Fatin Uluengin - muqarnas

chris cambré, Aug 7, 2020

In this GeoGebrabook we focus on the drawings in the book Mukarnas (ISBN 978-975-7618-64-5) by Fatin Uluengin. Stepwise we look at the construction of the plan and compare them with the plans drawn by Shiro Takahashi. There's a dutch version of this book at [url]https://www.geogebra.org/m/xkaaxdt4[/url] You can find a more general introduction on muqarnas at [url]https://www.geogebra.org/m/n7ps6rtv[/url]

Table of Contents

  1. construction and symmetry
    1. structure of muqarnas
    2. construction with cells
    3. symmetries
  2. 8/2 stars
    1. grid
    2. Sivas - Şifaiye Madrassa
    3. Sivas - Şifaiye Madrassa
    4. Malatya - Ulu Camii
    5. Kopie vanMalatya - Ulu Camii
  3. Alternative placing of the 8/2 ster
    1. alternative 8/2
    2. Diyarbakkir - Ulu Camii
  4. additional stars
    1. Erzurum - Hatuniye madrassa
    2. Erzurum - Hatuniye madrassa
    3. Kayseri - Sahibiye madrassa
    4. Kayseri - Sahibiye madrassa
  5. isometric grid
    1. Ankara - Arslanhane Cami mihrab
    2. Ankara - Arslanhane Cami mihrab
    3. Ankara - Arslanhane Cami mihrab
  6. unit cells
    1. Nigde - Ak madrassa
    2. Nigde - Ak madrassa
  7. stars as small domes and stalactites
    1. Edirne - Üç Şerefeli
    2. Edirne - Üç Şerefeli
    3. Amasya - Beyazit Cami
    4. Amasya - Beyazit Cami

1.

construction and symmetry

Fatin Uluengin catalogs muqarnas starting from their symmetry. He names them after the number of points of the star in the apex of the muqarnas. Then he constructs the plan of the muqarnas around the stars exploring different kinds of tiling.

  • 1. structure of muqarnas
  • 2. construction with cells
  • 3. symmetries

1.1.

structure of muqarnas

In nice drawing Fatin Uluengin shows the transition of a 2D plan to a 3D realisation.[br]From bottom to the top:[br][list][*]Upon the 2D plan cells are placed whose ground plane matches with the figures of the plan.[/*][*]These cellen form concentric circles.[/*][*]In 3D one puts these concentric circles one upon the other.[/*][/list]
Drawing: Fatin Uluengin
Next applet shows dynamicly this transition from a plan to a 3D construction.
– chris cambré

1.2.

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1.3.

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2.

8/2 stars

Frequently uses are 8/2 stars. In them there's a half 8-pointed star in the apex of the muqarnas.

  • 1. grid
  • 2. Sivas - Şifaiye Madrassa
  • 3. Sivas - Şifaiye Madrassa
  • 4. Malatya - Ulu Camii
  • 5. Kopie vanMalatya - Ulu Camii

2.1.

grid

Around a half 8-pointed star you can construct a regular gridof squares and rhombuses. [br]This combination is a wide spread basic scheme for muqarnas in Turkey.[br]The next applet how you can draw the outlines for muqarnas with different size around the half 8-pointed star. Fatin Uluengin gives Turkish examples fot the different options.[br]Click on the checkboxes to see how examples of plans fit within this tiling. Only the tiles at the edges diverge to fit with the border.
[list][*]1-1: Sivas Sifaiye Madrassa[/*][*]3-3: Ahlet: Hassan Padrisah Kümbeti[/*][*]5-5: Erzurum Sultan kümbet[/*][*]6-6: Kayseri Sultan Han[/*][*]7-7: Kayseri Cifte Madrassa[/*][/list][br]In next applet we're constructing this tiling stepwise around a half 8-pointed star.
– chris cambré

2.2.

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2.3.

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2.4.

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2.5.

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3.

Alternative placing of the 8/2 ster

When rotating the 8/2 star, we can apply a different kind of tiling around it.

  • 1. alternative 8/2
  • 2. Diyarbakkir - Ulu Camii

3.1.

alternative 8/2

Unlike the 8-pointed star in the muqarnas in Sivas and Malatya (left) we can start from a star rotated by 22.5°.[br]In next applet we start from this half star and we construct stepwise a tiling around it.
For this tiling too we can different outlines for muqarnas plans.[br]Drag the slider in the applet and explore different examplesfrom 1-1 to 9-9.[br]You can notice that the outer border for the muqarnas can as well be a half octagon as a rectangle.[br]On fist sight the 1-1 plan looks very different of the 8-8 plan, maar in the applet you can see they match with the same tiling.
– chris cambré

3.2.

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4.

additional stars

Instead of drawing a regular tiling arounda star in the apex of the muqarnas, we can create a circle of additional stars in a compass construction. Later on the space between the border of the muqarnas and the stars is filled up with irregular figures.

  • 1. Erzurum - Hatuniye madrassa
  • 2. Erzurum - Hatuniye madrassa
  • 3. Kayseri - Sahibiye madrassa
  • 4. Kayseri - Sahibiye madrassa

4.1.

Erzurum - Hatuniye madrassa

The plan of the muqarnas above the entrance of the Hanuniye madrassa from 1253 isn't built up with a set of basic figures. [br][list][*]In next applet you can fommow stepwise the construction of rays out of a central point.[/*][*]On these rays centers of circles are defined.[/*][/list]
[list][*]These circles defines stars.[/*][*]The space around these stars are filled up with irregular figures.[/*][/list]
The result in the plan of the muqarnas is[br][list][*]a circle of five connected 5-pointed stars,[/*][*]a circle of six 7-pointed stars,[/*][*]two additional 9-pointed stars. [/*][/list]Below you can see Shiro Takahashi's drawing:
– chris cambré

4.2.

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4.3.

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4.4.

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5.

isometric grid

Instead of using a tiling with squares, rhombuses etc. we can use an isometric grid instead.

  • 1. Ankara - Arslanhane Cami mihrab
  • 2. Ankara - Arslanhane Cami mihrab
  • 3. Ankara - Arslanhane Cami mihrab

5.1.

Ankara - Arslanhane Cami mihrab

The muqarnas of the mihrab in the [url=https://en.wikipedia.org/wiki/Aslanhane_Mosque]Arslanhane Mosque in Ankara[/url] from 1290 is built upon an isometric grid with a half 6-pointed star in the apex.[br]You can follow the construction stepwise in the applet.
This is Shiro Takahashi's plan:
– chris cambré

5.2.

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5.3.

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6.

unit cells

We can devide the plan of a muqarnas in unit cells, in which the same construction is repeated.

  • 1. Nigde - Ak madrassa
  • 2. Nigde - Ak madrassa

6.1.

Nigde - Ak madrassa

The [url=https://archnet.org/sites/2074]Ak madrassa[/url] in Nigde dates from 1409. Het plan of the muqarnas of the monumental gate is constructed out of 8 squares. [br]In next applet you can follow stepwise the construction of the unit square:[br][list][*]In the center of the square an 8-pointed star is drawn. [/*][*]Aroud this star squares define a regular octagon.[/*][*]In the four corners an irregular 5-pointed star is constructed[br][/*][*]The remaining space is filled in with irregular figures[/*][/list]
This basic square forms the unit cell of the muqarnas.
– chris cambré

6.2.

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7.

stars as small domes and stalactites

In 15th and 16th century spectacular muqarnas are constructed that break the smooth curvature of a normal dome. Additional stars create additional domes within the vault showing a large decorated stalactite in the middle.

  • 1. Edirne - Üç Şerefeli
  • 2. Edirne - Üç Şerefeli
  • 3. Amasya - Beyazit Cami
  • 4. Amasya - Beyazit Cami

7.1.

Edirne - Üç Şerefeli

Plan combining different types of stars
The [url=https://en.wikipedia.org/wiki/%C3%9C%C3%A7_%C5%9Eerefeli_Mosque]Üç_Şerefeli mosque in Edirne[/url] dates from the 5th century.[br]The same construction of this muqarnas is used in otherTurkish mosques too:[br][list][*]Üç Şerefeli mosque in Edirne (1447)[br][/*][*]Fatih mosque in Istanbul (1462)[/*][*]Hatuniye mosque in Tokat (1484)[/*][*]Beyazit mosque in Edirne (1487)[/*][*]Yavuz Selim mosque in Istanbul (1528)[/*][/list][br]In next applet you can follow stepwise how the plan is drawn using a compass construction:[br][list][*]In the rectangular plan a half circle is drawn around the apex.[/*][*]Additionally on the left and on the right large circles are drawb circumscribing a 9-pointed star.[/*][*]Around this 9-pointed star a circle of 5-pointed stars is created.[br][/*][*]Beneath in the middle a half 10-pointed star appears and in the upper corners we can see quarters of 10-pointed star.[br][/*][*]The remaining place is filled in with additional irregular figures.[/*][/list]Beneath the applet you can see how Shiro Takahashi accentuates the different types of stars using different colors.
On the picture you can recognise the different elements of the plan:[br][list][*]Below you recognise the supporting base shaped as a half 10-pointed star[/*][*]Left and right you see the big 9-pointed stars as domes with a big stalactite in the center[/*][*]The circles of 5-pointed stars around the big stars appear as circles of stalactites.[/*][*]The half 10-pointed star in the apex appears as a niche in the apex of the muqarnas.[/*][/list]
– chris cambré

7.2.

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7.3.

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7.4.

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Information