Flying Patterns

Jean-Marc Castéra
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (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).
    • Then, considerations about the ``prototiles'' (or ``girih tiles'') point of view.
    • 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.