Contribution to the investigation on Islamic pentatonic patterns,
trying to highlight a multiplicity of points of view.
- 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,  P. Cromwell ), the other in
Maragha, Iran (E. Makovicky [7,8], P.J.Lu and P.J.Steinhardt).
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.