The Study of the Characteristics of Geometrical Knots in Islamic Decorations from the Viewpoint of Fractal Geometry

One of the characteristics of Islamic arts is the present of geometrical images in the Iranian arch decorative elements such as vaults, Yazdibandi and Chinese Knots. This article is dealing with the features of the Islamic decorative geometry from a newer perspective. The reason is that the geometry of Islamic decorations is something beyond Euclid geometry which deals only with the study of classic shapes. To prove this claims, the knots have been selected on one side due to diversity, multiplicity, complexity, tone, balance and use of various types of geometrical images and on the other hand due to the vast studies made by authorities on this area. The results of the research show that one of the geometrical features of knots is their comparison with the features of Fractal geometry. Fractals are the unconventional non-Euclid, irregular and at the same time regular geometrical shapes whose most important similarities their self similarities. These features in the Islamic decorative geometry has not been made randomly, because in addition to the fact that Islamic artists have enjoyed mathematical knowledge, they have also used the nature as a source of main inspiration. This indicates that in the past, the artists have been well aware of the vast dimensions of the features of their own geometrical designs. As for this feature, they had used the non-Euclid features in their designs five hundred prior to their western counterparts