-'Attarin in Fez, Morocco, dating back to 1323. And the third case, dated to 1197, is seen on the external walls of the Gunbad-I Kabud tomb tower in Maragha, Iran.

From seed to beauty

In her paper, Ajlouni also shows that ancient Muslim designers were able to resolve the complicated long-range principles of quasicrystalline formations. In other words, these designers were fully aware of the extent of connectedness within their work. In all three examples, Ajlouni reconstructs the patterns and shows that the size of a central "seed" figure is proportional to the size of the overall framework of the pattern. She demonstrates that the three patterns could have been created using nothing more than a compass and a straightedge. This construction method that was widespread in Islamic societies to create a variety of media such as woodworks, ceramics and tapestries.

Diagram of quasicrystal pattern construction
Cartwheel pattern at the Gunbad-I Kabud tomb tower, Maragh

"We never gave these designers enough credit for the art they were creating. They were able to create some of the patterns of complex modern mathematics using basic principles alone," Ajlouni tells physicsworld.com. The strong geometries seen in Islamic architecture are said to reflect the deep philosophical and cosmological approach of the Islamic faith. Worshippers viewed the repetitive geometric formations as a reflection of the unity that can be derived from the multiplicity of forms. "The act of making the geometry was part of the worship," adds Ajlouni.

Ajlouni believes that her work could bring about a "paradigm shift" for designers, given that these ancient Islamic periodic patters can now be recreated using any simple drafting software. She also believes that the work could provide scientists with a deeper understanding of the structure of quasicrystals at an atomic scale.

"A fascinating conjecture"

Rónán McGrath, a quasicrystals researcher at the University of Liverpool in the UK, is fascinated by the strictly geometric approach developed by Ajlouni. "The suggestion that this method was used by the ancient Islamic architects is a fascinating conjecture, and the paper is an interesting contribution to the sometimes controversial debate on the degree of quasiperiodicity of these patterns," he says.

McGrath is not convinced, however, that the study will contribute much to the fundamental study of quasicrystals. "The structure of quasicrystals has been determined with great accuracy, at least in some questions, and the question is how they grow with such perfection. Geometric methods cannot address this question as they do not encompass the effects of chemical bonding."

The research will be published in the March issue of Acta Crystallographica Secion A.