A Modular Design System based on the Star and Cross Pattern

A Modular Design System based on
the Star and Cross Pattern
Peter R. Cromwell
Pure Mathematics Division, Mathematical Sciences Building,
University of Liverpool, Peach Street, Liverpool L69 7ZL, England.
We introduce a modular design system, which we call CAMS, that is based on the preIslamic Star and Cross pattern. It can be used to generate a large family of traditional
Islamic patterns found in Central Asia and Iran. In other examples of Islamic modular
systems, the modules form a substrate that is used in construction and then deleted;
in this case the modules themselves form the finished pattern. We also analyse some
traditional 2-level geometric patterns as hierarchical structures of CAMS modules, corroborating the principles of 2-level pattern construction found in other Islamic modular
Figure 1 shows a simple geometric design known as the Star and Cross pattern. It is
formed from 8-pointed regular star polygons of type {8/2} arranged on a square grid. The
interstitial spaces between the stars form crosses. Crosses with this pointed shape seem
not to have been used individually as emblems and are only found in the context of this
Use of the Star and Cross pattern is common among cultures that have developed a
geometric style of ornament. For example, in the Roman mosaic from Cherchel, Algeria [1,
Pl. 177d] shown in Figure 2(a), the stars are decorated with interlaced squares (shown in
grey in the figure but filled with guilloche in the original) and the crosses are subdivided
into squares and rhombi.
Figure 2(b) shows another non-Islamic treatment of the Star and Cross pattern —
it is from a sketch of a 13th-century Cosmati pavement in Rome, Italy [16, Fig. 4-105].
Figure 2(c) shows part of the Cosmatesque floor in Monreale Cathedral, Sicily. In general,
Figure 1: The Star and Cross pattern.
Figure 2: Variations on the Star and Cross design.
www.thejoyofshards.co.uk courtesy of Rod Humby.
Photograph reproduced from
the large-scale framework in Cosmati work is provided by a compass-work design, so the
use of the angular Star and Cross pattern here is evidence of Islamic influence.
In this paper we introduce a modular system based on the Star and Cross pattern that
conforms to the silver ratio system of proportion. We show many examples of traditional
Islamic patterns that can be produced using this system; they are mostly from Central
Asia and Iran of the Seljuk, Timurid and Mughal periods and include field patterns, star
patterns, and 2-level patterns. This complements previous studies of Islamic geometric
ornament [3, 5, 6, 8, 13], which have found evidence to support the traditional use of a
modular approach to pattern design, particularly in the construction of patterns based on
the geometry of 10-pointed stars and the golden ratio.
One of the benefits of the modular method is that it provides a natural route to the
production of 2-level designs via hierarchies of modules of different scales. We shall analyse
2-level patterns in which the small-scale pattern either fills or outlines the compartments
in the large-scale pattern; these two modes (filling or outlining) correspond to Type A and
Type B, respectively, in the classification of 2-level designs introduced by Bonner [3]. We
shall see that the principles for constructing 2-level patterns with the new system agree
with those found previously in the 10-point setting.
CAMS: an early modular design system
The construction of a large variety of different structures from a small set of basic elements
(modules) is known as modular design. Bricks are the simplest example. Modules are often
assembled to make repeating (periodic) units, but free-form arrangements that grow more
organically are also possible. In general, the modular approach brings benefits through ease
of manufacture with the mass production of interchangeable parts. In geometric ornament
it also has benefits for composition: the eye finds unity in the economy of motifs and re-use
of familiar forms as the same few shapes appear in a variety of contexts. It also means nonexperts can produce acceptable results as modular design naturally creates a satisfactory
distribution of related elements.
Figure 3 shows a set of tiles that form a modular system for creating geometric patterns.
I have named the individual tiles for ease of reference. The internal angles are all multiples
of 45◦ and the tiles have two edge lengths: the long and short edges are in the ratio 2 : 1.
In the top row, the large square is equilateral with long edges, the house has edges of both
lengths, and the other tiles are equilateral with short edges. The tiles in the bottom row can
be seen as composites of the square, house and hexagon tiles, as shown by the dotted lines.
(We shall see later that the star is also a composite figure, in many ways.) The strictly
limited range of side lengths and angles produces a system that can generate an abundance
of different patterns, but the shared properties also give a visual consistency both within a
single pattern and across a collection.
These tiles can be assembled to create many traditional Islamic patterns from Central
Asia: Transoxiana (modern Uzbekistan), Khorasan (Afghanistan plus areas of neighbouring
states, including north-east Iran), and India. For convenience we shall refer to the tiles in
Figure 3 as CAMS (Central Asian Modular System) tiles and to the patterns they generate
as CAMS patterns.
Figure 4 shows some examples. The first two patterns are field patterns (do not contain
stars) and are pre-Islamic. Figure 4(a) can be found among the brickwork patterns on the
small square
large square
Dutch bonnet
Figure 3: Tiles of the Central Asian modular design system (CAMS).
tomb tower at Damavand, Iran (mid 11th century) [19, Pl. 8], along with the Star and Cross
pattern. Figure 4(c) is another field pattern; by looking at the lines rather than the tiles,
it can be interpreted as overlapping regular octagons and seen as a polygonal version of a
common pre-Islamic arrangement of overlapping circles.
Figure 4(d) and (e) are obtained from the Star and Cross pattern by subdividing the
crosses. Figure 4(e) is very common. It can be found in the remains of the 9th-century
al-Tariq Mosque (Masjid-i Nuh Gunbad) at Balkh, Afghanistan. The crosses are oriented
diagonally and the tiles are outlined in alternating interlace; unusually for Islamic patterns,
the ribbons are not truncated at the edge of the pattern, and the design is adapted so that
what would be loose ends are connected and turn back to re-enter the composition. The
al-Tariq Mosque also contains the field pattern of Figure 4(a).
The pattern in Figure 4(f) is common and widespread. It appears in early brickwork
patterns of the Seljuk period — see, for example, the minarets at Damghan (mid 11th century) and Saveh (1110), both in Iran, and the 12th-century Minaret of Jam in Afghanistan.
In one of the ceilings at the Mausoleum of Oljeitu at Sultaniya, Iran (1304–13), the design
is executed in carved stucco with the tile outlines painted red — see photograph IRA 2631
in Wade’s collection [22]. It is the only pattern from this modular system to appear in
Bourgoin’s collection [2, Pl. 67] from his travels in Egypt and Syria.
Lee observes [12, p. 166] that Figure 4(f) can be obtained from Figure 4(c) by placing the
8-pointed stars of the Star and Cross pattern at the centres of some of the large overlapping
octagons in (c) and adapting things to fit. In this sense, (f) can be seen as a blend of
two simple early patterns. Its popularity may be an indicator that it was the first of a new
system of patterns, a sort of signature piece, distinct from what came before but still clearly
derived from it.
Figure 4(g) is another early CAMS pattern. A brickwork version fills the pishtaq framing
the entrance to the 12th-century Middle Mausoleum at Uzgen, Kyrgyzstan. The other
examples are from a variety of later sources. Figure 4(l) is from a sandstone balustrade
at the Amber Fort, India (1660) — see photograph IND 0914 [22]. Although it is not
immediately apparent, this field pattern is derived from the Star and Cross pattern by
subdivision: the pattern is rotated by 45◦ , the crosses are divided into a central square and
four house tiles as in Figure 4(e), and the stars are divided into four flasks as shown in
Figure 5(e); the handedness of the star filling switches in alternate rows.
Figure 4: Traditional patterns that can be built from the CAMS tiles.
Figure 5: Subdivisions of the star tile found in traditional patterns.
Figure 6: Traditional patterns closely related to CAMS.
Many other versions of the {8/2} star motif can be found in traditional patterns — see
Figure 5. Those in the top row are dissections of the star into CAMS tiles. People who
analyse patterns in terms of linear features rather than tile shapes may classify patterns
containing (e) as swastika designs. Figure 5(f) is from a design carved in relief with raised
flowers in the centre. The remaining designs are dissections that introduce new shapes: (g)
contains the {8/3} star; (h) is another subdivision that preserves the 8-fold symmetry of
the star; (i) is derived from (h) by deleting lines.
Figure 6 shows some interesting variants of CAMS patterns that require modified or
additional tiles. At first glance (a) appears to be a genuine CAMS pattern but, on inspection, we see that the Dutch bonnet tiles are mis-shaped: the edge lengths along the bottom
should be short-long-long-short, but here the sequence is long-short-short-long.
The Dutch bonnet tile has two adjacent long edges meeting at a re-entrant corner; the
large square is the only tile from Figure 3 that fits this space so Dutch bonnets are used
in opposing pairs, as in Figure 4(g). In Figure 6(b) this forced arrangement has been
broken and plus-shaped regions have been introduced. These regions are of similar size
to the CAMS tiles and share their geometric properties of edge length and angles, so a
plus-shaped tile could easily be added to the set. It is in this way that modular systems
grow and evolve: the modules are assembled in ways that leave vacant spaces, and the gaps
become new modules.
This ease of extensibility means that we cannot be definitive about which tiles are
CAMS tiles. There is no medieval instruction manual containing a diagram like Figure 3.
The CAMS tiles have been abstracted empirically after surveying many traditional patterns
on surviving buildings; membership of the family has been determined by frequency of use
and structural similarities of the tiles as much as by size, edge length, and angle. The most
common tiles are the star, house, large square, belt, bone and Dutch bonnet. The hexagon
tile appears in a few early patterns, but is rarely used later and perhaps should not be
included in the CAMS set. The flask tile is formed by fusing the hexagon with a square;
it has a more distinctive shape that has features characteristic of this set and is unlikely
to belong to any other. However, it is almost always used in groups of four arranged as
Figure 5(e).
The Dutch bonnet is reminiscent of the motif on the trapezium tile in a modular system
for producing patterns based on 10-pointed stars [6]; in that case it is a launch point for the
construction of 2-point patterns. Figure 6(c) is a modification of Figure 4(g) that produces
a similar effect — it can be interpreted as overlapping house tiles. However, there seems to
have been no general means to produce 2-point CAMS patterns.
Documentary evidence for the historical use of other modular systems is provided by
the Topkapı Scroll [8]. Panel 61 of the scroll, redrawn in Figure 7(a), is the only template
that corresponds to a CAMS pattern. It is unusual in that the star centres lie on the edges
of the template, not in the corners [7].
Besides the geometrically pure form presented so far, CAMS patterns were also applied
in what would today be called a pixellated form — the tile shapes are approximated on
a square grid. An example from Panel 47 of the Topkapı Scroll is shown in Figure 7(b).
To see that the pixellated form is approximate note that the star is not equilateral (the
diagonal edges are shorter than the other edges). However, the pattern is clearly closely
related to the modular system — the true form is shown in Figure 4(j). The Topkapı Scroll
contains four further examples of the approximated patterns: Panel 51d is the Star and
Cross pattern, Panel 43 is Figure 4(e), Panel 37b is the signature pattern of Figure 4(f) and
Panel 1 is related to Figure 11(d) that we shall discuss in §4. None of these panels provides
any hint to its construction — they are simply square grids with some of the squares filled
Glaze was rediscovered in Baghdad in the 9th century. Initially, it was expensive and
was only used for highlights. The pixellated patterns were an ideal application for the new
technology: the black and white pixels were realised in blue glazed and unglazed bricks,
respectively. CAMS patterns executed in this technique, known as banna’i, can be seen
on the muqarnas in the west iwan of the Friday Mosque in Isfahan — see [19, Pl. 83] or
photograph IRA 0529 [22].
There are many more traditional examples of CAMS patterns. Is the fact that the patterns have CAMS tiles in common sufficient to conclude that the tiles were used historically
as a modular system?
Islamic ornament drew on the classical and Sassanian traditions for its early work.
Much of the early ornament can be constructed in the Euclidean sense with straight edge
and compass: a set of lines and circles is drawn and a subset of the lines is chosen as the
figure. This was typical of Roman and Byzantine work; one circle-based form is even called
compass-work. It is not necessary to invoke a modular system to reproduce many of the
(a) Panel 61
(b) Panel 47
Figure 7: Templates from the Topkapı Scroll.
patterns in Figure 4. Books such as El-Said and Parman [17] use the Euclidean method to
explain how simple Islamic patterns can be constructed; it includes constructions for the
Star and Cross pattern and Figures 4(c) and (f) as its Figures 15, 19 and 31, respectively.
While many patterns can be reproduced in this way, reproduction and discovery may be
different processes.
Euclidean construction is a top-down method that focusses on lines. It produces a
dissection of a space into pieces, often of many different shapes, and the result can appear
cluttered if the lack of consistency in size and shape is too obvious. The modular approach
is a bottom-up method that proceeds by building up a pattern from a small set of simple
shapes. It enables a more experimental approach to composition so that a design can be
grown organically in an unplanned manner by continually attaching tiles to a patch. The
sheer variety of CAMS patterns, some of which are more free-form compositions, strongly
supports the modular system hypothesis of design. We shall find further evidence when we
consider the hierarchical properties of Islamic patterns.
Comparison with other modular systems
Although the CAMS tiles have not been described before, the suggestion that modular
systems underlie many Islamic geometric patterns is not new [3, 4, 5, 6, 8, 13, 18]. For
example, Castéra uses a modular system of 37 pieces [4, p. 114–5] to produce the intricate
patterns of 8-pointed stars found in Spain and Morocco. Only the star, house and small
and large squares occur in both the CAMS and Castéra sets of tiles. Modular design is also
now well established as one of the traditional methods for the creation of geometric designs
in the eastern Islamic world; it is supported by documentary evidence and has the power
to explain the structures of a variety of complex 2-level patterns.
Figure 8: A decorated modular system whose tiles have two edge lengths in the golden
In some widely used modular systems the modules provide an underlying structure for
the composition, but are not directly visible in the final design. We shall briefly describe
an example of such a system to provide a basis for the comparison with CAMS.
Figure 8 shows a set of tiles whose interior angles are all multiples of 36◦ . Like the tiles
in Figure 3, these tiles have two edge lengths but, in this case, the long and short edges
are in the golden ratio. The pentagon and decagon are regular polygons with short edges,
the bow-tie is equilateral with long edges, and the two other tiles have both long and short
Notice that in this system the tiles are decorated with motifs, shown here in black. All
the motifs meet the boundaries of the tiles in the midpoints of the edges. However, the
incidence angles are different on the short sides and the long sides. The geometry is dictated
by the {10/4} regular star polygon used to decorate the decagon: it leads to an incidence
angle of 72◦ on the short edges and 36◦ on the long edges. The motif on the pentagon is
the {5/2} star.
As with the CAMS tiles, a design is created by assembling these modules to produce
an edge-to-edge tiling. Figure 9 shows the construction of a design from the ceiling of the
Chehel Sotoon Palace in Isfahan: the template shown in (a) is composed of these tiles;
the template is repeated four times by reflection in the bottom and left sides to produce
the standard quartering shown in (b). Where a tile meets the boundary of the template,
it intersects along an edge or a mirror line of the tile and this ensures continuity of the
tiling across the joins between copies of the template. It is important to note that the tile
boundaries do not appear in the finished product — the black motifs form the ‘foreground’
regions of the pattern and the white areas in the corners of the tiles are fused to create
‘background’ regions. In Figures 8 and 9 the motifs are filled in to aid the discussion, but
they may be outlined in simple lines or interlacing. The somewhat irregular arrangement in
the template contains more than 60 tiles and is a good example of the free-form composition
that modular systems can produce.
As these decorated modules can be viewed as a special case of the ‘polygons in contact’
(PIC) method of construction [11], we shall refer to them as PIC modules in the following
The fact that the CAMS tiles do not carry motifs but appear themselves in the finished
pattern leads to some interesting structural differences in the families of CAMS patterns
and PIC patterns.
• The angles in the motif on a PIC module are of two kinds: those that meet an edge
of the module are determined by the incidence angle; the others are determined by
Figure 9: Construction of a ceiling design from the Chehel Sotoon Palace, Isfahan, using
the modular system of Figure 8.
the angles in the corners of the module. In particular, all the angles in the motifs
come from a small set. The angles in the corners of the background regions are the
complements of the angles in the motifs. In most cases, these angles will be different
from the angles in the motifs, and the background regions will have different shapes
from the foreground motifs. For example, in Figure 9 four of the motifs have an angle
of 36◦ , but this angle does not appear in any background region.
When two regions of a PIC pattern share an edge, one of them will be a foreground
motif and the other will be a background region. So it is unlikely that adjacent regions
in a PIC design will be congruent. However, there is no natural distinction into
foreground and background in CAMS patterns and adjacent tiles can be congruent.
Figure 4(i) contains pairs of adjacent house tiles, and all the tiles in Figure 4(b) are
• When two PIC modules share an edge, the midpoint of the edge will be a vertex in
the finished pattern, and the corners of two motifs will meet there. Hence, all the
vertices in a PIC pattern will be 4-valent. However, Figures 4(a) and (l) show that
CAMS patterns can contain 3-valent vertices.
• A pattern is said to have counter-change symmetry if its figure and ground can be
interchanged by a geometric symmetry operation. This is also known as antisymmetry.
Figure 10 shows three CAMS patterns coloured to exhibit counter-change symmetry
— the black and white regions are identical, and there exist symmetries that reverse
the colours. Figure 10(a) and (b) are star patterns; (b) is developed from the template
in Figure 7(a). Although these two patterns can be coloured in this way, I know of
no traditional Islamic star patterns that have been coloured to exhibit counter-change
symmetry. However, there are Islamic field patterns that display counter-change
symmetry. The CAMS example in Figure 10(c) is typical: all the tiles are congruent
and it has the topology of a chessboard — each tile is surrounded by four of the other
colour, and four tiles meet at each vertex.
By contrast, although a PIC design can be coloured in two colours so that adjacent
shapes have different colours, this corresponds to the natural division into foreground
(motifs) and background. If a PIC pattern had counter-change symmetry, the tiling
formed by the module edges would be self-dual. Self-dual tilings do exist [20, 21],
but they are not suitable for constructing Islamic star patterns (the tiles are irregular polygons and the dual tilings are not situated so that dual edges cross at their
midpoints). So PIC patterns cannot be coloured to show counter-change symmetry.
Type A 2-level patterns
Modular systems naturally lead to structural hierarchies as the basic modules can be
grouped together to form larger ones. We can see this process in the CAMS patterns
of Figure 11. These examples all use the 4.8.8 Archimedean tiling as an organising principle
and this underlying structure is highlighted in grey.
In Figure 11(a) CAMS tiles have been assembled to form the large squares and octagons
of the Archimedean tiling — these large shapes are the higher-level modules. Although the
Figure 10: Traditional CAMS patterns with counter-change symmetry.
pattern is a field pattern, the centre of each large octagon contains a star that has been
subdivided as in Figure 5(h). Figure 11(b) is identical to part (a) except that the central
star is subdivided as in Figure 5(d) — notice that this destroys the 8-fold symmetry of the
large octagon. Figure 11(c) is another field pattern constructed in a similar way, but with
more tiles per repeat unit. Figure 11(d) has a different method of construction: stars are
centred at the vertices of the Archimedean tiling so the large squares and octagons contain
some tile fragments along their edges.
In these examples the large-scale structure is used purely to organise the composition
and is not highlighted in the finished artwork. Figure 12 shows designs from some jali screens
at the tomb of Itimad-ad Daula in Agra, India — see [14, pp. 83–85] for photographs. In
these cases the grey lines in the figures correspond to thicker struts in the screen, producing
a design with complementary patterns on two different scales. These 2-level patterns are
Type A: the small-scale pattern fills the regions of the large-scale pattern.
The large-scale pattern in both examples of Figure 12 is a monohedral tiling of bone
tiles — the classical field pattern of Figure 4(b). In Figure 12(a) the small-scale pattern
produces a dissection of each large-scale bone into CAMS tiles. The central area of each
bone contains a small-scale star subdivided as shown in Figure 5(e); in the figure all these
chiral star centres have the same handedness, but they are not consistently oriented in the
In Figure 12(a) and (b) each vertex in the large-scale pattern has a neighbourhood that
is a regular octagon formed from small-scale tiles. In (a) this neighbourhood is formed
from eight house tiles and four squares; in (b) the tiles have been modified to produce a
neighbourhood with 8-fold symmetry. In (a) the edges of the large-scale bones coincide with
edges of the small-scale tiles; in (b) they coincide with mirror-lines of the small-scale tiles.
The examples in Figures 11 and 12 are from Mughal India, and hence quite late, but the
principles they illustrate were widely used much earlier. In Islamic ornament when a pattern
is applied to fill a space, it is not simply cropped to fit in an arbitrary manner (as in the
Cosmati pavements, for example); rather, it is constructed to be compatible with geometric
features of the boundary. For example, Figure 13 shows a large CAMS cross filled with
CAMS tiles and the modified octagonal configuration that we saw in Figure 12(b). This
example is taken from a painted strip of the Star and Cross pattern that runs around the
soffit of the arch in the portal of the Bala-Sar Madrasa, part of the Imam Reza Shrine
(a) IND 0821
(c) IND 1012
(d) IND 0423
Figure 11: CAMS patterns based on the 4.8.8 Archimedean tiling.
(a) IND 0335
Figure 12: Type A 2-level patterns from carved jali screens at the tomb of Itimad-ad Daula,
Agra (1622–28).
complex at Mashhad, Iran. The cross is marked out by placing a star centred at each
corner and a bone length-ways along each edge; the interior is completed in a way that
preserves the symmetry of the cross. The accompanying large-scale stars are filled with
As a final example of a Type A 2-level pattern Figure 14 shows a construction typical of
the decoration applied with cut ceramic tiles. The large-scale pattern, in grey and white, is
the divided Star and Cross pattern of Figure 4(e). The small-scale pattern is also composed
of CAMS tiles and includes chevron tiles. Notice that the filling of the large-scale star does
not preserve its 8-fold symmetry. This design is adapted from a spandrel in the Seyyed
Mosque in Isfahan (1840) — see photograph IRA 1617 [22] for the original. Although this
building dates from the relatively recent Qajar period, the design follows the traditional
practice of placing a small-scale star centred on every vertex of the large-scale pattern.
Type B 2-level patterns
Type B 2-level patterns are a continuation of the classical method of framing or outlining the
compartments containing the primary motifs. For example, in a Roman mosaic from SaintRomain-en-Gal, Vienna [10, Fig. 78], a geometric framework of regular hexagons divides the
composition into compartments displaying figurative designs of flowers; the pathways that
outline the compartments are covered with a simple arrangement of 6-pointed stars divided
into rhombi, and hexagons. The catalogue of designs from Roman mosaics [1] has other
examples in which Archimedean tilings are used to provide the compartmental framework: (Fig. 205), (Fig. 209) and 4.8.8 (Fig. 164). In these classical applications
of the outlining method, the geometry always plays a strictly supporting role — it is just
used to organise the space. In the Type B examples described here, the large-scale patterns
are standard Islamic geometric patterns and have the higher level of complexity one would
Figure 13: Filling of a CAMS cross from the Bala-Sar Madrasa, Mashhad.
Figure 15(a) shows a Type B 2-level design in which both the large- and small-scale
patterns are based on common CAMS patterns. It runs around the soffit of an arch in
the south iwan of the Friday Mosque of Gawhar Shad in Mashhad, Iran (1416–18). The
centre-line of the pathways defines the large-scale pattern — it is the classical field pattern
of Figure 4(c) and is easily recognised. The small-scale pattern is a mix of Figures 4(c)
and (e). The same few tiles are used in each case: the large square, house and belt are in
both the large- and small-scale patterns, and the star is also used in the small-scale pattern.
The grey compartments shaped like the large
√ square and house tiles have the correct
geometry for the tiles: the base of the house is 2 times the length of its other sides. The
path is covered by wrapping the small-scale pattern around these compartments. At the
corner of a (large) house where the roof meets a wall the small-scale pattern is mitred,
as shown in Figure 15(b). On the outside of the path two stars overlap and are fused to
produce a large white shape; in the centre of the path two houses are cut and fused to
produce a new black convex shape; on the inside of the path the two stars to be mitred are
concentric and have the same orientation and so are coincident — the small-scale pattern is
fully coherent along the boundaries of the square and house compartments. Except at these
mitred joints, the small-scale pattern is a proper edge-to-edge tiling of CAMS tiles. Except
at the outside of the mitred joints, the corners of the compartments lie at the centres of
small-scale stars. Almost all the black tiles are house tiles, which gives a strong feeling of
consistency to the design; the exceptions are the Dutch bonnets used in the frame and the
convex shape produced by the mitring.
Figure 16 shows the design from a relief panel in the south iwan of the Friday Mosque,
Isfahan (1475/6). The small-scale pattern is assembled from CAMS tiles. In fact, the con-
Figure 14: Type A 2-level pattern based on a design from the Seyyed Mosque, Isfahan
Figure 15: Type B 2-level pattern from the Friday Mosque of Gawhar Shad, Mashhad
Figure 16: Type B 2-level pattern from the Friday Mosque, Isfahan (1475/6).
struction is based on the same templates as Figure 11(d): the large square and a triangular
sector of the large octagon in the latter figure can be arranged as shown in the bottom-left of
Figure 16 to produce the central part of the panel. All the corners of the grey compartments
coincide with star centres of the small-scale pattern.
The thick black lines in the bottom-right of Figure 16 outline the equilateral polygons
that form the skeleton of the large-scale pattern. In Figure 15 the skeleton runs along the
centre-line of the white pathways, but here the skeleton is noticeably off-centre. This gives
the impression that the paths are not properly aligned and that the large-scale pattern is
not well-defined.
This paper has introduced a modular system derived from the Star and Cross pattern.
The family of patterns that can be produced by assembling the modules includes many
traditional Islamic patterns from Central Asia and Iran. Some of the simpler patterns,
including the Star and Cross pattern itself, are pre-Islamic.
The earliest Islamic examples of CAMS patterns are found among the Seljuk brickwork
designs on 11th- and 12th-century minarets. The restriction to 45◦ and 90◦ angles in the
modules may indicate that CAMS was developed in this medium as these are the angles
most compatible with working in brick.
As technical innovations provided new media, CAMS patterns were adapted and developed. The rediscovery of glaze led initially to approximate or pixellated versions of the
patterns being expressed in banna’i, and later to complex 2-level patterns in cut tile work
as more colours became available.
We have also seen that grouping modules together to form larger ones introduces hierarchical structure into a composition, either as a hidden organising principle or to generate
a complementary pattern on a different scale. Traditional examples include carved screens
from Mughal India and the more complex patterns possible with glazed tiles found in Iran.
The Iranian formula for constructing 2-level patterns that has been observed in other
modular systems [5, 8, 9] also applies to the CAMS examples: the large-scale pattern is
easily recognisable, usually simple and very familiar; in Type A patterns the corners and
intersections of the large-scale pattern are key points and in Type B patterns the corners
of the pathways are key points; small-scale stars are centred at the key points and the
remaining edge segments of the large-scale pattern are covered by edges or mirror-lines
of small-scale modules; the regions are infilled in a consistent manner (congruent regions
generally have the same filling) but the filling need not preserve the symmetry of a region.
The CAMS modules are undecorated and hence easier to produce than other modular
systems. Classical patterns provide some of the basic module shapes, and a range of CAMS
patterns is found among early brickwork ornament. These properties lead me to propose
that CAMS is one of the earliest Islamic modular systems for producing star patterns.
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