1. Assimilation of the traditional language’s components

Introduction
Observation and analysis of repetitive patterns from arabic art.
The main concepts : infinity, symmetry, periodicity, continuity,
variation and embellishment.
Pattern simplification and reduction according to symmetries.
Arabic-andalusian style particularities.
The octagonal family and its specific rules. The other families.
Handling with zellij tiles

Muqarnas : the 4 main units. Composition rules and code for
plane representation. Handling with muqarnas units.

A morphogenesis process.
The recursive application of simple rules operating on
elementary shapes generates a large set of traditional patterns,
and can be used to produce new ones.

The stellated octagon as the mother of each tile of the octagonal
family. The skeleton of the patterns. The zellij tile’s alphabet. The big stars.

Drawing techniques.
The basic approximation. Drawing exercises. Checking errors.
Approximative and exact constructions.
Muqarnas : drawing the maps.
Application : complex patterns fast analysis.

Embellishment and variations.
Colors, interlacesn double stars and variations.

Applications.
We will consider every available means to produce the patterns :
drawing, cutting, painting, computer graphics...
Students imagination will be strongly encouraged.


2. Links with contemporary mathematics

Rather than studying in depth the very well known question of
symmetry groups, we will work on fractals and non-periodic
patterns.

Introduction.
Various western approaches of geometrical arabesque, from
19th century to nowadays. The amazing success of the
symmetry groups theory.

Zellij and fractals.
An example from the Alhambra of Granada.
Other cases of self-similarity.

Basics of non-periodic patterns and quasicrystals.
Zellij and the simplest quasicrystal. Quasicrystals and muqarnas.


3. Experimentation and new perspectives.

Suggestions and experimentation of new developments of
geometrical arabesque according to contemporary
technologies, mathematics, and to student’s imagination.