Advertisement

Picking Knots from Trees

The Syntactic Structure of Celtic Knotwork
  • Frank Drewes
  • Renate Klempien-Hinrichs
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1889)

Abstract

Interlacing knotwork forms a significant part of celtic art. From the perspective of computer science, it is a visual language following mathematically precise rules of construction. In this paper, we study the syntactic generation of celtic knots using collage grammars. Several syntactic regulation mechanisms are employed in order to ensure that only consistent designs are generated.

Keywords

Syntactic Structure Graph Transformation Derivation Tree Graph Grammar Visual Language 
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. [Bai51]
    George Bain. Celtic Art. The Methods of Construction. Constable, London, 1951.Google Scholar
  2. [Buz]
    Cari Buziak. Aon celtic art and illumination. http://www.aon-celtic.com/.
  3. [Dav89]
    Courtney Davis. Celtic Iron-On Transfer Patterns. Dover Publications, New York, 1989.Google Scholar
  4. [DK99]
    Frank Drewes and Hans-Jörg Kreowski. Picture generation by collage grammars. In H. Ehrig, G. Engels, H.-J. Kreowski, and G. Rozenberg, editors, Handbook of Graph Grammars and Computing by Graph Transforma-tion, Vol. 2: Applications, Languages, and Tools, chapter 11, pages 397–457. World Scientific, 1999.Google Scholar
  5. [DK00]
    Frank Drewes and Renate Klempien-Hinrichs. Picking knots from trees. The syntactic structure of celtic knotwork. Report4/00, Univ. Bremen, 2000.Google Scholar
  6. [DKK00]
    Frank Drewes, Renate Klempien-Hinrichs, and Hans-Jörg Kreowski. Tabledriven and context-sensitive collage languages. In G. Rozenberg and W. Thomas, editors, Proc. Developments in Language Theory (DLT’99). World Scientific. To appear.Google Scholar
  7. [Dre00]
    Frank Drewes. Tree-based picture generation. Theoretical Computer Science. To appear.Google Scholar
  8. [Gla99a]
    Andrew Glassner. Andrew Glassner’s notebook: Celtic knotwork, part 1. IEEE Computer Graphics and Applications, 19(5):78–84, 1999.CrossRefGoogle Scholar
  9. [Gla99b]
    Andrew Glassner. Andrew Glassner’s notebook: Celtic knotwork, part 2. IEEE Computer Graphics and Applications, 19(6):82–86, 1999.CrossRefGoogle Scholar
  10. [Gla00]
    Andrew Glassner. Andrew Glassner’s notebook: Celtic knotwork, part 3. IEEE Computer Graphics and Applications, 20(1):70–75, 2000.CrossRefGoogle Scholar
  11. [HK91]
    Annegret Habel and Hans-Jörg Kreowski. Collage grammars. In H. Ehrig, H.-J. Kreowski, and G. Rozenberg, editors, Proc. Fourth Intl. Workshop on Graph Grammars and Their Application to Comp. Sci., volume 532 of Lecture Notes in Computer Science, pages 411–429. Springer, 1991.CrossRefGoogle Scholar
  12. [HKT93]
    Annegret Habel, Hans-Jörg Kreowski, and Stefan Taubenberger. Collages and patterns generated by hyperedge replacement. Languages of Design, 1:125–145, 1993.Google Scholar
  13. [KRS97]
    Lila Kari, Grzegorz Rozenberg, and Arto Salomaa. L systems. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages. Vol. I: Word, Language, Grammar, chapter 5, pages 253–328. Springer, 1997.Google Scholar
  14. [Mee91]
    Aidan Meehan. Knotwork. The Secret Method of the Scribes. Thames and Hudson, New York, 1991.Google Scholar
  15. [PL90]
    Przemyslaw Prusinkiewicz and Aristid Lindenmayer. The Algorithmic Beauty of Plants. Springer-Verlag, New York, 1990.zbMATHGoogle Scholar
  16. [Roz73]
    Grzegorz Rozenberg. T0L systems and languages. Information and Control, 23:262–283, 1973.CrossRefMathSciNetGoogle Scholar
  17. [Slo95]
    Andy Sloss. How to Draw Celtic Knotwork: A Practical Handbook. Blandford Press, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Frank Drewes
    • 1
  • Renate Klempien-Hinrichs
    • 2
  1. 1.Department of Computing ScienceUmeå UniversityUmeåSweden
  2. 2.Department of Computer ScienceUniversity of BremenBremenGermany

Personalised recommendations