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Crystallographic patterns in nature and Turkish art
Crystal Engineering 6 (2003) 153–166 www.elsevier.com/locate/cryseng
Crystallographic patterns in nature and Turkish art Hacali Necefoglu Department of Chemistry, Kafkas University, Dereici, 36100 Kars, Turkey Received 3 August 2003; accepted 28 March 2004
Abstract 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. Keywords: Crystallographic patterns; Symmetry; Tight packing; Turkish ornaments
Tel./fax: +90-474-212-2706. E-mail address: [email protected] (H. Necefoglu).
1463-0184/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryseng.2004.03.001
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The famous Dutch painter M. Escher (1898–1972) is one of those who attract a great deal of attention among the most eminent European artists. Sticking to his own creative principles, M. Escher created a series of interesting art works, some of which are patterns without background, which made most crystallographers interested [1,2]. Art critics have tried to explain that the reason why geometrical patterns were created in the Middle Ages in the places where Islam was dominant is that Islam prohibited the figuring of living things; yet this view may not be strictly true because the advent of geometrical pattern goes back as far as to many years BC. M. Escher’s works draw the crystallographer’s attention from the beginning. The exhibitions of these works were held in various congresses. Besides, they began to be used in teaching of crystallography, and the books which study these works in respect of crystallography were published. How can we explain such an interest of crystallographers for M. Escher’s creativity? Crystallographers are scientists who study how solid matters are formed from atoms and molecules. Their aim is to establish correlation between their internal structure and their properties. From the 12th year of the 20th century onwards, crystallographers began to discover the structure of crystals by using X-rays. Atoms and molecules dispose themselves in crystals as M. Escher illustrated. For comparison, see Fig. 1. This is the projection of the structure of an organic compound. Unlike the pictures M. Escher painted, the atom groups or molecules forming crystal are periodically arranged in three-dimensional space. Inside the crystals, atoms and molecules arrange themselves at the maximum tight as the components of
Fig. 1. Crystal structure of 1,3,5-triphenylbenzene.
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Fig. 2. Six ‘‘Ali’’ in Palace of Shirvanshahs, Baku, Azerbaijan, XIV–XVth centuries.
M. Escher’s pictures. The reason why the crystallographers are so interested in the patterns without background must be considered within this similarity. The first person, who drew attention to this similarity, was professor of crystallography, Mamedov [3,4]. For that reason, Mamedov named two-dimensional periodically arranged patterns without background, as crystallographic patterns (CPs). Pay attention to Fig. 2. There is an architectural hexagonal medallion with six equally divided elements, three of which are written in the shape of hollows on the stone and the other three just between the hollows. This pattern ornaments Shirvanshahlar Palace, which is the monument of XV century in Baku. Six-sided elements are the inscription of ‘‘Ali’’ in Arabic. The guides call this pattern which was created by engraving on a stone, medallion and say that ‘‘Ali’’ pattern is inscribed here six times but it is not aesthetically important how many times the pattern ‘‘Ali’’ was inscribed nor is it important in any respect. The most important and interesting fact is how they were inscribed. As can be seen, one of the crystallographic patterns was created in Baku 500 years before M. Escher. Thus the following questions arise: – How such patterns became widespread in Azerbaijan and neighbouring countries?
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– From what period onwards they came into being? – What is the reason of the creation of such an art branch? If you happen to go to Berde, a distinguished city of Azerbaijan, do visit Nushabe Castle in the center of the city. Here a cylindric holly tomb will attract your attention. On it you can see pictures, which you can meet in the books published in America and Europe under the names of Islamic Architecture or Persian Architecture. It is surprising that neither in ancient Persia, nor in pre-Islamic periods nothing was mentioned about the existence of such a tomb in Arabia. Then a question arises. How can something be given to others which is not owned? The pattern, which ornaments the cylindrical surface of Berde Tomb, is given in Fig. 3. This pattern is made up of by those whose repeating element is ‘‘Allah’’ written in the Arabic alphabet. Master Ahmet Eyyu¨boglu created an immortal wholeness between the tomb and the pattern in 1322. Those who study the history of architecture say that the master belongs to the Nakhchivan Architecture School. The founder of this school is Adjemi Nahchivani, the son of Ebubekir, who lived 850 years before. Nearly everyone must have seen his Mumine Hatun Tomb he created, at least in the pictures, which still stands with all its beauty and magnificence (the year 1186). The outline of the pattern of surface structure of a tomb in Karabaglar village which belongs to Nahchivani School is shown in Fig. 4. To ornament the surface of this tomb, a writing much more complex than that of Berde was chosen, but the creativity principle of the pattern is still the same: the principle of creating crystallographic patterns. While studying on the creation of such patterns chronologically and geographically, we saw that the CPs were widespread in Middle Asia, North Persia, Azerbaijan and Turkey. Excellent examples of CPs were created in Isfahan and Tabriz in the period of Seljuks and Safavids;
Fig. 3. ‘‘Allah’’ in kufic script. Berde, Azerbaijan (1322).
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Fig. 4. ‘‘Kelime-i shehadet’’ (the Islamic confession of faith) in kufic script. Karabaglar, Nakhchivan, XVIIIth sentury.
and in the period of Timurids in Middle Asia. It is the fact that Timur took many masters to Samarkand from Azerbaijan to have it published and there exists information in Baburname about how Azerbaijan Turkish masters were taken to India. It is obvious that no art branch comes into being spontaneously. One hundred years before the pattern ‘‘Ali’’ in Shirvanshahlar Palace in Baku, the pattern of Berde tomb, and 150 years before another variant of ‘‘Ali’’ pattern in Aksaray (Turkey) had been created (Fig. 5).
Fig. 5. Six ‘‘Ali’’. Aksaray, Turkey.
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How many years were to pass to create Berde and Aksaray patterns? To answer these questions, we have to go through the periods before the first CPs were created in Middle Ages. After a long interval, CPs are seen in the examples of Scythian culture. The characteristics of Scythian pattern creation, which is also known as Animal style, were to fill plane with patterns. Scythians are known to have been the nomadic tribes dwelling on the wide plains between the North of Black Sea and North Turkistan (many marks exist which impose the Turkish influence on them). Nomads try to inscribe their intense artistic knowledge as much as possible on the goods which they carry with them. See Fig. 6. Found in West Siberia, it is a pattern of a ceramic, dated 1000 years BC. The meaning of the details of this figure is not clear to us, but it is a typically crystallographic pattern (it is of great interest that we meet the same patterns in the contemporary artistic works of American Indians). Pattern makers of the Middle Age created the same order using words written with Arabic letters instead of these elements. It is also possible to encounter such magnificent examples in ancient Altaic Culture. Pay attention to Fig. 7. Two birds of spirit are fighting against each other. There is no space here between the figures. The black bird is the background for the white one and the white bird is the background for the black one. The medallion with ‘‘Ali’’ is inscribed with the same principle. In the latter, six elements were used instead of two elements. As can be seen, the beginning of our pattern creation goes as far back as 1000 years BC and it is no wonder that Arabic letters were used as the prior element in the periods during which Islam was dominant. We can see in Fig. 8 that such pattern creation was also widespread in 1000 years BC. Compare the pattern of the seals made of clay, which were found in the excavations in Saritepe near Kazak city (Azerbaijan) with that of Fig. 9.
Fig. 6. An ornament on ceramics. Tomsk, Russia.
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Fig. 7. Example of Altaic culture.
The latter figure is a pattern created with four ‘‘Ali’’. These patterns are so alike that those who can read Arabic letters also try to find the word Ali in these patterns created BC. But it is not easy to comment concretely about what were written in these patterns. The similarity of these patterns implies that the way to create patterns which existed in Azerbaijan from the times of bronze age has a close relation with the Siberian patterns. It is very interesting that we meet the patterns seen around Kazakh on the bronze axes dated BS XII–X centuries in Central Caucasus (Fig. 10). It is therefore of great importance to learn systematically about our certain patterns of BC. We should also remember what evidences are hidden below ground. Cultural history of the world’s population shows that culture can be brought in and carried out. If a nation is inspired by the culture of another one, it keeps it alive and makes it a tool of creativity. The art and culture, which are brought by foreigners and invaders, are similar to foreign blood. Such blood does not develop in a new organism. There are no works of art existing through centuries without not taking its root from creativity of people. That is, we suppose that the crystallographic patterns existing in works of art and rediscovered in Europe now are hidden in the creativity of the people. Are there traces of crystallographic patterns in the creativity of people? These traces are countless. Thumb through the books written about our carpets, and take another look at the patterns on carpets that are still kept at homes. We clearly see how the proper language of the patterns was kept in the creativity of the people in the countries where crystallographic patterns are widespread. This principle is also preserved available for music, folk creativity and poetry: less words, more meaning, plainness.
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Fig. 8. Seals from Kazakh, Azerbaijan.
Patterns in carpets and other waiving are called geometric. These patterns are the compositions made of geometric figures. Most of their elements are stylized pictures and probably bear a specific meaning. The patterns made of plain geometric polygons are more widespread in architectural structures, for example, pattern in Fig. 11. It is seen in the interior ornament of Berde Tomb and Green Tomb in Bursa (Turkey) and some other monuments. When we go through the books written about the structures of matters, we see that this pattern is also the formation schema of compounds expressed by the chemical formula AX2, e.g. the formation of a mineral having SiO2 formula. The other figure (Fig. 12) is the structure schema of some complex borate and silicate compounds, which have recently been discovered.
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Fig. 9. Four ‘‘Ali’’. Isfahan, Iran, XIV–XVth centuries.
This pattern also ornaments a mosque built in the period of Fatimids (AD 1094), and the pattern in Fig. 13 is the ornament of a mosque in Isfahan. This pattern generally reminds us of zeolite structures. Such examples are countless. As it is seen, patterns made from Arabic letter and alike complex figures are similar to structures of organic compounds. The patterns made of plain geometrical figures such as triangle, tetragon, hexagon are equal to structures of some inorganic compounds. What is the reason of the similarity between crystal structures and crystallographic patterns. Of course, pattern creators could not have knowledge about matter formation then. The reason of the similarity may be accounted for by the way of some formation styles. How are crystals formed from atoms, atom groups and molecules? In the same way as crystallographic patterns are formed by ornament elements. In other words, particles of materials should be placed so that maximum tightness can be achieved and a particle touches the maximum number of particles and particles be free in their positions. If such an ordered structure is not formed by the given particles, three-dimensional translation will not occur and the matter will turn into glass even if it hardens. That is crystal is not formed by arbitrary shaped molecules. Molecules should have complementary shapes. The figures in crystallographic patterns without background are complementary for one another. The plane is so covered with them that no space is seen among them, they complete one another. The molecules forming crystals should be such that they can fill the space of the
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Fig. 10. The ornament on bronze axes. Osetia, Rep. of Georgia.
Fig. 11. A wall decoration. Berde, Azerbaijan (1322).
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Fig. 12. A wall decoration. Egypt (1094).
Fig. 13. A wall decoration. Isfahan, Iran (XVIth century)
crystal. Crystals form themselves by two, three or more shaped atom groups or molecules. In that case different shaped atom groups and molecules will have to be complementary for one another. It is usually difficult to foretell the complementary quality of molecules and atom groups for the time being. Crystallographic patterns are formed according to the complementary principles. The figures used as the ornament elements are placed on the plane such that there exists no space among them or the spaces are at equal sizes. In other words, pattern elements should be placed at a maximum tightness as molecules dispose themselves inside crystals. As is seen the way crystals are formed is the same with those of crystallographic patterns. Such is the case that if there is a resemblance between pattern elements and molecules or atom groups the illustration of the formation of a pattern and a crystal will be the same. Of course, it is not possible to form crystallographic patterns from every kinds of shapes. It is necessary for the selected shape or shapes of a pattern to be comp-
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lementary for one another. We know no rule to try whether they will be complementary for one another for the moment, but we are sure that it will be discovered in the future. We suppose that creation of crystallographic patterns depends on geographical surroundings as well as nomadic life [2,3]. The trace of such a creation is observed in some tribes, which lead a nomadic life up to the present time. In the carpets, the illustrations of plants and animals are associated mostly with ‘‘settled life’’. What is widespread with nomadic tribes, who are dependent on Steppe culture, is especially geometric patterns. The man of steppe would not use ordinary things for ornaments. According to them ornaments ought to have been different from the plain, which was the background. That is why crystallographic patterns were commonly used in the life of nomad. Nomad did not need to use flowers, horses or figures of other animals as pattern elements. This principle is seen in the creativity of poetry and music in Turkish people. Greeks used symmetry concept to explain the content of beauty BC. Today, we interpret it more concretely, but Greeks also interpreted symmetry as harmony to nature. If a structure keeps its initial position every time the elements forming it are changed their position, it means that it is symmetric. In other words for a structure to be symmetric, it should have at least two elements from the same elements. Or the structure should be divided into two equally. The ‘‘Ali’’ pattern in Fig. 9 remains the same although it is turned four times around an axes, which is perpendicular to its center. The difference of the crystallographic patterns we mention about here from symmetric patterns is that in the first ones symmetry appears as a result of the formation of patterns. But in the latter ones symmetry is used for the formation of patterns. Pay attention to the ‘‘Four horses’’ figure made by Reza Abbasi, who was Shah Abbas’s palace painter. Through using symmetry, the number of the details (heads and legs) has been reduced twice (Fig. 14). Such a usage of symmetry of the painter shows its painter’s profound image about symmetry concept. A bird eye’s view on crystallographic patterns shows that every art language has its own grammar. We will fail if we try to perceive one art’s language through the grammar of another art. How can it be possible to discover ancient art grammar? – Of course by a thorough analysis of art formats studied by taking account general principles available for all art grammars. In crystallographic patterns such a goal has been achieved by using crystallography and its symmetry principles. Now we can make use of this field of science in the depiction and analysis of crystallographic patterns. Another opportunity is to use the similarity between matter structures and patterns in education. This brings an aesthetic aspect to education. The invisible part of the nature can be learned as
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Fig. 14. Four horses by Reza Abbasi (1587–1628).
a creativity of patterns. Every newly created crystallographic pattern is the structure plan of possible compounds (Figs. 15 and 16). Thus it is of great importance to be introduced with such patterns and the talent to create them in understanding a structure of the matters. Through giving the illustrations of some of crystallographic patterns created by Amiraslanov [5], I wanted to point out that we have the chance to continue our distinguished art tradition. Some other way is to use all these learnt structures in our practical fine arts, for all these structures which are learned and made known
Fig. 15. I.R. Amiraslanov. A hypothetical structure. Subsequently, it was realized from chemical elements for a Fe4Ni3B4O15.
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Fig. 16. I.R. Amiraslanov. Crystallographic pattern. A hypothetical structure.
are the varieties of ancient patterns, ancient masters created. To sum up we are of the opinion that natural sciences can contribute a lot in the understanding of art principles although they cannot be used to create them directly. Of course what we mention is that crystallography is far from decisiveness. But it is a plain fact that patterns should be learned systematically in this respect. In that case, the grammar of Turkish traditional pattern art can be learnt and contemporary pattern creativity can be established. References [1] J.L. Locher, W.F. Veldhuysen, The Magic of M.C. Escher, Abrams, New York, London, 2000. [2] S. Jan Abas, Islamic patterns: the spark in Escher’s genius, in: D. Schattschneider, M. Emmer (Eds.), M. C. Escher’s Legacy, A Centennial Celebration, Springer-Verlag, 2002, pp. 100–112. [3] Kh. S. Mamedov, Compt. Math. Appl. 128 (1986) 511. [4] Hudu Mamedov, I.R. Amiraslanov, H. Necefoglu, A. Mursaliyev, Nahislarin Yaddasi, TDAV Press, Istanbul, 1996. [5] I.R. Amiraslanov, H. Necefoglu, Second Kizilirmak International Congress of Science, 20–22 May 1998, Kirikkale, Turkey, Book of Abstracts (Chemistry), p. 107.
Crystallographic patterns in nature and Turkish art Hacali Necefoglu Department of Chemistry, Kafkas University, Dereici, 36100 Kars, Turkey Received 3 August 2003; accepted 28 March 2004
Abstract 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. Keywords: Crystallographic patterns; Symmetry; Tight packing; Turkish ornaments
Tel./fax: +90-474-212-2706. E-mail address: [email protected] (H. Necefoglu).
1463-0184/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryseng.2004.03.001
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The famous Dutch painter M. Escher (1898–1972) is one of those who attract a great deal of attention among the most eminent European artists. Sticking to his own creative principles, M. Escher created a series of interesting art works, some of which are patterns without background, which made most crystallographers interested [1,2]. Art critics have tried to explain that the reason why geometrical patterns were created in the Middle Ages in the places where Islam was dominant is that Islam prohibited the figuring of living things; yet this view may not be strictly true because the advent of geometrical pattern goes back as far as to many years BC. M. Escher’s works draw the crystallographer’s attention from the beginning. The exhibitions of these works were held in various congresses. Besides, they began to be used in teaching of crystallography, and the books which study these works in respect of crystallography were published. How can we explain such an interest of crystallographers for M. Escher’s creativity? Crystallographers are scientists who study how solid matters are formed from atoms and molecules. Their aim is to establish correlation between their internal structure and their properties. From the 12th year of the 20th century onwards, crystallographers began to discover the structure of crystals by using X-rays. Atoms and molecules dispose themselves in crystals as M. Escher illustrated. For comparison, see Fig. 1. This is the projection of the structure of an organic compound. Unlike the pictures M. Escher painted, the atom groups or molecules forming crystal are periodically arranged in three-dimensional space. Inside the crystals, atoms and molecules arrange themselves at the maximum tight as the components of
Fig. 1. Crystal structure of 1,3,5-triphenylbenzene.
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Fig. 2. Six ‘‘Ali’’ in Palace of Shirvanshahs, Baku, Azerbaijan, XIV–XVth centuries.
M. Escher’s pictures. The reason why the crystallographers are so interested in the patterns without background must be considered within this similarity. The first person, who drew attention to this similarity, was professor of crystallography, Mamedov [3,4]. For that reason, Mamedov named two-dimensional periodically arranged patterns without background, as crystallographic patterns (CPs). Pay attention to Fig. 2. There is an architectural hexagonal medallion with six equally divided elements, three of which are written in the shape of hollows on the stone and the other three just between the hollows. This pattern ornaments Shirvanshahlar Palace, which is the monument of XV century in Baku. Six-sided elements are the inscription of ‘‘Ali’’ in Arabic. The guides call this pattern which was created by engraving on a stone, medallion and say that ‘‘Ali’’ pattern is inscribed here six times but it is not aesthetically important how many times the pattern ‘‘Ali’’ was inscribed nor is it important in any respect. The most important and interesting fact is how they were inscribed. As can be seen, one of the crystallographic patterns was created in Baku 500 years before M. Escher. Thus the following questions arise: – How such patterns became widespread in Azerbaijan and neighbouring countries?
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– From what period onwards they came into being? – What is the reason of the creation of such an art branch? If you happen to go to Berde, a distinguished city of Azerbaijan, do visit Nushabe Castle in the center of the city. Here a cylindric holly tomb will attract your attention. On it you can see pictures, which you can meet in the books published in America and Europe under the names of Islamic Architecture or Persian Architecture. It is surprising that neither in ancient Persia, nor in pre-Islamic periods nothing was mentioned about the existence of such a tomb in Arabia. Then a question arises. How can something be given to others which is not owned? The pattern, which ornaments the cylindrical surface of Berde Tomb, is given in Fig. 3. This pattern is made up of by those whose repeating element is ‘‘Allah’’ written in the Arabic alphabet. Master Ahmet Eyyu¨boglu created an immortal wholeness between the tomb and the pattern in 1322. Those who study the history of architecture say that the master belongs to the Nakhchivan Architecture School. The founder of this school is Adjemi Nahchivani, the son of Ebubekir, who lived 850 years before. Nearly everyone must have seen his Mumine Hatun Tomb he created, at least in the pictures, which still stands with all its beauty and magnificence (the year 1186). The outline of the pattern of surface structure of a tomb in Karabaglar village which belongs to Nahchivani School is shown in Fig. 4. To ornament the surface of this tomb, a writing much more complex than that of Berde was chosen, but the creativity principle of the pattern is still the same: the principle of creating crystallographic patterns. While studying on the creation of such patterns chronologically and geographically, we saw that the CPs were widespread in Middle Asia, North Persia, Azerbaijan and Turkey. Excellent examples of CPs were created in Isfahan and Tabriz in the period of Seljuks and Safavids;
Fig. 3. ‘‘Allah’’ in kufic script. Berde, Azerbaijan (1322).
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Fig. 4. ‘‘Kelime-i shehadet’’ (the Islamic confession of faith) in kufic script. Karabaglar, Nakhchivan, XVIIIth sentury.
and in the period of Timurids in Middle Asia. It is the fact that Timur took many masters to Samarkand from Azerbaijan to have it published and there exists information in Baburname about how Azerbaijan Turkish masters were taken to India. It is obvious that no art branch comes into being spontaneously. One hundred years before the pattern ‘‘Ali’’ in Shirvanshahlar Palace in Baku, the pattern of Berde tomb, and 150 years before another variant of ‘‘Ali’’ pattern in Aksaray (Turkey) had been created (Fig. 5).
Fig. 5. Six ‘‘Ali’’. Aksaray, Turkey.
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How many years were to pass to create Berde and Aksaray patterns? To answer these questions, we have to go through the periods before the first CPs were created in Middle Ages. After a long interval, CPs are seen in the examples of Scythian culture. The characteristics of Scythian pattern creation, which is also known as Animal style, were to fill plane with patterns. Scythians are known to have been the nomadic tribes dwelling on the wide plains between the North of Black Sea and North Turkistan (many marks exist which impose the Turkish influence on them). Nomads try to inscribe their intense artistic knowledge as much as possible on the goods which they carry with them. See Fig. 6. Found in West Siberia, it is a pattern of a ceramic, dated 1000 years BC. The meaning of the details of this figure is not clear to us, but it is a typically crystallographic pattern (it is of great interest that we meet the same patterns in the contemporary artistic works of American Indians). Pattern makers of the Middle Age created the same order using words written with Arabic letters instead of these elements. It is also possible to encounter such magnificent examples in ancient Altaic Culture. Pay attention to Fig. 7. Two birds of spirit are fighting against each other. There is no space here between the figures. The black bird is the background for the white one and the white bird is the background for the black one. The medallion with ‘‘Ali’’ is inscribed with the same principle. In the latter, six elements were used instead of two elements. As can be seen, the beginning of our pattern creation goes as far back as 1000 years BC and it is no wonder that Arabic letters were used as the prior element in the periods during which Islam was dominant. We can see in Fig. 8 that such pattern creation was also widespread in 1000 years BC. Compare the pattern of the seals made of clay, which were found in the excavations in Saritepe near Kazak city (Azerbaijan) with that of Fig. 9.
Fig. 6. An ornament on ceramics. Tomsk, Russia.
H. Necefoglu / Crystal Engineering 6 (2003) 153–166
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Fig. 7. Example of Altaic culture.
The latter figure is a pattern created with four ‘‘Ali’’. These patterns are so alike that those who can read Arabic letters also try to find the word Ali in these patterns created BC. But it is not easy to comment concretely about what were written in these patterns. The similarity of these patterns implies that the way to create patterns which existed in Azerbaijan from the times of bronze age has a close relation with the Siberian patterns. It is very interesting that we meet the patterns seen around Kazakh on the bronze axes dated BS XII–X centuries in Central Caucasus (Fig. 10). It is therefore of great importance to learn systematically about our certain patterns of BC. We should also remember what evidences are hidden below ground. Cultural history of the world’s population shows that culture can be brought in and carried out. If a nation is inspired by the culture of another one, it keeps it alive and makes it a tool of creativity. The art and culture, which are brought by foreigners and invaders, are similar to foreign blood. Such blood does not develop in a new organism. There are no works of art existing through centuries without not taking its root from creativity of people. That is, we suppose that the crystallographic patterns existing in works of art and rediscovered in Europe now are hidden in the creativity of the people. Are there traces of crystallographic patterns in the creativity of people? These traces are countless. Thumb through the books written about our carpets, and take another look at the patterns on carpets that are still kept at homes. We clearly see how the proper language of the patterns was kept in the creativity of the people in the countries where crystallographic patterns are widespread. This principle is also preserved available for music, folk creativity and poetry: less words, more meaning, plainness.
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Fig. 8. Seals from Kazakh, Azerbaijan.
Patterns in carpets and other waiving are called geometric. These patterns are the compositions made of geometric figures. Most of their elements are stylized pictures and probably bear a specific meaning. The patterns made of plain geometric polygons are more widespread in architectural structures, for example, pattern in Fig. 11. It is seen in the interior ornament of Berde Tomb and Green Tomb in Bursa (Turkey) and some other monuments. When we go through the books written about the structures of matters, we see that this pattern is also the formation schema of compounds expressed by the chemical formula AX2, e.g. the formation of a mineral having SiO2 formula. The other figure (Fig. 12) is the structure schema of some complex borate and silicate compounds, which have recently been discovered.
H. Necefoglu / Crystal Engineering 6 (2003) 153–166
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Fig. 9. Four ‘‘Ali’’. Isfahan, Iran, XIV–XVth centuries.
This pattern also ornaments a mosque built in the period of Fatimids (AD 1094), and the pattern in Fig. 13 is the ornament of a mosque in Isfahan. This pattern generally reminds us of zeolite structures. Such examples are countless. As it is seen, patterns made from Arabic letter and alike complex figures are similar to structures of organic compounds. The patterns made of plain geometrical figures such as triangle, tetragon, hexagon are equal to structures of some inorganic compounds. What is the reason of the similarity between crystal structures and crystallographic patterns. Of course, pattern creators could not have knowledge about matter formation then. The reason of the similarity may be accounted for by the way of some formation styles. How are crystals formed from atoms, atom groups and molecules? In the same way as crystallographic patterns are formed by ornament elements. In other words, particles of materials should be placed so that maximum tightness can be achieved and a particle touches the maximum number of particles and particles be free in their positions. If such an ordered structure is not formed by the given particles, three-dimensional translation will not occur and the matter will turn into glass even if it hardens. That is crystal is not formed by arbitrary shaped molecules. Molecules should have complementary shapes. The figures in crystallographic patterns without background are complementary for one another. The plane is so covered with them that no space is seen among them, they complete one another. The molecules forming crystals should be such that they can fill the space of the
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Fig. 10. The ornament on bronze axes. Osetia, Rep. of Georgia.
Fig. 11. A wall decoration. Berde, Azerbaijan (1322).
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Fig. 12. A wall decoration. Egypt (1094).
Fig. 13. A wall decoration. Isfahan, Iran (XVIth century)
crystal. Crystals form themselves by two, three or more shaped atom groups or molecules. In that case different shaped atom groups and molecules will have to be complementary for one another. It is usually difficult to foretell the complementary quality of molecules and atom groups for the time being. Crystallographic patterns are formed according to the complementary principles. The figures used as the ornament elements are placed on the plane such that there exists no space among them or the spaces are at equal sizes. In other words, pattern elements should be placed at a maximum tightness as molecules dispose themselves inside crystals. As is seen the way crystals are formed is the same with those of crystallographic patterns. Such is the case that if there is a resemblance between pattern elements and molecules or atom groups the illustration of the formation of a pattern and a crystal will be the same. Of course, it is not possible to form crystallographic patterns from every kinds of shapes. It is necessary for the selected shape or shapes of a pattern to be comp-
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lementary for one another. We know no rule to try whether they will be complementary for one another for the moment, but we are sure that it will be discovered in the future. We suppose that creation of crystallographic patterns depends on geographical surroundings as well as nomadic life [2,3]. The trace of such a creation is observed in some tribes, which lead a nomadic life up to the present time. In the carpets, the illustrations of plants and animals are associated mostly with ‘‘settled life’’. What is widespread with nomadic tribes, who are dependent on Steppe culture, is especially geometric patterns. The man of steppe would not use ordinary things for ornaments. According to them ornaments ought to have been different from the plain, which was the background. That is why crystallographic patterns were commonly used in the life of nomad. Nomad did not need to use flowers, horses or figures of other animals as pattern elements. This principle is seen in the creativity of poetry and music in Turkish people. Greeks used symmetry concept to explain the content of beauty BC. Today, we interpret it more concretely, but Greeks also interpreted symmetry as harmony to nature. If a structure keeps its initial position every time the elements forming it are changed their position, it means that it is symmetric. In other words for a structure to be symmetric, it should have at least two elements from the same elements. Or the structure should be divided into two equally. The ‘‘Ali’’ pattern in Fig. 9 remains the same although it is turned four times around an axes, which is perpendicular to its center. The difference of the crystallographic patterns we mention about here from symmetric patterns is that in the first ones symmetry appears as a result of the formation of patterns. But in the latter ones symmetry is used for the formation of patterns. Pay attention to the ‘‘Four horses’’ figure made by Reza Abbasi, who was Shah Abbas’s palace painter. Through using symmetry, the number of the details (heads and legs) has been reduced twice (Fig. 14). Such a usage of symmetry of the painter shows its painter’s profound image about symmetry concept. A bird eye’s view on crystallographic patterns shows that every art language has its own grammar. We will fail if we try to perceive one art’s language through the grammar of another art. How can it be possible to discover ancient art grammar? – Of course by a thorough analysis of art formats studied by taking account general principles available for all art grammars. In crystallographic patterns such a goal has been achieved by using crystallography and its symmetry principles. Now we can make use of this field of science in the depiction and analysis of crystallographic patterns. Another opportunity is to use the similarity between matter structures and patterns in education. This brings an aesthetic aspect to education. The invisible part of the nature can be learned as
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Fig. 14. Four horses by Reza Abbasi (1587–1628).
a creativity of patterns. Every newly created crystallographic pattern is the structure plan of possible compounds (Figs. 15 and 16). Thus it is of great importance to be introduced with such patterns and the talent to create them in understanding a structure of the matters. Through giving the illustrations of some of crystallographic patterns created by Amiraslanov [5], I wanted to point out that we have the chance to continue our distinguished art tradition. Some other way is to use all these learnt structures in our practical fine arts, for all these structures which are learned and made known
Fig. 15. I.R. Amiraslanov. A hypothetical structure. Subsequently, it was realized from chemical elements for a Fe4Ni3B4O15.
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Fig. 16. I.R. Amiraslanov. Crystallographic pattern. A hypothetical structure.
are the varieties of ancient patterns, ancient masters created. To sum up we are of the opinion that natural sciences can contribute a lot in the understanding of art principles although they cannot be used to create them directly. Of course what we mention is that crystallography is far from decisiveness. But it is a plain fact that patterns should be learned systematically in this respect. In that case, the grammar of Turkish traditional pattern art can be learnt and contemporary pattern creativity can be established. References [1] J.L. Locher, W.F. Veldhuysen, The Magic of M.C. Escher, Abrams, New York, London, 2000. [2] S. Jan Abas, Islamic patterns: the spark in Escher’s genius, in: D. Schattschneider, M. Emmer (Eds.), M. C. Escher’s Legacy, A Centennial Celebration, Springer-Verlag, 2002, pp. 100–112. [3] Kh. S. Mamedov, Compt. Math. Appl. 128 (1986) 511. [4] Hudu Mamedov, I.R. Amiraslanov, H. Necefoglu, A. Mursaliyev, Nahislarin Yaddasi, TDAV Press, Istanbul, 1996. [5] I.R. Amiraslanov, H. Necefoglu, Second Kizilirmak International Congress of Science, 20–22 May 1998, Kirikkale, Turkey, Book of Abstracts (Chemistry), p. 107.