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I suspect that once most first-time observers of ancient Islamic architecture get over its astonishing beauty and rigorous interplay of geometry and pattern-work (such as the in-laid tiles above the arch of this 15th-century school in Bukhara, Uzbekistan), they immediately wonder how it could possibly have been built by a bunch of uneducated craftsmen.

I also wondered about this, particularly after recent research revealed that mathematically-speaking, much of the patterns applied to Islamic architecture are based on concepts that weren’t fully understood until the 1970s.

To appreciate the complexity of the above tiles, you first need to know that there are patterns and then there are patterns.  The former are repeating patterns, where geometric shapes can be oriented in certain groupings anywhere in the pattern (e.g., your bathroom floor, kitchen backsplash, or patio); the latter are non-repeating patterns.  These patterns also consist of geometric shapes, but at some point, the shapes always force non-repetitive placements in the pattern.  These patterns are extremely complex - so much so that their irregularity is almost imperceptible to our brains.

Only in the 1960s did researchers overturn an old assumption that there weren’t any shapes that could only be arranged non-periodically.  They discovered that such patterns did exist, but only by employing a library of over 20,000 shapes in a single arrangement.  Naturally, it was hard to believe that Islamic architecture’s craftsmen could manage a library of so many patterns; Sir Roger Penrose validated this doubt with a major breakthrough in 1974.

Penrose found that there were two shapes (a “kite” and a “dart”), both triangles, that supplied the geometric basis for a non-repeating pattern.  The pattern’s combination of kites and darts incidentally approached the Golden Ratio as it expanded toward infinity.

Physicist Peter Lu deserves the most credit for linking the Penrose patterns with Islamic architecture. After being taken with the complexity of Islamic architecture’s ornamentation, he began analyzing its shapes in order to deduce an underlying framework that might explain how the patterns could be executed in the first place.

Lu found that a set of five shapes in particular (decagon, pentagon, hexagon, rhombus, and bowtie), called girih tiles, were the common basis for the non-repeating patterns of many Islamic buildings.  What’s more, Lu discovered that these shapes could be reduced even further to the same two shapes of the Penrose pattern.

Having found that a relatively simple set of shapes existed - small enough in number to be comprehensible to craftsmen, the question still remained: how did craftsmen across a vast civilization - stretching from Spain to Central Asia - know how to use girih tiles to ornament their buildings?

Pattern books, it turns out.  Actually, pattern scrolls.  Lu’s snooping led to the Topkapi Scroll, which is essentially a 97-foot long map of both flat and three-dimensional patterns made up of girih tiles.  Notably devoid of text, the scroll consists of shapes, grids, and color coding to illustrate each pattern’s layout; this method of documentation would have been ideal for giving illiterate craftsmen - even local architects - a functional understanding of how to execute their own non-repeating patterns, importantly, without having to comprehend the mathematics underlying them.

American architecture has its own modern analogue to the ancient Islamic pattern scrolls; much of America’s 19th-century architecture was built thanks to Andrew Jackson Downing’s pattern books.  Just as Downing’s books included detailed information about the “correct” proportions, details, and materials of many architectural styles (e.g., Greek Revival, Italianate, or Gothic Revival), Islamic scholars located in learning centers (such as Alexandria, Istanbul, or Isfahan) did the same.  Less-educated builders and architects in far flung places simply took these how-to manuals and ran.  Far.

Related post:  Well, I could do that…

Via: Saudi Aramco World

Images courtesy of (1) AudreyH, (2) Neilbanas, (3) horizon, (4) jazand_rani.