Advertisement

The Design of 2-Colour Wallpaper Patterns Using Methods Based on Chaotic Dynamics and Symmetry

  • Michael Field
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

We describe the theoretical basis for the design of symmetric patterns using dynamics, chaos and symmetry. We show examples of some of the one- and two-colour wallpaper patterns that we have created using these ideas.

Keywords

Iterate Function System Ergodic Measure Symmetric Pattern Symmetric Design Random Dynamical System 
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.
    M. A. Armstrong, Groups and Symmetry, (Undergraduate texts in Mathematics, Springer-Verlag, New York, Berlin, Heidelberg, 1988 ).Google Scholar
  2. 2.
    L. Arnold, Random Dynamical Systems, (Springer Monographs in Mathematics, Springer-Verlag, Berlin-Heidelberg, 1998 ).Google Scholar
  3. 3.
    G. Bain, Celtic Art: The Methods of Construction, (Dover Publications, 1973 ).Google Scholar
  4. 4.
    M. F. Barnsley, Fractals Everywhere ( Academic Press, San Diego, 1988 ).zbMATHGoogle Scholar
  5. 5.
    P. Chossat, M. Golubitsky, ‘Symmetry increasing bifurcations of chaotic at-tractors’, Physica D 32 (1988), 423–436.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    H. S. M. Coxeter, ‘Colored symmetry’, In: M C Escher: Art and Science ( H. S. M. Coxeter et al, eds., Elsevier, Amsterdam and New York, 1986 ), 15–33.Google Scholar
  7. 7.
    K. Falconner, Fractal Geometry (John Wiley and Sons, Chichester, 1990 ).Google Scholar
  8. 8.
    M. J. Field, ‘Harmony and Chromatics of Chaos’, In: Bridges, Mathematical Connections in Art, Music, and Science, ( Conference Proceedings, ed. Reza Sarhangi, Southwestern College, Kansas, 1999 ), 1–20.Google Scholar
  9. 9.
    M. J. Field, ‘Color Symmetries in Chaotic Quilt Patterns’, In: Proc. ISAMA 99, (eds. N. Friedman, J. Barrallo, San Sebastian, Spain, 1999 ), 181–188.Google Scholar
  10. 10.
    M. J. Field, ‘The Art and Science of Symmetric Design’, In: Bridges, Mathematical Connections in Art, Music, and Science, ( Conference Proceedings, ed. Reza Sarhangi, Southwestern College, Kansas, 2000 ), 53–60.Google Scholar
  11. 11.
    M. J. Field, ‘Designer Chaos’, J. Computer Aided Design, 33 (5) (2001), 349365.Google Scholar
  12. 12.
    M. J. Field, ‘Mathematics through Art–Art through Mathematics’, In: Proc. MOSAIC 2000, (eds. D Salesin and C Séquin, University of Washington, 2000 ), 137–146.Google Scholar
  13. 13.
    M. J. Field, ‘Dynamics, Chaos and Design’, In: The Visual Mind 2 (ed. M. Em-mer, MIT Press), to appear.Google Scholar
  14. 14.
    M. J. Field, M. Golubitsky, Symmetry in Chaos, (Oxford University Press, New York and London, 1992 ).Google Scholar
  15. 15.
    M. J. Field, I. Melbourne, M. Nicol, ‘Symmetric Attractors for Diffeomorphisms and Flows’, Proc. London Math. Soc., (3) 72 (1996), 657–696.MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    B. Grünbaum, G. C. Shephard. Tilings and Patterns. An Introduction, ( W H Freeman and Company, New York, 1989 ).zbMATHGoogle Scholar
  17. 17.
    S. Jablan, Theory of Symmetry and Ornament, ( Mathematics Institute, Beograd, 1995 ).zbMATHGoogle Scholar
  18. 18.
    C. S. Kaplan, ‘Computer generated Islamic star patterns’, In: Bridges, Mathematical Connections in Art, Music, and Science, ( Conference Proceedings, ed. Reza Sarhangi, Southwestern College, Kansas, 2000 ), 105–112.Google Scholar
  19. 19.
    I. Melbourne, M. Dellnitz, M. Golubitsky, ‘The structure of symmetric attractors’, Arch. Rat. Mech. Anal. 123 (1993), 75–98.MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    D. Washburn, D. Crowe, Symmetries of Culture, (University of Washington Press, Seattle, 1988 ).Google Scholar
  21. 21.
    H. J. Woods, ‘The Geometrical basis of pattern design. Part 4: Counterchange symmetry in plane patters’, Jn. of the Textile Institute, Trans. 27 (1936), 305320.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Michael Field
    • 1
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA

Personalised recommendations