Flying Patterns

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Jean-Marc Castéra: Flying Patterns. In: Bridges 2011. Pages 263–270



Contribution to the investigation on Islamic pentatonic patterns, trying to highlight a multiplicity of points of view. 1. Firstly, I propose a morphogenesis of the Persian style, and give the following applications : - An analysis of two famous traditional patterns that have yet be studied through different view points. One in Karatay, Turkey (J. Rigby, [10] P. Cromwell [4]), the other in Maragha, Iran (E. Makovicky [7,8], P.J.Lu and P.J.Steinhardt[6]). Where we can see that both are basically the same, coming from the same step in the proposed morphogenesis. - The “X-puzzle”, an application from the first step of our morphogenesis (there will be a workshop at the conference).

2. Then, considerations about the “prototiles” (or “girih tiles”) point of view.

3. Last, a relationship is given between “fundamental” and Persian patterns, through a process of decoration. Consequently, definition of a new set of prototiles.

All those concepts can be used by designer to create new patterns.

This contribution belongs to a pattern designer point of view, more than to a mathematical or historical point of view. As Bridges is dedicated to a meeting of Art and Maths, but inherit a scientific format for its publications, please consider this paper as experimental in the sense that the demonstration is given by images more than by words.

Extended Abstract


Used References

[1] Jay Bonner, Three traditions of self-similarity in fourteenth and fifteenth century Islamic geometric ornament, Meeting Alhambra, Proc. ISAMA-Bridges, pp.1-12, 2003.

[2] J.Bourgoin, LesEléments de l’ArtArabe, Firmin-Didot,1879. Plates reprinted in Arabic Geometric Pat- tern and Design, Dover Publications,1973.

[3] J.M. Castera. Arabesques, Paris, ACR, 1996. English version, 1999.

[4] Peter R. Cromwell, The Search for Quasi-periodicity in Islamic 5-fold Ornament, Math. Intelligencer 31 no 1, pp36-56, 2009.

[5] C.S.Kaplan, Islamic star patterns from polygons in contact, Graphics Interface, ACM International Conference Proceeding Series 112, pp.177-186, 2005.

[6] P.J. Lu and P.J. Steinhardt, Decagonal and quasi-crystalline tilings in medieval Islamic architecture, Science 315, pp. 1106-1110, 2007.

[7] E.Makovicky, 800-year old pentagonal tiling fromMaragha, Iran, and the new varieties of aperiodic tiling it inspired, Fivefold Symmetry, ed. I. Hargittai, World Scientific, pp.67-86, 1992.

[8] E.Makovicky, Another look at the Blue Tomb of Maragha, a site of the first quasicrystaline Islamic pattern, Symmetry: Culture and Science Vol. 19, Numbers 2-3, pp. 127-151, 2008.

[9] G.Necipogglu, The TopkapiScroll : Geometry and Ornament in Islamic Architecture, GettyCenter Publication,1995.

[10] J.Rigby, A Turkish interlacing pattern and the golden ratio, Mathematics in School, Vol. 34 N°.1, pp. 16-24, 2005.


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