Skip to main content
SpringerLink
Log in

Aperiodic Tilings on the Computer

  • Chapter
Quasicrystals

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 55))

Summary

We briefly review the standard methods used to construct quasiperiodic tilings, such as the projection, the inflation and the grid method. A number of sample Mathematica programs, implementing the different approaches for oneand two-dimensional examples, are discussed. Apart from small examples, the corresponding programs are not contained in the text, but are archived on the WWW.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ammann, R., Grünbaum, B., Shephard, G.C. (1992): Discr. Comput. Geom. 8, 1

    Article  MATH  Google Scholar 

  2. Baake, M. (2002) : See Chapter 2 of this book

    Google Scholar 

  3. Baake, M., Grimm, U., Joseph, D. (1993): Int. J. Mod. Phys. B 7, 1527

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Baake, M., Joseph, D. (1990): Phys. Rev. B 42, 8091

    Article  ADS  Google Scholar 

  5. Bak, P. (1986) : Scr. Metall. 20, 1199

    Article  Google Scholar 

  6. de Bruijn, N.G. (1981): Proc. Kon. Ned. Akad. Wet. A (Indagationes Mathematicae) 84, 39 and 53

    Google Scholar 

  7. Duneau, M., Katz, A. (1985): Phys. Rev. Lett. 54, 2688

    Article  MathSciNet  ADS  Google Scholar 

  8. Duneau, M., Mosseri, R., Oguey, C. (1989): J. Phys. A 22, 4549

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Durand, E. (1994): QuasiTiler 3.0 (WWW front end by P. Burchard, D. Meyer and E. Durand, Geometry Center, University of Minnesota) http://www.geom.umn.edu/apps/quasitiler

    Google Scholar 

  10. Elser, V. (1986) : Acta Crystallogr. A 42, 36

    Article  MathSciNet  MATH  Google Scholar 

  11. Elser, V. (1998): IQtools (for detailed information, please contact the author by email: )

    Google Scholar 

  12. Gähler, F., Klitzing, R. (1997): In The Mathematics of Long-Range Aperiodic Order (NATO ASI C 489), ed. R.V. Moody, Kluwer, Dordrecht, p. 141

    Chapter  Google Scholar 

  13. Golomb, S. (1994): Polyominoes: Puzzles, Patterns, Problems and Packings (2nd ed.), Princeton University Press, Princeton

    MATH  Google Scholar 

  14. Grimm, U., Baake, M. (2002): See the Appendix of this book

    Google Scholar 

  15. Grimm, U., Joseph, D. (2002): See Chapter 9 of this book

    Google Scholar 

  16. Grimm, U., Schreiber, M. (1998): Constructing Aperiodic Tilings with Mathematica: Some Example Programs, http://www.tu-chemnitz.de/physik/HERAEUS/2000/springer.html

    Google Scholar 

  17. Grünbaum, B., Shephard, G.C. (1987): Tilings and Patterns, W.H. Freeman, New York

    MATH  Google Scholar 

  18. Janot, C. (1994): Quasicrystals: A Primer (2nd ed.), Clarendon Press, Oxford

    MATH  Google Scholar 

  19. Janner, A., Janssen, T. (1986): Phys. Rev. B 15, 643

    Google Scholar 

  20. Kalugin, P.A., Kitayev, A.Y., Levitov, L.S. (1985): JETP Lett. 41, 145

    ADS  Google Scholar 

  21. Kalugin, P.A., Kitayev, A.Y., Levitov, L.S. (1985): J. Phys. Lett. (France) 46, L601

    Article  Google Scholar 

  22. Katz, A., Gratias, D. (1994) : In Lectures on Quasicrystals, ed. F. Hippert, D. Gratias, Les Editions de Physique, Les Ulis, p. 187

    Google Scholar 

  23. Korepin, V.E., Gähler, F., Rhyner, J. (1988): Acta Crystallogr. A 44, 667

    Article  Google Scholar 

  24. Kramer, P. (1982) : Acta Crystallogr. A 38, 257

    Article  ADS  Google Scholar 

  25. Kramer, P. (1987): Mod. Phys. Lett. B 1, 7

    Article  ADS  Google Scholar 

  26. Kramer, P., Neri, R. (1984): Acta Crystallogr. A 40, 580; 41, 691 (1985) [Erratum]

    Article  MathSciNet  MATH  Google Scholar 

  27. Kramer, P., Schlottmann, M. (1989) : J. Phys. A 22, L1097

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. Maeder, R. (1990) : Programming in Mathematica, Addison—Wesley, Redwood City (California)

    Google Scholar 

  29. Oguey, C., Duneau, M, Katz, A. (1988): Commun. Math. Phys. 118, 99

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Penrose, R. (1974): Bull. Inst. Math. Applics. 10, 266

    Google Scholar 

  31. Penrose, R. (1978) : Eureka 39, 16; reprinted in Math. Intell. 2, 32 (1979)

    Google Scholar 

  32. Penrose R. (1989): In Introduction to the Mathematics of Quasicrystals (Aperiodicity and Order, vol. 2), ed. M.V. Jaric, Academic Press, San Diego, p. 53

    Chapter  Google Scholar 

  33. Schlottmann, M. (1993): Int. J. Mod. Phys. B 7, 1351; and Geometrische Eigenschaften quasiperiodischer Strukturen, PhD Thesis, Universität Tübingen

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. Senechal, M. (1995): Quasicrystals and Geometry, Cambridge University Press, Cambridge

    MATH  Google Scholar 

  35. Skiena, S. (1990): Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica, Addison—Wesley, Redwood City (California)

    MATH  Google Scholar 

  36. Trebin H.-R. (2002): See Chapter 12 of this book

    Google Scholar 

  37. Wolfram, S. (1991): Mathematica: A System for Doing Mathematics by Computer (2nd ed.), Addison—Wesley, Reading (Massachusetts)

    Google Scholar 

  38. Zometool Marketing, 1526 South Pearl Street, Denver, CO 80210, USA; http://www.zometool.com

Download references

Authors
  1. Uwe Grimm
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Schreiber
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Physik, TU Chemnitz, 09107, Chemnitz, Germany

    Jens-Boie Suck  & Peter Häussler  & 

  2. International University Bremen, Postfach 75 05 61, 28725, Bremen, Germany

    Michael Schreiber

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Grimm, U., Schreiber, M. (2002). Aperiodic Tilings on the Computer. In: Suck, JB., Schreiber, M., Häussler, P. (eds) Quasicrystals. Springer Series in Materials Science, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05028-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-05028-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08390-7

  • Online ISBN: 978-3-662-05028-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation