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1 The Historical Antecedents, Initial Development, Maturity, and Dissemination of Islamic Geometric Patterns

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Abstract

Since the earliest period of Islamic history the ornamental traditions of Muslim cultures have found expression in a highly diverse range of styles and media. Throughout this broad sweep of ornamental diversity and historical longevity there remained an essential Islamic quality that differentiates this tradition from all others. One of the primary characteristics responsible for such cohesion is the pervasive triadic nature of Islamic ornament. From its onset, this ornamental tradition employed three principal design idioms: calligraphy, geometry, and stylized floral. It can be argued that figurative art depicting both human and animal forms is also characteristic of Islamic art. This additional feature of Islamic art requires brief mention, if only to legitimately dismiss it for the purposes of this discussion. During the Umayyad period figurative motifs were widely used in both architecture and the applied arts, and virtually all subsequent Muslim cultures used figurative depictions to a greater or lesser extent. Such work has always been anathema to Islamic religious sentiments and frequently to Muslim cultural sensibilities. Even among the Umayyads, who inherited the figural traditions of the late antique period, the use of figurative depictions was invariably secular and often associated with courtly life. The eighth-century Umayyad palaces of Qusayr ‘Amra and Khirbat al-Mafjar are replete with figurative decoration, the former carried out in fresco and the latter in mosaic and carved stucco. Such notable examples notwithstanding, the surviving religious architecture of the Umayyads is evidence of the interdiction in the use of human and animal depiction within mosques. It is significant that the Umayyad architectural motifs in the mosaics of the Great Mosque of Damascus and the Dome of the Rock were entirely devoid of human and animal figures; and the one area of carved stone ornament that is entirely without animal representation at the eighth century Umayyad palace of Qasr al-Mshatta is a wall directly adjacent to the mosque. The figurative restraint in the ornament of Mosques was adhered to strictly throughout succeeding Muslim cultures, and the continued use of human and animal figures was generally limited to the decoration of utility objects such as ceramic pottery, textiles, metal vessels, furniture, wood and ivory boxes, and the occasional architectural expression in murals and carved relief in such secular locations as palaces, private homes, and bath houses. However, with the exception of the miniature traditions, this form of decoration was certainly never a primary feature in Islamic art or architectural ornament. For all of their beauty and refinement, the figurative aesthetics of the Persian, Mughal, and Turkish miniature traditions were for the most part insular, and did not significantly overlap with other artistic traditions within these Muslim cultures. Notable exceptions include the “miniature” style of the enameled minai’i ware of late twelfth- and thirteenth-century Kashan; the so-called Kubachi painted ceramic vessels created in northeastern Persia during the Safavid period; and the many Persian painted tile panels produced during the Qarjar period. Perhaps the greatest indication of the lesser role that figurative imagery played throughout the history of Islamic art and architecture is the fact that the non-miniature figurative art of Muslim cultures was not subject to the concerted effort toward continued refinement and stylistic development that is a hallmark of the calligraphic, geometric, and floral traditions. As such, with the exception of the miniature traditions, figurative art can be regarded as tangential rather than integral to Islamic art, and to have been occasionally employed rather than part of an ongoing developmental evolution.

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Notes

  1. 1.

    Hillenbrand (1994a), 8.

  2. 2.

    Allen (1988), 17–37.

  3. 3.

    The depiction of the human figure in the fine art traditions of Persian, Turkish, and Mughal miniature painting is an exception to the conventions of human representation occasionally found in the ornamental and applied arts of various Islamic cultures. The reconciliation of these miniature traditions with the Islamic religion and Islamic cultures is a fascinating study, but outside the scope of this work.

  4. 4.

      –Watson (1973–75), 1–19.

    –Watson (1985).

    –Hillenbrand (1994b), 134–41.

  5. 5.

    Golombek et al. Chap. 4: “The Kubachi Problem and the Isfahan Workshop.”

  6. 6.

    Schimmel (1990), 77–114.

  7. 7.

    Each of the six principal cursive scripts (al-Aqlam as-Sitta) is associated with a student of Yaqut al-Musta’simi. These are Naskh (‘Abdallah as-Sayrafi), Muhaqqaq (‘Abdullah Arghun), Thuluth (Ahmad Tayyib Shah), Tauqi (Mubarakshah Qutb), Rihani (Mubarakshah Suyufi), and Riqa (Ahmad as-Suhrawardi). See Schimmel (1990), 22.

  8. 8.

    Tabbaa (2001), 34–35.

  9. 9.

    Tabbaa (2001), 34–44.

  10. 10.

    Schimmel (1990), 11.

  11. 11.

      –Furuzanfar, Badi’ al-Zaman (1956), no. 70.

    –Ernst (1997), 52.

  12. 12.

      –Weyl (1952).

    –Hargittai (1986).

    –Washburn and Crowe (1988).

    –Farmer (1996).

  13. 13.

      –Fedorov (1891), 345–291.

    –Pólya (1924), 278–282.

  14. 14.

      –Lalvani (1982).

    –Lalvani (1989).

    –Abas and Salman (1995).

  15. 15.

      –Müller (1944).

    –Grünbaum, Grünbaum and Shepherd (1986).

    –Pérez-Gómez (1987), 133–137.

  16. 16.

    A comparison and descriptive analysis of differing generative methodologies is covered in Chap. 2.

  17. 17.

    Bonner (2003).

  18. 18.

    Necipoğlu (1995), 239–283.

  19. 19.

    Bonner (2003).

  20. 20.

    From the collection of the El Djem Archaeological Museum, El Djem, Tunisia.

  21. 21.

    Kitzinger, Ernst. (1965), 341–352.

  22. 22.

    Creswell (1969), 75–79.

  23. 23.

    Several stucco window grilles were found in the ruins of the Umayyad palace of Qasr al-Hayr al-Gharbi (724–727): now in the National Museum of Damascus. The design of each of these is comprised of a central palm motif flanked by floral scrollwork rather than the overlapping circles under discussion.

  24. 24.

    Originally known as Bab al-Wuzara.

  25. 25.

    The portal of the palace of Qasr al-Hayr al-Gharbi is now in the National Museum of Dasmascus.

  26. 26.

    For a detailed analysis of pre-Islamic influences upon the development of early Islamic architecture, see Hillenbrand (1994a).

  27. 27.

    Necipoğlu (1995), 99–100.

  28. 28.

    Schimmel (1990), 18–19.

  29. 29.

    Creswell (1969), 75–79.

  30. 30.

    Caiger-Smith (1985), 21–31.

  31. 31.

    Necipoğlu (1995), 123.

  32. 32.

    Kitab fima yahtaju ilayhi al-sani min a’mal al-handasa, MS Persan 169, sec. 23, folios. 141b–179b, Bibliotheque Nationale, Paris.

  33. 33.

      –Özdural (1995), 54–71.

    –Necipoğlu (1995), 123.

  34. 34.

    Chester Beatty Library Ms. 1431, fol. 7b–8a.

  35. 35.

    Creswell (1969), 77.

  36. 36.

    King Ferdinand III of Castile converted the Great Mosque of Córdoba into a cathedral in 1236.

  37. 37.

    It is speculated that these two window screens may have been made for a country residence outside Córdoba: possibly that of al-Mansur. See Dodds [ed.] (1992), 252.

  38. 38.

    For a detailed exposition on the importance of Baghdad in the development of Islamic science and mathematics, and the influence of these developments upon the origins of the geometric design idiom, see Necipoğlu (1995), 131–166.

  39. 39.

    The Persian terms hazarbaf and parceh are also used for brickwork ornament. It is interesting that these terms are also associated with the woven rush matting and textile industries.

     –Wolff (1966), 118.

     –Creswell (1969), 186.

  40. 40.

    Hillenbrand (1994a), 144.

  41. 41.

    Blair (1991), 55.

  42. 42.

    This panel from Sabz Pushan, Nishapur, is now in the permanent collection of the Metropolitan Museum of Art, New York: Accession Number 40.170.442.

  43. 43.

    The Samanid Mausoleum is also known as the Tomb of Ismail the Samanid.

  44. 44.

    Hillenbrand (1994a), 373.

  45. 45.

    Ward (1993), 57.

  46. 46.

    Hoag (1977), 189.

  47. 47.

    This Ilkhanid Quran is in the National Library in Cairo: 72, pt. 19.

  48. 48.

    The Tomb of Abu Sa’id Abul Khayr in Mayhaneh, Turkmenistan, is known locally as the Tomb of Meana Baba.

  49. 49.

    Wilber (1939), 35.

  50. 50.

    Schneider (1980), pattern no. 225.

  51. 51.

    Currently in the collection of the Islamic Museum in Cairo.

  52. 52.

    MS Persan 169, fol. 188b.

  53. 53.

      –Özdulral (1996).

    –Necipoğlu [ed.] (Forthcoming).

  54. 54.

    Bier (2012).

  55. 55.

      –Makovicky (1992), 67–86 and (2007).

    –Lu and Steinhardt (2007b), 1106–1110.

    –Cromwell (2009), 36–56.

    –Cromwell (2015), 1–15.

  56. 56.

    MS Persan 169, fol. 192a.

  57. 57.

    MS Persan 169, fol. 193a.

  58. 58.

    Ettinghausen, Grabar and Jenkins-Madina (2001), 141, pl. 215.

  59. 59.

    Schneider (1980), pattern no. 352.

  60. 60.

    Schneider (1980), pattern no. 351.

  61. 61.

    Ettinghausen, Grabar and Jenkins-Madina (2001), 140–143.

  62. 62.

    Bonner (2016).

  63. 63.

      –Grabar (1990), 85, note 5.

    –Özdural (1998), 699–715.

    –Hogendijk (2012), 37–43.

  64. 64.

    The works of the mathematician and astronomer, Abu al-Wafa Buzjani (940–998), would have been familiar to ‘Umar Khayyam, and of especial relevance to this discussion would have been his work on right-angled spherical triangles and spherical trigonometry.

  65. 65.

    Bonner (2016).

  66. 66.

    In the collection of the National Museum of Afghanistan in Kabul, Afghanistan.

  67. 67.

    In the collection of the National Museum of Afghanistan in Kabul, Afghanistan. See Crane and Trousdale (1972), 215–226.

  68. 68.

    Terry Allen identifies the origin of the portal as predating the rest of the Bimaristan Arghun. See Allen (1999).

  69. 69.

    Schneider (1980), pattern no. 281.

  70. 70.

    Istanbul, Topkapi Sarayi Müzesi Kütüphanesi, MS A. 3472, fols. 165v–166r.

  71. 71.

    Necipoğlu (1995), 150–152.

  72. 72.

    Allen (1999), Chap. 2.

  73. 73.

    The al-Aqsa Mosque in Jerusalem is primarily a Fatimid building. However, the minbar was commissioned by the Zangid ruler Nur al-Din in 1168, placing it within the sphere of Seljuk influence. See Tabbaa (2001), 86–88.

  74. 74.

    Allen (2003).

  75. 75.

    Different dates for this portal have been posited. See Allen (1999).

  76. 76.

    This minbar is in the collection of the Hama National Museum in Syria.

  77. 77.

    Allen (1999), Chap. 8.

  78. 78.

    Azarian (1973), pl. 58.

  79. 79.

    Dar al-Athar al-Islamiyya Kuwait National Museum.

  80. 80.

    This pair of doors is no longer present at the Lower Maqam Ibrahim in Aleppo. Ernst Herzfeld published a drawing and description of this pattern, and this is the only record of its existence. See Herzfeld (1954–56), Fig. 56.

  81. 81.

    “It is the most complicated design ever produced by that branch of art. The almost unsolvable problem of a design based on horizontal groups of 11-pointed stars is solved by alternative intercalation of a parallel group of 12-pointed and one of 10-pointed stars between them”: Herzfeld (1943), 65.

  82. 82.

    Tabbaa (2001), 80–84.

  83. 83.

    Ettinghausen, Grabar and Jenkins-Madina (2001), 195.

  84. 84.

    Bloom (1988), 27–28.

  85. 85.

    One possible example of the Fatimid use of the fivefold system is a window grille in the northeast wall at the al-Hakim Mosque in Cairo. This is an acute dart motif generated from just the barrel hexagon, and one of the simplest fivefold field patterns. However, it is very likely that this window grille dates to the post-earthquake restoration by Amir Baybars al-Jashankir in 1303, or the restorations by Sultan al-Nasir Hasan in 1360.

  86. 86.

    For detailed accounts of Zangid and Ayyubid architecture and architectural ornament in Aleppo and Damascus, see

     –Allen (1999).

     –Tabbaa (2001).

  87. 87.

    For details on the dating of this portal, see Allen (1999), Chap. 5.

  88. 88.

    This mosaic panel was moved to the Christian chapel of the Mexuar by Morisco artists during the sixteenth century, and now resides at the Museo Nacional de Arte Hispanomusulmán in Granada. See Dodds [ed.] (1992), 374–375.

  89. 89.

    Allen (1999), Chap. 8.

  90. 90.

    Not to be confused with the city of Mazar-i Sharif in Afghanistan. The village of Mazar-i Sharif, where the Mausoleum of Muhammad Basharo is sited, is approximately 25 km east of Penjikent, Tajikistan, and located in the Zarafshan River valley.

  91. 91.

    Necipoğlu (1995), diagram no. 35.

  92. 92.

    Wilber (1939), 40.

  93. 93.

    Schneider (1980), pattern no. 198.

  94. 94.

    Schneider (1980), pattern no. 250.

  95. 95.

    Schneider (1980), pattern no. 206.

  96. 96.

    Schneider (1980), pattern no. 226.

  97. 97.

    Schneider (1980), pattern no. 227.

  98. 98.

    Gerd Schneider illustrates the close relationship between these examples in his patterns 227 and 228. However, in keeping with the totality of his illustrations, he does not provide generative methodologies or underlying formative structures. Schneider (1980).

  99. 99.

    Schneider (1980), pattern no. 215.

  100. 100.

    Schneider (1980), pattern no. 397.

  101. 101.

    Schneider (1980), pattern no. 403.

  102. 102.

    Schneider (1980), pattern no. 256.

  103. 103.

    Schneider (1980), pattern no. 413.

  104. 104.

    Schneider (1980), pattern no. 298.

  105. 105.

    Schneider (1980), pattern no. 441.

  106. 106.

    Schneider (1980), pattern no. 325.

  107. 107.

    Schneider (1980), pattern no. 281.

  108. 108.

    Schneider (1980), pattern no. 302.

  109. 109.

    Schneider (1980), pattern no. 303.

  110. 110.

    Schneider (1980), pattern no. 306.

  111. 111.

    Schneider (1980), pattern no. 236.

  112. 112.

    Schneider (1980), pattern no. 330.

  113. 113.

    Schneider (1980), pattern numbers 91–98.

  114. 114.

    Schneider (1980), pattern no. 91.

  115. 115.

    Schneider (1980), pattern no. 321. Schneider identifies no less than 38 examples of this pattern scattered throughout the many monuments built by the Sultanate of Rum: pp. 183–4.

  116. 116.

    Schneider (1980), pattern no. 217.

  117. 117.

    Schneider (1980), pattern no. 322.

  118. 118.

    Schneider (1980), pattern no. 320.

  119. 119.

    Schneider (1980), pattern no. 219. Schneider identifies 45 examples of the fivefold classic acute pattern in the many Anatolian Seljuk buildings he studied.

  120. 120.

    Schneider (1980), pattern no. 279.

  121. 121.

    Schneider (1980), pattern no. 377.

  122. 122.

    Schneider (1980), pattern no. 392.

  123. 123.

    A nineteenth century reproduction of the original panel is in the collection of the Victoria and Albert Museum, London; museum number 887–1184.

  124. 124.

    Schneider (1980), pattern no. 374.

  125. 125.

    Schneider (1980), pattern no. 376.

  126. 126.

    Schneider (1980), pattern no. 380.

  127. 127.

    Schneider (1980), pattern no. 370.

  128. 128.

    Schneider (1980), pattern no. 388. This door panel currently resides in the Ince Minare madrasa History Museum in Konya, Turkey.

  129. 129.

    Schneider (1980), pattern no. 363.

  130. 130.

    Schneider (1980), pattern no. 362.

  131. 131.

    Schneider (1980), pattern no. 367.

  132. 132.

    Schneider (1980), pattern no. 367.

  133. 133.

    Schneider (1980), pattern no. 369.

  134. 134.

    Schneider (1980), pattern no. 360.

  135. 135.

    Schneider (1980), pattern no. 365.

  136. 136.

    Schneider (1980), pattern no. 368.

  137. 137.

    Schneider (1980), pattern no. 204.

  138. 138.

    Schneider (1980), pattern no. 361.

  139. 139.

    The author is indebted to both Emil Makovicky and Jean-Marc Castéra for independently discovering the geometric similarity between these two fivefold patterns. See Castéra (2016).

  140. 140.

    Schneider (1980), pattern no. 366.

  141. 141.

    Schneider (1980), pattern no. 382.

  142. 142.

    Schneider (1980), pattern no. 386.

  143. 143.

    Schneider (1980), pattern no. 387.

  144. 144.

    Schneider (1980), pattern no. 216.

  145. 145.

    Schneider (1980), pattern no. 205.

  146. 146.

    Schneider (1980), pattern no. 209.

  147. 147.

    Schneider (1980), pattern no. 359.

  148. 148.

    Schneider (1980), pattern no. 218 (pl. 19 and 34).

  149. 149.

    Schneider (1980), pattern no. 218 (pl. 34). Schneider compares the similarity between the nonagonal pattern from the Alaeddin Mosque in Konya with those from the Huand Hatun and Agzikara Han in this figure. However, he does not identify the reason for their similarity: that being the single underlying polygonal tessellation that is responsible for both these acute patterns.

  150. 150.

    Schneider (1980), pattern no. 211.

  151. 151.

    Schneider (1980), pattern no. 356.

  152. 152.

    Schneider (1980), pattern no. 402.

  153. 153.

    Schneider (1980), pattern no. 398.

  154. 154.

    Schneider (1980), pattern no. 401.

  155. 155.

    Schneider (1980), pattern no. 412.

  156. 156.

    Schneider (1980), pattern no. 358.

  157. 157.

    Schneider (1980), pattern no. 414.

  158. 158.

    Now spolia in the city walls of Egridir.

  159. 159.

    Schneider (1980), pattern no. 418.

  160. 160.

    Schneider (1980), pattern no. 407.

  161. 161.

    Schneider (1980), pattern no. 435.

  162. 162.

    Schneider (1980), pattern no. 408.

  163. 163.

    Schneider (1980), pattern no. 406.

  164. 164.

    Schneider (1980), pattern no. 423.

  165. 165.

    Schneider (1980), pattern no. 429.

  166. 166.

    This stone panel currently resides in the Museum of Wooden Artifacts and Stone Carving in Konya: collection number 157092.

  167. 167.

    Schneider (1980), pattern no. 427.

  168. 168.

    Schneider (1980), pattern no. 416.

  169. 169.

    Bibliothèque Nationale de France, Paris, MS Persan 169, fol. 195b.

  170. 170.

    Necipoğlu (1995), diagram no. 44.

  171. 171.

    Schneider (1980), pattern no. 421.

  172. 172.

    Schneider (1980), pattern no. 420.

  173. 173.

    Schneider (1980), pattern no. 417.

  174. 174.

    Herzfeld (1954–6), Fig. 56.

  175. 175.

    Schneider (1980), pattern numbers 437, 438, and 439.

  176. 176.

    Atil (1982), 195–196.

  177. 177.

    Cairo, National Library, 72, pt. 19.

  178. 178.

    Cairo, National Library, 8, ff. IV-2r.

  179. 179.

    The panel from this minbar is in the collection of the Victoria and Albert Museum, London: museum number 1051–1869.

  180. 180.

    Mamluk mashaf: Quranic manuscript No. 16; Islamic Museum, al-Aqsa Mosque, al-Haram al-Sharif, Jerusalem.

  181. 181.

    Metropolitan Museum of Art: gift of the Hagop Kevorkian Fund; 1970.327.8.

  182. 182.

    This Quran is in the collection of the Museum of Turkish and Islamic Arts; Sultanahmet, Istanbul, Turkey: Museum Inventory Number 450.

  183. 183.

    Mols (2006), cat. no. 46/1, pl. 191–194.

  184. 184.

    This minbar is in the collection of the Victoria and Albert Museum in South Kensington, London: 1050: 1 to 2–1869.

  185. 185.

    This fivefold pattern is from a nineteenth-century copy of the original Mamluk minbar door panel, and is part of the collection of the Victoria and Albert Museum in South Kensington, London: 887–1884.

  186. 186.

    This minbar is in the collection of the Victoria and Albert Museum in South Kensington, London: 1050: 1 to 2–1869.

  187. 187.

    This design was illustrated in the Monument Survey of Tripoli, Lebanon by Hala Bou Habib, Karl Sharro, and Hind Abu Ibrahim for the American University of Beirut, Department of Architecture, 1991 and 1992.

  188. 188.

    Bourgoin (1879), pl. 166. As with all Bourgoin’s illustrations, this pattern is not shown with its formative structure.

  189. 189.

    This pattern is also identical to a pattern in raised brick in one of the ground-level blind arches in the courtyard of the Mustansiriyah in Baghdad (1227–34). This building stems from the late Abbasid period just decades prior to the Mongol conquest. However, the incorporation of this sevenfold design appears to date from the nineteenth-century Ottoman restoration of this building. The earlier Ottoman provenance of this sevenfold pattern appears to have been the source of influence for the example at the Mustansiriya in Baghdad.

  190. 190.

    Bourgoin (1879), pl. 168.

  191. 191.

    In The Drawing of Geometric Patterns in Saracenic Art Hankin illustrates this underlying tessellation along with its associated obtuse pattern lines, but does not attribute the historical location of this design. As with his other published pattern analyses, he does not represent the polygonal elements used in creating his design examples as being part of a systematic methodology for pattern generation. In analyzing this design, it is likely that Hankin worked from the pattern collection of Joules Bourgoin (1879), plate 167. Hankin (1925a).

  192. 192.

    Bourgoin (1879), pl. 169.

  193. 193.

    Bourgoin (1879), pl. 165.

  194. 194.

    This pair of minbar doors is in the collection of the Metropolitan Museum of Art in New York City: accession number 91.1.2064.

  195. 195.

    This Mamluk bi-fold door presently serves as the entry door of the French Embassy in Egypt.

  196. 196.

    The author has extrapolated the reconstruction of this pattern from the Qartawiyya Madrasa in Tripoli, Lebanon, from an indistinct photograph taken by Hana Alamuddin [Aga Khan Visual Archive, Massachusetts Institute of Technology; catalogue number IHT0078]. This is the only image of this compound isometric pattern that the author has been able to find. The analysis represented in Fig. 355d is based upon the inherent logic of the 15- and 12-fold regions of local symmetry as exemplified in the indistinct proportions indicated within this photograph. A closer examination of this example may reveal slightly different angles in the crossing pattern lines, and pattern line relationships.

  197. 197.

    In the collection of the Royal Museum of Scotland: museum inventory number A.1884.2.1.

  198. 198.

    Cairo National Library; 7, ff. IV-2r.

  199. 199.

    Moved in 1416–17 to the Sultan Mu’ayyad Mosque in Cairo where it functions as the main entry door to this day. See Mols (2006), 214.

  200. 200.

    Necipoğlu (1995), 101.

  201. 201.

    In the collection of the Metropolitan Museum of Art, New York, Fletcher Fund, (1929), 29.22.

  202. 202.

    Castéra (1996).

  203. 203.

    London; British Library, Or. 1405, ff. 370v–371r.

  204. 204.

    Makovicky (2000), 37–41.

  205. 205.

    O’Keeffe and Hyde (1996).

  206. 206.

    In the collection of the Museo del Ejército, Madrid: no. 24.902.

  207. 207.

    For more information on this distinctive regional style see:

     –Piccard (1983).

     –Castéra (1996).

  208. 208.

    The cultural adoption of Islamic geometric patterns as a primary ornamental devise was primarily promulgated under the auspices of Turkic, Persian, and Arab patronage. The ornamental traditions of the Muslim populations in the more peripheral regions of sub-Saharan Africa, southeastern Europe, central Russia, the southern portion of the Indian subcontinent, southeast Asia, and China utilized this design aesthetic to a far less degree. When geometric patterns were employed, they were, more often than not, simplistic and derivative. All of these more peripheral cultures had their own distinctive and rich ornamental traditions that would have satisfied the aesthetic expectations of their artists and patrons. However, it is possible that the wider incorporation of more sophisticated Islamic geometric patterns would have likely appealed to these Muslim cultures had their artists been privy to the very specific design methodology required for their production.

  209. 209.

    The Persian historian Ata al-Mulk Jujayni wrote in his account of the Mongols, Ta’rikh-i jahan-gusha (History of the World Conqueror) that the order was given for the whole population of Merv, including women and children, to be put to death except for 400 artisans.

  210. 210.

    An inscription on a panel of faience mosaic at the Sirçali Madrasa in Konya, Turkey (1242) states that the work was carried out by “Muhammad, son of Muhammad, son of Othman, architect of Tus.” See Wilber (1939), 40.

  211. 211.

    Pope (1965), 171.

  212. 212.

    Wilber (1955), 124–126.

  213. 213.

    Calligraphed by ‘Ali ibn Muhammad al-Husayni in Mosul (1310). British Library, Or. 4945, ff. IV-2r.

  214. 214.

    Chester Beatty Library Ms. 1614 (Arberry No. 92).

  215. 215.

    Cairo National Library; 72, pt. 19.

  216. 216.

    Necipoğlu (1995), diagram number 67.

  217. 217.

    Another example of this unusual arrangement of acute five-pointed stars is found in the pattern that fills the tympanum of the arched entry portal at the hospital of the Great Mosque of Darussifa in Divrigi, Turkey (1228–29): although this Mengujekid pattern is simplistic by comparison.

  218. 218.

    Hankin (1925a), Figs. 45–50.

  219. 219.

    Necipoğlu (1995), diagram number 90a.

  220. 220.

    Necipoğlu (1995), diagram no. 8.

  221. 221.

    Schneider (1980), pattern no. 73.

  222. 222.

    This Quran is often given the appellation of the Uljaytu Quran. National Museum, Cairo; 72, part. 22.

  223. 223.

    Necipoğlu (1995), diagram no. 72d.

  224. 224.

    Necipoğlu (1995), diagram no. 30.

  225. 225.

    Necipoğlu (1995), diagram no. 35.

  226. 226.

    Necipoğlu (1995), diagram no. 81a.

  227. 227.

    Hankin (1925a), Fig. 34, pl. VII.

  228. 228.

    Necipoğlu (1995), 37–38.

  229. 229.

    Necipoğlu (1995), diagram no. 44.

  230. 230.

    Bibliothèque Nationale de France, Paris, MS Persan 169, fol. 195a.

  231. 231.

    Necipoğlu (1995), diagram no. 39.

  232. 232.

    Necipoğlu (1995), diagram no. 42.

  233. 233.

    Hankin (1925a).

  234. 234.

    Hankin (1925a), pl. XIII, Figs 45–50.

  235. 235.

    The alif is the first letter of the Arabic alphabet. It is an ascender that is made from a single vertical stroke.

  236. 236.

    Bonner (2003), 3.

  237. 237.

    Bonner (2003).

  238. 238.

    One has to assume the likelihood that the artists who developed the systematic dual-level methodology were unfamiliar with the sevenfold system of pattern generation.

     –Bonner and Pelletier (2012), 141–148.

     –Pelletier and Bonner (2012), 149–156.

  239. 239.

    It has been suggested that the Persian artists responsible for a dual-level pattern within an arch spandrel at the Imamzada Darb-i Imam in Isfahan applied quasiperiodic substitution rules while designing this example of dual-level geometric design; and that these artists may have had specific knowledge of the science of quasiperiodicity some 500 years before the discoveries of Sir Roger Penrose in the 1970s. However, the fact that the recursive use of the fivefold system of pattern generation can be used to create true quasiperiodic designs does not mean that the dual-level use of this system at the Imamzada Darb-i Imam is actually quasiperiodic. A rudimentary examination of the cited example reveals that both levels of the overall design repeat within the same rhombic unit cell: the very definition of periodic tiling. The claim to have found quasicrystallinity in the design from the Imamzada Darb-i Imam is based upon overlooking the unit cell in favor of arbitrarily isolating and analyzing limited portions of the overall structure. See Lu and Steinhardt (2007a). See also:

     –Makovicky and Hach-Ali (1996), 1–26.

     –Saltzman (2008), 153–168.

     –Cromwell (2009), 36–56 and (2015).

  240. 240.

    Cromwell (2009), 47.

  241. 241.

    In an earlier publication the author identified just three varieties of Islamic geometric self-similar design, but has since identified a fourth historical variety as a hybrid of his original type A and type B. As such, in this work the hybrid form is designated as type C, and the former type C is now renamed as type D. See Bonner (2003).

  242. 242.

    The Imamzada Darb-i Imam employs a second example of this particular fivefold type A dual-level design in a pair of arch spandrels. This is a vastly inferior representation of this fine design, with multiple mistakes in the application of the secondary design. It is also poorly constructed with grossly disproportional polygonal figures, such as the pentagons, in the primary design. Its poor construction and myriad mistakes in the layout of the secondary elements lead one to assume that this was produced by a separate set of artists possibly working at a later date.

  243. 243.

    This may have been produced during the sixteenth century during Safavid rule.

     –Necipoğlu (1995), 37.

  244. 244.

    This may date from the Safavid period.

  245. 245.

    Peter Cromwell’s detailed methodological analysis of the type C dual-level design in the entry portal of the Friday Mosque at Yazd demonstrates the use of the fourfold system A in its creation. See Cromwell (2012a), 159–168.

  246. 246.

    The large number of examples of type D dual-level patterns at the Alhambra has led Jean-Marc Castéra, a renowned specialist in Islamic geometric art, to refer to this variety of design as the Alhambra Technique. See Castéra (1996), 276–277.

  247. 247.

    –Makovicky and Hach-Ali (1996), 1–26.

    –Bonner (2003), 10–11.

  248. 248.

    Hutt and Harrow (1979), 61–65.

  249. 249.

    O’Kane (1987), 70.

  250. 250.

    Hutt and Harrow (1979), 61.

  251. 251.

    Bonner (2003), 5.

  252. 252.

    Necipoğlu (1995), Chap. 1.

  253. 253.

    The author is using the diagram numbers for each separate design as attributed by Gülru Necipoğlu: See Necipoğlu (1995).

  254. 254.

    Allen (1988), 1–15.

  255. 255.

    Kuhnel (1962), 58.

  256. 256.

    Coomaraswamy (1944), 109–28.

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Bonner, J. (2017). 1 The Historical Antecedents, Initial Development, Maturity, and Dissemination of Islamic Geometric Patterns. In: Islamic Geometric Patterns. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0217-7_1

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