Bibliography
M. Arik and M. Sancak, ‹Turkish–Islamic art and Penrose tilings’, Balkan Physics Letters 15 (1 Jul 2007) 1–12.
J. Bonner, ‹Three traditions of self-similarity in fourteenth and fifteenth century Islamic geometric ornament’, Proc. ISAMA/Bridges: Mathematical Connections in Art, Music and Science, (Granada, 2003), eds. R. Sarhangi and N. Friedman, 2003, pp. 1–12.
J. Bonner, Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Derivation, unpublished manuscript.
J. Bourgoin, Les Eléments de l’Art Arabe: Le Trait des Entrelacs, Firmin-Didot, 1879. Plates reprinted in Arabic Geometric Pattern and Design, Dover Publications, 1973.
J.-M. Castéra, Arabesques: Art Décoratif au Maroc, ACR Edition, 1996.
J.-M. Castéra, ‹Zellijs, muqarnas and quasicrystals’, Proc. ISAMA, (San Sebastian, 1999), eds. N. Friedman and J. Barrallo, 1999, pp. 99–104.
G. M. Fleurent, ‹Pentagon and decagon designs in Islamic art’, Fivefold Symmetry, ed. I. Hargittai, World Scientific, 1992, pp.␣263–281.
B. Grünbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman, 1987.
E. H. Hankin, ‹On some discoveries of the methods of design employed in Mohammedan art’, J. Society of Arts 53 (1905) 461–477.
E. H. Hankin, The Drawing of Geometric Patterns in Saracenic Art, Memoirs of the Archaeological Society of India, no 15, Government of India, 1925.
E. H. Hankin, ‹Examples of methods of drawing geometrical arabesque patterns’, Math. Gazette 12 (1925) 370–373.
E. H. Hankin, ‹Some difficult Saracenic designs II’, Math. Gazette 18 (1934) 165–168.
E. H. Hankin, ‹Some difficult Saracenic designs III’, Math. Gazette 20 (1936) 318–319.
C. S. Kaplan, ‹Computer generated Islamic star patterns’, Proc. Bridges: Mathematical Connections in Art, Music and Science, (Kansas, 2000), ed. R. Sarhangi, 2000, pp. 105–112.
C. S. Kaplan, ‹Islamic star patterns from polygons in contact’, Graphics Interface 2005, ACM International Conference Proceeding Series 112, 2005, pp. 177–186.
A. J. Lee, ‹Islamic star patterns’, Muqarnas IV: An Annual on Islamic Art and Architecture, ed. O. Grabar, Leiden, 1987, pp.␣182–197.
P. J. Lu and P. J. Steinhardt, ‹Decagonal and quasi-crystalline tilings in medieval Islamic architecture’, Science 315 (23 Feb 2007) 1106–1110.
P. J. Lu and P. J. Steinhardt, ‹Response to Comment on “Decagonal and quasi-crystalline tilings in medieval Islamic architecture”, Science 318 (30 Nov 2007) 1383.
F. Lunnon and P. Pleasants, ‹Quasicrystallographic tilings’, J.␣Math. Pures et Appliqués 66 (1987) 217–263.
E. Makovicky, ‹800-year old pentagonal tiling from Maragha, Iran, and the new varieties of aperiodic tiling it inspired’, Fivefold Symmetry, ed. I. Hargittai, World Scientific, 1992, pp. 67–86.
E. Makovicky, ‹Comment on “Decagonal and quasi-crystalline tilings in medieval Islamic architecture”, Science 318 (30 Nov 2007) 1383.
E. Makovicky and P. Fenoll Hach-Alí, ‹Mirador de Lindaraja: Islamic ornamental patterns based on quasi-periodic octagonal lattices in Alhambra, Granada, and Alcazar, Sevilla, Spain’, Boletín Sociedad Española Mineralogía 19 (1996) 1–26.
E. Makovicky and P. Fenoll Hach-Alí, ‹The stalactite dome of the Sala de Dos Hermanas—an octagonal tiling?’, Boletín Sociedad Española Mineralogía 24 (2001) 1–21.
E. Makovicky, F. Rull Pérez and P. Fenoll Hach-Alí, ‹Decagonal patterns in the Islamic ornamental art of Spain and Morocco’, Boletín Sociedad Española Mineralogía 21 (1998) 107–127.
G. Necipoğlu, The Topkapi Scroll: Geometry and Ornament in Islamic Architecture, Getty Center Publication, 1995.
J. Rigby, ‹A Turkish interlacing pattern and the golden ratio’, Mathematics in School 34 no 1 (2005) 16–24.
J. Rigby, ‹Creating Penrose-type Islamic interlacing patterns’, Proc. Bridges: Mathematical Connections in Art, Music and Science, (London, 2006), eds. R. Sarhangi and J. Sharp, 2006, pp. 41–48.
F. Rull Pérez, ‹La noción de cuasi-cristal a través de los mosaicos árabes’, Boletín Sociedad Española Mineralogía 10 (1987) 291–298.
P. W. Saltzman, ‹Quasi-periodicity in Islamic ornamental design’, Nexus VII: Architecture and Mathematics, ed. K. Williams, 2008, pp. 153–168.
M. Senechal, Quasicrystals and Geometry, Cambridge Univ. Press, 1995.
M. Senechal and J. Taylor, ‹Quasicrystals: The view from Les Houches’, Math. Intelligencer 12 no 2 (1990) 54–64.
Internet Resources
ArchNet. Library of digital images of Islamic architecture, http://archnet.org/library/images/
E. Harriss and D. Frettlöh, Tilings Encyclopedia, http://tilings.math.uni-bielefeld.de/
C. S. Kaplan, taprats, computer-generated Islamic star patterns, http://www.cgl.uwaterloo.ca/~csk/washington/taprats/
P. J. Lu and P. J. Steinhardt, Supporting online material for [17], http://www.sciencemag.org/cgi/content/full/315/5815/1106/DC1
D. Wade, Pattern in Islamic Art: The Wade Photo-Archive, http://www.patterninislamicart.com/
Acknowledgments
I would like to thank Paul Steinhardt for clarifying some statements in [17] and Peter Saltzman for sharing a draft of his article [29]. I am also very grateful to the following people for their critical reading of an early draft of this article and for suggesting improvements: Helmer Aslaksen, Elisabetta Beltrami, Jean-Marc Castéra, Dirk Frettlöh, Chaim␣Goodman-Strauss, Emil Makovicky, John Rigby, Joshua Socolar, and John Sullivan.
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Cromwell, P.R. The Search for Quasi-Periodicity in Islamic 5-fold Ornament. Math Intelligencer 31, 36–56 (2009). https://doi.org/10.1007/s00283-008-9018-6
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DOI: https://doi.org/10.1007/s00283-008-9018-6