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.
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References
M. A. Armstrong, Groups and Symmetry, (Undergraduate texts in Mathematics, Springer-Verlag, New York, Berlin, Heidelberg, 1988 ).
L. Arnold, Random Dynamical Systems, (Springer Monographs in Mathematics, Springer-Verlag, Berlin-Heidelberg, 1998 ).
G. Bain, Celtic Art: The Methods of Construction, (Dover Publications, 1973 ).
M. F. Barnsley, Fractals Everywhere ( Academic Press, San Diego, 1988 ).
P. Chossat, M. Golubitsky, ‘Symmetry increasing bifurcations of chaotic at-tractors’, Physica D 32 (1988), 423–436.
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.
K. Falconner, Fractal Geometry (John Wiley and Sons, Chichester, 1990 ).
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.
M. J. Field, ‘Color Symmetries in Chaotic Quilt Patterns’, In: Proc. ISAMA 99, (eds. N. Friedman, J. Barrallo, San Sebastian, Spain, 1999 ), 181–188.
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.
M. J. Field, ‘Designer Chaos’, J. Computer Aided Design, 33 (5) (2001), 349365.
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.
M. J. Field, ‘Dynamics, Chaos and Design’, In: The Visual Mind 2 (ed. M. Em-mer, MIT Press), to appear.
M. J. Field, M. Golubitsky, Symmetry in Chaos, (Oxford University Press, New York and London, 1992 ).
M. J. Field, I. Melbourne, M. Nicol, ‘Symmetric Attractors for Diffeomorphisms and Flows’, Proc. London Math. Soc., (3) 72 (1996), 657–696.
B. Grünbaum, G. C. Shephard. Tilings and Patterns. An Introduction, ( W H Freeman and Company, New York, 1989 ).
S. Jablan, Theory of Symmetry and Ornament, ( Mathematics Institute, Beograd, 1995 ).
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.
I. Melbourne, M. Dellnitz, M. Golubitsky, ‘The structure of symmetric attractors’, Arch. Rat. Mech. Anal. 123 (1993), 75–98.
D. Washburn, D. Crowe, Symmetries of Culture, (University of Washington Press, Seattle, 1988 ).
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.
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Field, M. (2002). The Design of 2-Colour Wallpaper Patterns Using Methods Based on Chaotic Dynamics and Symmetry. In: Bruter, C.P. (eds) Mathematics and Art. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04909-9_4
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DOI: https://doi.org/10.1007/978-3-662-04909-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07782-1
Online ISBN: 978-3-662-04909-9
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