Imagine Math pp 197-208 | Cite as

Aperiodic Tiling

  • Gian Marco Todesco


These is an aesthetic pleasure when contemplating orderly structures that contain some disorder. A completely disordered pattern is typically not very interesting, but neither is a very regular one, like a check board. The check board and most images that we will meet in the following are examples of tessellations. A plane tessellation (or tiling) is a covering without gaps or overlaps, by figures called tiles. Tessellations can have very different degrees of order and disorder and illustrate well the concept expressed in the first statement.


Internal Space Control Shape Polygonal Chain Rhombic Dodecahedron Aesthetic Pleasure 
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.


  1. 1.
    L. Saffaro, Tassellature centrali e non-archimedee. Le Scienze 271, pp. 32–40, 1991.Google Scholar
  2. 2.
    B. Grünbaum, G.C. Shephard, Tilings and Pattern’s. W.H. Freeman, New York, 1986.Google Scholar
  3. 3.
    R. Penrose, Pentaplexity. Eureka 39, 1978; reprinted in: The Mathematical Intelligencer 2(1), 1979; italian edition in: M. Emmer (ed.), L’occhio di Horus. Istituto Enciclopedia Italiana, Roma, 1989, 196-201. See also R. Penrose making the aperiodic tiling with kite and dard in the film “Symmetry and Tessellations”, by M. Emmer, 1982.Google Scholar
  4. 4.
    P.J. Lu, P.J. Steinhardt, Decagonal and quasi-crystalline tilings in medieval Islamic architecture. Science 315, 1106–1110, 2007.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    D. Shechtman, I. Blech, D. Gratias, J. Cahn, Metallic Phase with Longrange Orientational Order and no Traslational Symmetry. Phys. Rev. Lett. 53, 1951, 1984.CrossRefGoogle Scholar
  6. 6.
    M. Gardner, Penrose tiles to trapdoor cipher. W.H. Freeman, New York, 1989.Google Scholar
  7. 7.
    N.G. de Bruijn, Algebraic theory of Penrose’s non-periodic tilings of the plane. I, II, Nederl. Akad. Wetensch. Indag. Math. 43(1), 39–52, 53–66, 1981.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    E. Harriss, D. Frettlöh, Tilings Encyclopedia. In rhombs, and wedges, and half-moons, and wings. Scholar
  9. 11.
    E.O. Harriss, On Canonical Substitution Tilings. PhD thesis, Imperial College London, 2003. Scholar
  10. 12.
    L. Effinger-Dean, The Empire Problem in Penrose Tilings. Honors thesis, Williams College, 2006. Scholar
  11. 13.
    T. Smith, Penrose tilings and wang tilings. Scholar
  12. 15.
    J. Sólyom, Fundamentals of the physics of solids. Springer, Heidelberg Berlin, 2007.Google Scholar
  13. 16.
    G. Egan, de Bruijn notes. 2008. Scholar
  14. 17.
    P. Bourke, Non Periodic Tiling of the Plane. 1995. colour/nonperiodic/Google Scholar
  15. 18.
    C. Kaplan, +Plus magazine. The trouble with five. 2007. Scholar
  16. 19.
    A. Boyle, +Plus magazine. From quasicrystal to Kleenex. 2000. Scholar
  17. 20.
    P.J. Lu, P.J. Steinhardt, Decagonal and Quasi-crystalline Tilings in Medieval Islamic Architecture. Science 315, pp. 1106–1110, 2007.MathSciNetMATHCrossRefGoogle Scholar
  18. 21.
    A. Feldman, My Bathroom Floor. Scholar
  19. 22.
    S. Collins, Bob — Penrose Tiling Generator and Explorer. Scholar
  20. 23.
    D. Austin, Feature Column. Monthly essay on mathematical topics, Penrose Tiles Talk Across Miles. Scholar

Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  • Gian Marco Todesco
    • 1
  1. 1.Digital Video S.r.l.RomeItaly

Personalised recommendations