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ON THE EARLIER OCCURRENCES OF THE
cm-TYPE NETS AND WALLPAPER PATTERNS
IN ORNAMENTAL ARTS OF CENTRAL EURASIA
by
Szaniszló Bérczi
Eötvös University
Faculty of Science
Department of General Physics
Budapest, Hungary
© Symmetry Foundation. Digitized 2004 by permission of publisher.
Bérczi, S. (2001). On the earlier occurrences of the cm-type nets and wallpaper patterns
in ornamental arts of central Eurasia [Special issue of Symmetry: Culture and Science].
Symmetry in Ethnomathematics, 12(1-2), 5-24. Budapest, Hungary: International
Symmetry Foundation.
This product was funded by the National Science Foundation (NSF) as a component of the National Science,
Technology, Engineering, and Mathematics Education Digital Library (NSDL), award number DUE0121749. Any
opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not
necessarily reflect the views of NSF.
Symmetry: Culture and Science
Vol. 12, Nos. 1-2, 5-24, 2001
ON THE EARLIER OCCURRENCES OF THE
cm-TYPE NETS AND WALLPAPER PATTERNS
IN ORNAMENTAL ARTS OF CENTRAL EURASIA
Szaniszló Bérczi
Address: Eötvös University, Faculty of Science, Department of General Physics, H-1117 Budapest, Pázmány
Péter sétány 1/a., Hungary.
Abstract: The cm-type wallpaper pattern has a rich occurrence in the old Hungarian
art in the archaeology of the Carpathian Basin in the Árpád Age of 9th-10th centuries
AD. Several earlier occurrences of this structure have been studied here since the
archaeological finds of Urartu from the 9th-7th centuries BC, through the tomb finds of
Ziwiyeh from the 7th centuries BC, from Scythian-Hun kurgans of Pazyryk 5th centuries
BC, Chinese stone sculpture from the 1st centuries BC, the Sasanian stone reliefs of
Firuzabad from the 3rd-4th centuries AD till the Central Asian murals of BactrianChoresmian-Sogdian art from the 6th-7th centuries AD. We show some younger
occurrences of this structure from the Romanesque architectural and ornamental art of
Hungary in the 11th-12th centuries AD, too. We compare these earlier and some younger
occurrences of the cm-type structure and sketch their distribution in the Central
Eurasian ornamental arts.
INTRODUCTION
Ornamental artworks from various cultural communities of Eurasia show that
recognition and design of patterns follow some systematic way of development.
Ornamental works contain an important aspect, which is inherent both in natural and in
artificial products: the larger material structures are built up of smaller, frequently
congruent units. This is a common structural background of natural and technological
materials systems. This background is a constraint for pattern formation and the
recognition of this idea helped in forming new artistic wallpaper types. Not only the
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copying of the observed arrangements opened possibilities of pattern design but the
recognition and learning of how to connect repeated elements was also a way to form
intuitive developments in patterns.
In the last decades it has been shown that intuitive developments of patterns may
represent different ethnomathematical sources. In our earlier works the construction of
double friezes from the basic frieze patterns was studied (Bérczi 1986, Bérczi 1989).
The rich set of Avar-Onogurian ornamental structures triggered the suggestion of double
ornamental threads, which gave a more detailed set of patterns and a new principle to
the pattern generation. This new concept was used to find various cultures as
ethnomathematical sources with rich design set shown by their double friezes. One of
these cultures was the Celtic art. We also found a chin to follow how the very frequently
occurring type of m-g double frieze and the related cm-type wallpaper pattern
distributed in the steppe belt of Eurasia (Bérczi 1989).
The last decades of the Eurasian archaeology revealed new sources useful for studies
and comparisons of other known wallpaper pattern structures. Both the excavations of
Afrasiab and some new finds of Urartu helped to follow a sequence of the heritage of the
cm-type wallpaper structures into earlier times. These new observations are the object of
this paper.
cm
p2
p1
pmm
pgg
pg
cm-TYPE NETS AND WALLPAPER PATTERNS IN ORNAMENTAL ARTS
pmm
pgg
7
pg
Figure 1: The 17 wallpaper groups with their simple patterns (all drawings of the paper are by the author)
with the emerged cm-type pattern with woven structure: glide reflection of
columns and mirror reflection of rows as generators.
In the first figure we show 9 of the 17 wallpaper patterns. They have a common
characteristic: they have the maximum of 2-fold rotations and they can be woven from
friezes patterns (Bérczi 1989) (Figure 1). In the second figure we show how the famous
cm-type wallpaper pattern is related to the Hungarian sabretache plate structure (László
1943a, 1955). This cm-type pattern can be drawn in the triangular mosaic of the plane,
too. It contains a g-type frieze pattern (in vertical position) placed between two parallel
(vertical) mirrors. If only one line of mirror reflection is used, the m-g-type double frieze
is produced. The two parallel mirrors are the generators of the m-type frieze pattern
running in horizontal rows of our cm-type patterns. This way the cm-type patterns are
woven lattices: from g-type „columns” and m-type „rows” (Figure 2).
OLD HUNGARIAN ART OF ÁRPÁD AGE
In the late 19th and the early 20th century AD in archaeological excavations of the Great
Hungarian Plain several silver plates with golden cover were found. These archaeologic
finds were the most representative objects of the horse and warrior’s mount in tombs
from the age of the Hungarian Conquest, late 9th and early 10th century AD. At that time
the actual use of the objects was to hold the fire instruments in a small ladder sack
(sabretache) and that is why these silver plates were named sabretache plates. (The army
of the Austro-Hungarian Monarchy had cavalry corps in World War I and Hungarian
Kingdom had such corps even in World War II, too.)
Sabretache plates were put into 2 main groups according to their ornamental
adornations. One half of the plates were covered with central symmetric type pattern,
more or less with a D2-type structure. The other half of the sabretache plates were
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adorned with cm type nets and patterns. Some plates were decorated by enlarged
portions of the cm-type patterns which could be related to the life-tree motif, too
(Figures 3 and 4). On the overwhelming majority of these archaeological finds the
repeated figural element is the palmette. The cm-type patterns also occur on cup-peaks
(Beregszász) and on saddle bone carvings (Izsák-Balázspuszta) from the Carpathian
Basin and along the route of migrating Hungarians, like the sword of Kijev (Ukraine)
from conquest ages (Figure 5). Some of these structures were shown in the works on
Old-Hungarian archaeological art by László (1943b, 1955) and in symmetry studies by
Bérczi (1986, 1989, 2000).
Figure 2: The relations in construction of the m-g double frieze pattern and the cm-type wallpaper pattern.
cm-TYPE NETS AND WALLPAPER PATTERNS IN ORNAMENTAL ARTS
Bodrogvécs
Eperjeske
Szolyva
Galgóc
Figure 3: Cm-type patterns with palmette motifs are the favourite adornations of the sabretach plates in the
ornamental art of Old-Hungarians from the migration and conquest ages (9th-10th centuries AD).
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Rakamaz
Turkeve
Tarcal
Dunavecse
Figure 4: Cut cm-type patterns and centralized sabretach plates in the ornamental art of Old-Hungarians
cm-TYPE NETS AND WALLPAPER PATTERNS IN ORNAMENTAL ARTS
11
Figure 5: Ornamental cm-type patterns from the Hungarian Migration and Conquest Period: a) on a saddle
(Izsák-Balázspuszta, Bács-Kiskun County), b) on a cup-peak cover, (Beregszász, Bereg County), and
c) on the haft of a sword (Kiev, Ukraine) from the 9th-10 th centuries AD.
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cm-TYPE ORNAMENTS IN THE ROMANESQUE ART AGES OF
ÁRPÁD HOUSE KINGS IN HUNGARY
During the organization of the Christian Hungarian Kingdom this palmette art with
Sassanian reminescences gradually disappeared. However, the cm-type structures and
artistic motifs survived in the Romanesque architectural art in the ages of the Árpád
house kings.
A beautiful mantle was presented as a gift for the Abbey of the Metz Monastery by the
first king St. István and the queen Gizella. The ornamental adornation of this mantle is
also a cm-type pattern where a tree of life scene is repeated with two birds on the sides
of the lifetree (Figure 6). If we compare this structure to that of the sabretache plates
(Figure 2) we can correspond the birds to the edge forming palmettes and the central
trees to the mirror symmetric central palmettes of Figure 2 easily, and the same
triangular mosaic can be applied, too.
Figure 6: The ornamental pattern of the Metz blanket, a gift from King St. István, Hungary (11th century AD.)
The architectural remnants of the romanesque age is rather rich in Hungary from the
11th-13th centuries, but many important church buildings were destroyed during the
fights, mostly in the 16th-17th centuries against the Turkish Islamic Empire. This is why
we have few famous details of the old cathedrals, such as the southern doorway of the
cm-TYPE NETS AND WALLPAPER PATTERNS IN ORNAMENTAL ARTS
13
Cathedral of Gyulafehérvár (recently Alba Julia, Transylvania, Romania, Figure 7) or
the beautiful head of column found in the 19th century AD archaeological excavation of
Szekszárd (Figure 8) survived.
Another architectural remnants are from Benedictian monasteries of which a tiling with
a senmurv-like chimera cm-type arrangement from Pannonhalma is shown (Figure 9).
Figure 7: Ornamental adornation of cm-type in the southern doorway of the romanesque cathedral of
Gyulafehérvár, Alsó-Fehér County, Árpád Age Hungary.
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Figure 8: Ornamental adornation strongly resembling cm-type in a columnar head from Szekszárd,
romanesque architecture, Árpád Age, Hungary.
Other architectural remnants are from Benedictian monasteries of which a tiling with a
senmurv-like chimera cm-type arrangement from Pannonhalma is shown (Figure 9).
cm-TYPE NETS AND WALLPAPER PATTERNS IN ORNAMENTAL ARTS
Figure 9: Tiling from a Benedictian monastery with a senmurv-like chimera cm-type arrangement
(Pannonhalma)
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CENTRAL ASIAN MURALS
In the archaeological excavation of Afrasiab and Pendjikent murals revealed the rich life
of this Central Asian region even during the centuries of the great migrations (Bakay
1997, 1998). These murals were painted in the palace of the Sogdian dux in the 6th-7th
centuries AD period (Figure 10). For example we show a dress of a noble participant
worn on the reception of the local authority (dux). This is a cmm-type net pattern, but
oriented up and down. This vertical use is emphasized by the senmurvs placed into the
open central parts of the net. This is why the equivalence of the up and down is violated,
and even the net can be considered as cm-type. So this net pattern is closely related to
the cm-type group, if it is oriented by its vertically „standing” figures.
Figure 10: Cm-type ornamental patterns of the noble visitors in a party.
(Murals of Afrasiab, Central Asia, Uzbeghistan)
Further analysis of the pattern decide that the strict symmmetry group of the whole
pattern is pg because of the alternating direction of the senmurv in the rows. So the
symmetry of the net of the dress pattern (cmm) is first reduced to cm by the distinction
of the up and down by the vertical animals, but finally must be further reduced to pgtype because of the pg-structure of the senmurvs in the centres of the net units.
cm-TYPE NETS AND WALLPAPER PATTERNS IN ORNAMENTAL ARTS
17
STONE RELIEFS OF FIRUZABAD, IRAN
From the Sasanian Age Iran (3rd century AD) a well-known historical relict is the great
frieze carving memorial of the triumph of Sasanians in a battle on a relief of the stone
walls of Firuzabad. In the historic battle the Sassanian cavalry attacks and defeats the
Arsacid (Parthian) warriors. (The defeated Parthians were relatives of the Saka people,
the Scythians of the Central Asian area at the eastern bank of the Caspian Sea.) Sasanian
horses are covered with armoured shabracks which have an ornamental adornation with
cm-type pattern (Figure 11). In this pattern only the position of the repeated mirror
symmetric units exhibit the cm-type structure.
Figure 11: Stone relief of Firuzabad with cavalry attack of Sasanians against the last Arsacid ruler. The
armour of the shabrack of the horses is with cm-type adornation. (Firuzabad, Iran, Sasanian Age, 3rd-4th
centuries AD)
CM-TYPE PATTERN IN CHINESE ART
There is a frequently referred stone carving on a beautiful tombstone from China from
the 1st century BC (Chavanne 1893, Huszka 1930). There are horse driven cars in the
surrounding scene and a large palmette tree ornament in the central portion of the
tombstone can be seen on it (Figure 12). In the central portion of the broad leaf tree the
leaves are arranged in a cm-type pattern.
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Figure 12: Cm-type pattern (detail) on a tombstone from China. (1st century BC)
cm-TYPE PATTERN IN THE PAZYRYK SCYTHIAN KURGAN
FROM THE ALTAJ MOUNTAINS
Shabracks with applied patterns from the famous Kurgan excavations of Rudenko in the
first half of the 20th century are frequently referred to (Rudenko 1953, Bérczi 2000). In
Figure 13 the first – chesstable-like – pattern itself is a p4m if the squares and the
circular ornaments were considered. But the horsehead-like figures are inserted as
applications into the pattern according to the positions of the black chess squares on the
chesstable, and they reduce the p4m symmetry to a cm-type structure (Figure 13a). (We
note that one horse head is applied upside down in the original drawing of Rudenko, so
it violates the cm structure on the original shabrack.)
There is another applied shabrack from these Pazyrik excavations (Rudenko 1953). It
has a cell-structure where the contour of the applied cells have a global cm-type pattern
and the inner figural units reduce it to a colorful, but simple p1-type wallpaper pattern
(Figure 13b).
cm-TYPE NETS AND WALLPAPER PATTERNS IN ORNAMENTAL ARTS
Figure 13: Two cm-type applied patterns on shabracks from the Scythian (or Hun) Pazyryk Kurgans.
(5th century BC)
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SCYTHIAN TYPE TOMB ART FROM ZIWIYEH
Going back in time, a famous archaeological relict is the tomb found in Ziwiyeh from
the Scythian Iron Age (7th century BC). Among the rich treasury of the tomb a gold belt
plate with an extended cm-type net structure was found (Ghirshman 1964). The cultural
relations of the motifs and the spirit of adornations on the tomb finds of Ziwiyeh are
reminiscent to the archaeological finds of the Pontusian Scythian kurgans (.e. Kelermes).
For example there were plates adorned with repeated net (p1-type) where deers are
placed into the cells of the net. In the characteristic cm-type net of the Ziwiyeh gold
plate (Figure 14) deers and goats form regular rows in the cm-type net pattern. In the
central region of the belt all rows are mirror-reflected and the animals see in opposite
direction. The whole net and arrangement is very similar to the oldest among such type
patterns: that belt patterns are from Urartu.
Figure 14: cm-type gold plate belt from the Ziwiyeh Tomb Treasury (7th century BC)
URARTU
Till today the oldest occurrence of the cm-type structures is from Urartu. This pattern
was probably among the most popular structures in the Urartu ornamental art in the 7th9th centuries BC (Kendall 1977, Kádár 1996). The Urartuian wallpaper pattern
cm-TYPE NETS AND WALLPAPER PATTERNS IN ORNAMENTAL ARTS
21
occurrences are mainly on bronze belt patterns. Everybody wears the belts in a
horizontal position, so the belt frieze always runs in a horizontal row. The symmetry
elements of the net on the Uratian belt were repeated by mirror reflection (with
perpendicular axis) along the horizontal friezes and by glide reflection in the verticular
direction. On the meeting points of the net, and inside the net cells individual figures
were shown such as faces, flowers, chimera, priests, so thier orientation also emphasized
the vertical direction (Figure 15).
Figure 15: cm-type ornamental pattern from Urartu (7th-9th centuries BC)
In all four Urartian bronze belts the net elements separate rhombic (or flat hexagonal)
spaces where rich graphic drawings are standing separately. The figures in the network
are sometimes repeated. The carved figural elements are well-known from the
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Mesopotamian art where priests or chimera serve at the tree of life. But here the
traditional tree of life scene (Pr. Mikasa 1996) in the centre is replaced by all the
network of the net made of a plant-like motif. So the magic tree of life is represented by
the net itself.
cm-TYPE NETS AND WALLPAPER PATTERNS IN ORNAMENTAL ARTS
23
Figure 16: Urartuian bronze belts with wider cm-type layers. (7th-9th centuries BC)
The cells formed by the net extend to the edge of the belts up and down. In the simplest
case only 3 rows of the cm-type pattern can be identified as a net background of various
figures. Other belt bronzes have one row more up to 5 rows of the widest such pattern
(Figure 16) Note the widest occurrence in this width sequence of the belts is the gold
belt from the Ziwiyeh tomb with 6 rows (Figure 14).
SUMMARY
We collected the cm-type ornamental patterns from the earlier ages then the Hungarian
sabretache plates, where they were first described in details (Bérczi 1986). We found that
sometimes patterns or net patterns with higher symmetry (cmm, p4m) were reduced by
repeated elements or by the orientation of the elements to lower cm-type symmetry. This
also means that the primary background mosaics were various net types.
We found that the earliest occurrence of the cm-type patterns are from Urartu.
Occurrences in Iran, Central Asia, Altai Mts. and China were also found. This type of
ornament was a favourite type ornamental decoration during the 1st Millennium BC till
the end of the 1st Millennium AD and was continuously used in Romanesque ornamental
art of the architectural stone carvings.
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More and more occurrences of this cm-type pattern witness earlier recognition and long
time use of this structure. Using the ethnomathematical relations in the distribution and
occurrence on farther places we can imply related communities: Urartu to Scythians
(short time interval between them) or to the Scythian-Hun-Chinese relations in the first
millennium BC. Comparisons and projecting all the sites of the occurrences of the cmtype patterns show overlapping regions with the earlier m-g-type double friezes, too
(Bérczi 1989). On this basis we may conclude that cultural communities using m-g and
cm-type patterns were in cultural contact.
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