The similarity between the structure of Islamic decorative patterns and quasicrystals has aroused the interest of several crystallographers. Many of these patterns have been analysed by different approaches, including various kinds of ornamental quasiperiodic patterns encountered in Morocco and the Alhambra (Andalusia), as well as those in the eastern Islamic world. In the present work, the interest is in the quasiperiodic patterns found in several Moroccan historical buildings constructed in the 14th century. First, the zellige panels (fine mosaics) decorating the Madrasas (schools) Attarine and Bou Inania in Fez are described in terms of Penrose tiling, to confirm that both panels have a quasiperiodic structure. The multigrid method developed by De Bruijn [Proc. K. Ned. Akad. Wet. Ser. A Math. Sci. (1981), 43, 39–66] and reformulated by Gratias [Tangente (2002), 85, 34–36] to obtain a quasiperiodic paving is then used to construct known quasiperiodic patterns from periodic patterns extracted from the Madrasas Bou Inania and Ben Youssef (Marrakech). Finally, a method of construction of heptagonal, enneagonal, tetradecagonal and octadecagonal quasiperiodic patterns, not encountered in Moroccan ornamental art, is proposed. They are built from tilings (skeletons) generated by the multigrid method and decorated by motifs obtained by craftsmen.

Many works report the classification and analysis of geometric patterns, particularly those found in the Alhambra, Spain, but few authors have been interested in Moroccan motifs, especially those made on wood. Studies and analyses made on nearly a thousand Moroccan patterns constructed on wood and belonging to different periods between the 14th and 19th centuries show that, despite their great diversity, only five plane groups are present. Groups p4mm and c2mm are predominant, p6mm and p2mm are less frequent, while p4gm is rare. In this work, it is shown that it is possible to obtain the 17 plane symmetry groups by using a master craftsmen's method called Hasba. The set of patterns are generated from n‐fold rosettes, considered as the basic motif, by the Hasba method. The combination and the overlap between these basic elements generate other basic elements. By repeating these basic elements, it is possible to construct patterns having various symmetry groups. In this article, only uncoloured patterns are considered and the interlace patterns are disregarded.

This work is devoted to the study of the 12‐fold rosettes frequently encountered in Islamic art, especially in Moroccan ornamentation. Several types of 12‐fold rosettes are described according to the geometric shape of their petals. They have a large number of variants and offer the possibility of building new, previously unknown rosettes, while respecting the construction method Hasba used by master craftsmen. Artisans developed a technique for combining different types of 12‐fold rosettes to construct infinite periodic tiling belonging to the 17 crystallographic groups. This technique enabled them to diversify the repeated patterns based on 12‐fold rosettes. An analysis of their tiling suggests a method based on elementary geometry to build new patterns with different types of 12‐fold overlapped rosettes and their variants. A procedure based on combination of the distances between two overlapped rosettes is then proposed, which enables generation of new periodic and quasiperiodic patterns.

Moroccan decorative art, especially geometric art or "Tastir" is one of the most complex and one of the most refined expressions of Arab-Islamic art. The rosettes may be the essential elements of the ornamental panel or be used as a repetitive element to construct an infinite periodic tiling. Periodic tilings of the plane are Moorish ornamental tradition (Andalusia and the Maghreb), which culminated between the 13th and 14th centuries. This presentation is devoted to the study of 12-fold rosettes frequently found in Islamic art in general and Moroccan in particular. There are several 12-fold rosettes types according to the geometric shape of its petals. They have a large number of variants and also offer the possibility of building new rosettes previously unknown, while respecting the construction method "Hasba" used by master craftsmen (Thalal & Al, 2011; Aboufadil & Al, 2013). The craftsmen have developed a technique for combining different types of 12-fold rosettes to construct infinite periodic tilings belonging to the 17 crystallographic groups. This technique enabled them to diversify the repeated patterns based on 12-fold rosettes. By analysing their tilings, we propose a method based on elementary geometry and symmetry to build new patterns with different types of rosettes and their variants. We also present a procedure, based in combination of the distances between two overlapped rosettes, which simplifies the method of construction used by artisans and which enables to generate new periodic patterns as well as and quasi-periodic.

No abstract