The Mathematical Intelligencer

, Volume 40, Issue 1, pp 73–78 | Cite as

Integer-Digit Functions: An Example of Math-Art Integration

Open Access



The author thanks artist Puri Pereira for useful discussions. He also thanks the Royal Society of London for a Wolfson Research Merit Award. Finally he thanks Gizem Karaali for her editorial assistance.


  1. 1.
    A. Åström, and C. Åström, Circular knotworks consisting of pattern no. 295: a mathematical approach, Journal of Mathematics and the Arts 5 (2011), 185–197.Google Scholar
  2. 2.
    R. Bosch, Simple-closed-curve sculptures of knots and links, Journal of Mathematics and the Arts 4 (2010), 57–71.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    R. Bosch, and U. Colley, Figurative mosaics from flexible Truchet tiles, Journal of Mathematics and the Arts 7 (2013), 122–135.MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    J. Briggs, Fractals: The patterns of chaos: a new aesthetic of art, science, and nature, Simon and Schuster (1992).Google Scholar
  5. 5.
    P. R. Cromwell, Celtic knotwork: mathematical art, The Mathematical Intelligencer 15 (1993), 36–47.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    P. R. Cromwell, The search for quasi-periodicity in Islamic 5-fold ornament, The Mathematical Intelligencer 31 (2009), 36–56.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    E. Estrada, and L. A. Pogliani, A new integer sequence based on the sum of digits of integers. Kragujevac Journal of Sciences 30 (2008), 45–50.Google Scholar
  8. 8.
    K. Fenyvesi, Bridges: A World Community for Mathematical Art, The Mathematical Intelligencer 38 (2016), 35–45.CrossRefGoogle Scholar
  9. 9.
    F. A. Farris, Symmetric yet organic: Fourier series as an artist’s tool, Journal of Mathematics and the Arts 7 (2013), 64–82.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    L. Gamwell, Mathematics and Art: A Cultural History, Princeton University Press (2015).Google Scholar
  11. 11.
    G. Irving, and H. Segerman, Developing fractal curves, Journal of Mathematics and the Arts 7 (2013), 103–121.MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    G. Kaplan, The Catenary: Art, Architecture, History, and Mathematics, Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture. Tarquin Publications (2008).Google Scholar
  13. 13.
    L. Koudela, Curves in the history of mathematics: the late renaissance, WDS’05 Proceedings of Contributed Papers, Part I (2005), pp. 198–202.Google Scholar
  14. 14.
    C. Mauduit, Substitutions et ensembles normaux, Habilitation Dir. Rech., Universit Aix-Marseille II, 1989.MATHGoogle Scholar
  15. 15.
    C. H. Séquin, Topological tori as abstract art, Journal of Mathematics and the Arts 6 (2012), 191–209.MathSciNetCrossRefGoogle Scholar
  16. 16.
    N. J. A. Sloane and S. Plouffe, The Encyclopedia of Integer Sequences, Academic Press. Web, edition at
  17. 17.
    N. J. A. Sloane, My Favorite Integer Sequences, in C. Ding, T. Helleseth, and H. Niederreiter, eds. Sequences and their Applications (Proceedings of SETA ’98), Springer-Verlag, pp. 103–130, 1999.Google Scholar
  18. 18.
    The Bridges Organization, Bridges, website,
  19. 19.
    H. Yanai, and K. Williams, Curves in traditional architecture in East Asia, The Mathematical Intelligencer 23 (2001), 52–57.MathSciNetCrossRefGoogle Scholar
  20. 20.
    R. C. Yates, A Handbook of Curves and their Properties, Literary Licensing, LLC (2012).Google Scholar
  21. 21.
    X. Zheng, and N. S. Brown, Symmetric designs on hexagonal tiles of a hexagonal lattice, Journal of Mathematics and the Arts 6 (2012), 19–28.MathSciNetCrossRefMATHGoogle Scholar

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of StrathclydeGlasgowUK

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