Advertisement

The Mathematical Intelligencer

, Volume 37, Issue 4, pp 30–44 | Cite as

Cognitive Bias and Claims of Quasiperiodicity in Traditional Islamic Patterns

  • Peter R. Cromwell
Article

Keywords

Mathematical Intelligencer Small Module Penrose Tiling Substitution Tiling Mirror Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. A. al Ajlouni, “The global long-range order of quasi-periodic patterns in Islamic architecture,” Acta Crystallographica A 68 (2012) 235–243.CrossRefMathSciNetGoogle Scholar
  2. 2.
    E. Baer, Islamic Ornament, Edinburgh University Press, Edinburgh, 1998.Google Scholar
  3. 3.
    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), R. Sarhangi and N. Friedman, eds. 2003, pp. 1–12.Google Scholar
  4. 4.
    J.-M. Castéra, Arabesques: Art Décoratif au Maroc, ACR Edition, Paris, 1996.Google Scholar
  5. 5.
    P. R. Cromwell, “The search for quasi-periodicity in Islamic 5-fold ornament,” Math. Intelligencer 31 no 1 (2009) 36–56.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    P. R. Cromwell, “Hybrid 1-point and 2-point constructions for some Islamic geometric designs,” J. Math. and the Arts 4 (2010) 21–28.zbMATHCrossRefGoogle Scholar
  7. 7.
    P. R. Cromwell, “Islamic geometric designs from the Topkapı Scroll II: a modular design system,” J. Math. and the Arts 4 (2010) 119–136.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    P. R. Cromwell, “A modular design system based on the Star and Cross pattern,” J. Math. and the Arts 6 (2012) 29–42.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    P. R. Cromwell, “Modularity and hierarchy in Persian geometric ornament,” preprint 2013. http://www.liv.ac.uk/∼spmr02/ islamic/.
  10. 10.
    P. R. Cromwell and E. Beltrami, “The whirling kites of Isfahan: geometric variations on a theme,” Math. Intelligencer 33 no 3 (2011) 84–93.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    R. Elwes, Maths in 100 Key Breakthroughs, Quercus, New York, 2013.Google Scholar
  12. 12.
    B. Goldacre, Bad Science, Fourth Estate, London, 2008.Google Scholar
  13. 13.
    B. Grünbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman, New York, 1987.Google Scholar
  14. 14.
    B. Grünbaum and G. C. Shephard, “Interlace patterns in Islamic and Moorish art,” Leonardo 25 (1992) 331–339. Reprinted in The Visual Mind: Art and Mathematics, ed. M. Emmer, MIT Press, Cambridge, 1993, pp. 147–155.Google Scholar
  15. 15.
    A. J. Lee, “Islamic star patterns,” Muqarnas IV: An Annual on Islamic Art and Architecture, O. Grabar, ed. E. J. Brill, Leiden, 1987, pp. 182–197.Google Scholar
  16. 16.
    D. Levine and P. J. Steinhardt, “Quasicrystals I: definition and structure,” Physical Review B 34 (1986) 596–616.CrossRefGoogle Scholar
  17. 17.
    P. J. Lu and P. J. Steinhardt, “Decagonal and quasi-crystalline tilings in medieval Islamic architecture,” Science 315 (23 Feb 2007) 1106–1110.zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    R. Lück, “Penrose sublattices,” J. Non-Crystalline Solids 117–118 (1990) 832–835.CrossRefGoogle Scholar
  19. 19.
    E. Makovicky, “800-year old pentagonal tiling from Maragha, Iran, and the new varieties of aperiodic tiling it inspired,” Fivefold Symmetry, I. Hargittai, ed. World Scientific, Singapore, 1992, pp. 67–86.CrossRefGoogle Scholar
  20. 20.
    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.Google Scholar
  21. 21.
    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.Google Scholar
  22. 22.
    E. Makovicky and N. M. Makovicky, “The first find of dodecagonal quasiperiodic tiling in historical Islamic architecture,” J. Applied Crystallography 44 (2011) 569–573.CrossRefGoogle Scholar
  23. 23.
    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.Google Scholar
  24. 24.
    I. El-Said and A. Parman, Geometric Concepts in Islamic Art, World of Islam Festival Publishing Company, London, 1976.Google Scholar
  25. 25.
    R. Schekman, “How journals like Nature, Cell and Science are damaging science,” The Guardian, 9 Dec 2013.Google Scholar
  26. 26.
    J. E. S. Socolar, T. C. Lubensky, and P. J. Steinhardt, “Phonons, phasons, and dislocations in quasicrystals,” Physical Review B 34 (1986) 3345–3360.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Pure Mathematics Division Mathematical Sciences BuildingUniversity of LiverpoolLiverpoolUK

Personalised recommendations