The Math and Magic of Muqarnas

A style of architectural ornamentation that dates back to the middle of the 10th century, originating in Iran and North Africa, Muqarnas compositions are 3D manifestations of 2D Islamic geometric designs, meaning these insanely complex designs were made using nothing more than a humble compass and ruler.

In our world of digital manufacturing, it’s hard to imagine these intricate, perfect geometries were made by hand, one unit at a time, hundreds of years ago.

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In this picture, you can see the wood scaffolding and cement used to piece one style of Muqarnas together:

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And what the finished product would look like:

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Each Muqarnas composition has five common qualities:

1. A three-dimensional shape that can readily be flattened into a two-dimensional geometric outline (and begins as such)

2. The depth of design is variable and determined entirely by the maker

3. Simultaneously architectural and ornamental by nature

4. No intrinsic logical or mathematical boundaries so can be scaled ad infinitum

5. Consists of stacked tiers made up of cells, each of which has a facet and a roof of sorts

UK-based author, educator, and artist Eric Broug is a renowned scholar on Islamic geometrics who has made it his mission to spread the knowledge and joy of muqarnas through his workshops, lectures, books, and tutorials, all housed under the School of Islamic Geometric Design.  Be sure to check out the Resources page, which features tutorials as well as a teacher guide. 

 

Broug has also created a fascinating TED-Ed video on the complex geometry of Islamic design that’s definitely worth a watch.

His “Practical Introduction to Muqarnas” gives a great, illustrative overview:

It’s all about carefully arranging the pieces of the composition.

Watch three minutes of Nhari assembling a Muqarnas composition and realize how incredibly painstaking the process would be for a large-scale area:

How to hand-carve each of the pieces, as artisans have done for centuries:

The 2D Behind the 3D

For example, here’s the Iwan (the large, arched entrance) of the Jameh Mosque in Yazd, Iran:

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And Takahashi’s line drawing:

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And a closeup of the Iwan ceiling:

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Infinite Material Possibilities

The beauty of such intricate designs based on classic geometries is that they’re infinitely scalable in a vast array of materials.  No picture can capture how amazing it is to physically be standing under a giant muqarnas composition.  Each material inspires a different effect.  The most surreal, perhaps, are the mirror-encrusted muqarnas, most often found in mosques and shrines.  Even though you’re surrounded by mirrors, the angles and small size of the individual pieces make it so you never see a reflection, only brightness, and light.

Plaster

Fatimah Masumeh Shrine in Qom:

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Water Museum in Yazd:

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Hand-painted, in one of the luxury suites at the Abbasi Hotel in Isfahan:

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Tile

The Shah Mosque in Isfahan:

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Be sure to take a look at Nevit Dilman’s super-high-resolution image on Wikipedia, where you can really zoom in and see all the glorious details.

The Jameh Mosque in Yazd:

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Poet Hafiz’s Shrine in Shiraz:

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Brick

Jameh Mosque in Yazd:

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Mirrored

Fatimah Masoumeh Shrine in Qom:

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Chehel Sotun Palace in Isfahan:

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Shah-e Cheragh Shrine in Shiraz:

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Wood

The Music Room of the Ali Qapu Palace in Isfahan (photographed by Mohammad Reza Domiri Ganji):

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A great assembly shot from a style of wooden Muqarnas on this site:

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Gold

Fatimah Masumeh Shrine in Qom:

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Modern Rendition: Gadeken’s Roshanai

Great things happen when makers incorporate ancient designs into modern works.

Bay Area artist Charles Gadeken recently incorporated metal Muqarnas compositions in the entryways of his latest large-scale piece, entitled Roshanai (meaning illuminate), a 108-ft long tunnel of light and sound.

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Here’s the 3D rendering of the entryway:

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The flattened Geometry:

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A section of the metal Muqarnas:

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And the finished product at night:

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We’ll wrap up with one more Muqarnas just for the sake of eye candy.

I’d love to see the Alhambra, particularly the Muqarnas, in the Hall of the Two Sisters.

Wow!

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Check out one of our Secret Energy courses to learn about how classic geometries relate to the building blocks of life.

Go on a Mandelbulb / Mandelbox Trip here!

 

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