Crystallographic patterns in nature and Turkish art

In this paper, crystallographic aspects of ancient, medieval and modern Turkish ornaments are dealt with. Crystallographic patterns (CPs) are considerably different from other patterns. The following are characteristic of CPs: the edge of ornament elements draws the edge of the figure; maximal compactness of the ornament elements; lack of background or transformation of background to ornament elements; minimization of the variety of ornament elements; symmetry is not used for form creation. In the process of the construction of CPs, symmetry appears as a result of combination, not as a means of its formation that is characteristic of other ornaments. Their symmetries are analogous to symmetries of natural objects. The atoms and molecules dispose themselves in crystals just as elements arrange themselves in CPs. In other words, CPs are constructed according to the same principles of crystal formation, i.e. the principle of tight packing. The similarity (isomorphism) of crystals and ornaments enables us to describe the ornaments with structural analysis terms, and the similarity between ornaments and crystal structures can be also used in chemistry education. This will bring an aesthetical aspect to education. An invisible part of nature can be studied as ornament creation. Each newly created CP is the structural scheme of a number of possible compounds. The familiarity with such ornaments and the ability to create them are important for solving compound structures. Similarity of patterns with some crystal structures enables us to reach the following conclusions: mankind may make use of the principles from which nature was created, and he may achieve a resemblance to the creation of nature in ideal; mankind may create nothing whose prototype does not exist in nature. # 2004 Elsevier Ltd. All rights reserved.