Aby Szabó, Csaba #1 - „Summer”

15 x 15 cm

2007 – 2010

The composition of this work consist of lot’s os geometrical elements: lines, arces, circles, points. I tried to express the combination of these elemets the essence of Summer. The main part in the central of the composition the simbol of the Sun. (A circle with eight triangle: like a shineing Sun.) Around this are the other signs of Summer.

Aby Szabó, Csaba #2 - „Winter”

15 x 15 cm

2007 – 2010

The composition of this work consist of lot’s os geometrical elements too: lines, arces, circles, points. I tried to express the combination of these elemets the essence of Winter. The main part in the central of the composition the simbol of a snowflake. Around this are the other signs of Winter: hoarfrost and frostwork.

Aurora Submission #1 - 6 inches x 6 inches 2008

from the original handpainted artwork “Square Root of 2” acrylic on wood (this image has been minimally retouched)

“The Square Root of 2” explores the growth pattern seen in sunflowers, pine cones, and other aspects of the natural world. As a visual representation of the square root of 2, it is also an expression of an impossible number. The impossible number can be understood as the noumenal form of the organisms in the physical world.

Aurora Submission #2 - tile: 6 inches x 6 inches 2008

from the original handpainted work “The Bridge Between Squares and Hexagons” (this image is not computer generated)

original work: 24 inches x 24 inches, acrylic on wood

“The Bridge Between Squares and Hexagons” solves the problem of how to integrate a square grid and a hexagonal grid. This relationship is also presented as the experience of perception, where two hexagons of the exact same size and shape are interpreted by the viewer alternately as a 2-D hexagon or a 3-D cube depending upon how the hexagon is colored.

Aurora Submission #3 - tile is 6 inches x 6 inches 2007

from the original handpainted work “Perfect Number, Perfect Nature” (this image has been minimally retouched) acrylic on wood

This tile is taken as a detail from “Perfect Number, Perfect Nature”, a painting that shows the interaction of the perfect world of abstract number which is the framework for the natural world and the physical expression of that abstract perfection which we perceive with our senses. This detail is an expression of the square root of 2, a growth pattern often found in nature (e.g. Sunflowers, pine cones)

Aurora Submission #4 - 12 inches x 12 inches 2009

from the original handpainted artwork “Large Quantum Froth” (this is not computer generated and is minimally retouched)

original work: 48 inches x 48 inches, acrylic on wood

This tile is a detail of the work “Large Quantum Froth”, a piece which explores a pattern of circle packing and how it relates to a Mobius transformation-inspired impossible grid. (The grid is impossible because, although it does not look so to our eye, all of the angles are right angles.) This pattern of bubbles within bubbles mimics the arrangement of matter down to its smallest level.

Aurora Submission #5 - tile: one inch x one inch 2007

from the original work “Portal” 60 inches x 60 inches (the original work is comprised of over 4,000 individually painted 1 inch tiles which were painted by hand over the course of many years)

This simple shape of two vortexes placed mouth to mouth is one of the basic shapes of energy in the universe. On this tile, the length of each colored line corresponds to the wavelength of its color of light, with red the longest down to violet the shortest.

When these tiles are placed together as a grid, the shapes and colors appear to scintillate, giving the image a sense of inner movement.

Briony, Thomas - Zsolnay #1 2010

tile 7.5” x 6.5”, tessellation 26.2” x 19.5”

This piece was created through manipulation of the virology-inspired tiling used in the patterned rhombic triacontahedron Reidun #1, shown at the Bridges Art exhibit in Pécs 2010. Inspired by a novel approach to the description of viral capsid assembly proposed by Reidun Twarock, the faces of this rhombic triacontahedron are tessellated with kites, darts and rhombs. The Islamic-inspired design was developed from biological imagery, which is reminiscent of Islamic interlace patterns. The tiling has been manipulated in the plane to form a p6m repeating design.

Briony, Thomas - Zsolnay #2 2010

tile 7.5” x 6.5”, tessellation 26.2” x 19.5”

This design was developed from biological imagery sourced during an investigation into virus structures. Inspired largely by the work of Reidun Twarock, who proposed a novel approach to virus capsid structure based on tiling theory, the tile originally formed a component of the patterned rhombic triacontahedron Reidun #1, and has been manipulated to form a p6m tessellation.

Erdély, Dániel and von Ballegooijen, Walt

A 2,5 dimensional spidronized Archimedean tile with eosin glase.

Farkas, Tamás #1

Farkas, Tamás #2

Farkas, Tamás #3

Farkas, Tamás #4

Farkas, Tamás #5

Fathauer, Robert #1 - Eight-crossing Link, Joined

6" x 6" (15.2 cm x 15.2 cm) - 2008

This tile is based on a stylized link with two strands and eight crossings. Each tile contains one such link, and the strands join where the tiles join to create a interwoven design that borrows its esthetic from Islamic latticework designs.

Fathauer, Robert #2 - Iterated Eight-crossing Link, Joined

8" x 8" (20.3 cm x 20.3 cm) - 2008

Each tile contains one quarter of a design that is based on a stylized link with two strands and eight crossings that has been iterated to consist of four strands and eighty crossings. The full design is formed by a group of four tiles, and these the strands of these groups join where the groups meet.

Fathauer, Robert #3 - Dragons

6" x 5.2" (15.2 cm x 13.2 cm) - 2003

Black and white dragons face in opposite directions in this design inspired by M.C. Escher's artwork. Ignoring the color difference, the design has two distinct lines of glide reflection symmetry.

Fathauer, Robert #4 - Three Fish

6" x 6.9" (15.2 cm x 17.5 cm) - 1994

Three fish in three different orientations and colors make up this design inspired by the art of M.C. Escher. Ignoring the color differences, there are three distinct points of three-fold rotational symmetry in the design: where three tails meet, where three top fins meet, and where three lower jaws meet.

Frank, Natalie Priebe - Swirls made up of swirls made up of swirls

2010

My inspiration for this design was that of a painted Spanish tile.

This tiling is the superposition of two copies of a tiling made of unit square tiles. One copy uses red and white tiles and the other uses blue and white tiles, which is why there is purple in the final image. Each physical tile I created is, in theory, the superposition of 14,641 tiny red and white tiles onto 14,641 tiny blue and white tiles, and these tiny tiles are acting as pixels to produce a larger image.

Garousi, Mehrdad #1 - Starry Tessellation

40” x 15” - 2010

Lonely tiles of this tessellation, at first glance, look simple combinations of different triangles, kites, and darts with white, black, yellow and blue colors. However, in the tessellation, the neighboring of alone tiles discloses more complex geometrical forms. Stars, hexagons and some large diamond-like forms can be easily seen. The more our tessellation continues and the larger area it paves, the more complex forms and shapes there appear. A deeper investigation will discover some kind of large dodecagons composed of black rhombuses. But, where is the fractality? If we continue the tessellation to a more comprehensive area, large triangles made up of smaller ones will emerge. The more we keep on, the better show of Sierpinski triangle we will have.

Garousi, Mehrdad #2 - Two-layered Tessellation).

40” x 15” - 2010

In addition to general properties like being constructed of triangles and kites or conforming a Sierpinski pattern, the more interesting part of this piece is its way of coloring and exploitation of some semi-curves. But, its main exclusivity appears when it is watched from a distance. That way, it will be discovered that the tessellation has two layers and looks 3-dimentional. It seems as if a uniform pattern paves the plane beneath and hexagonal diamonds place on it with a distance from the below layer. Arrangement of triangles and special way of coloring provide such a 3-dimensionality.

Garousi, Mehrdad #3 - Complementarity

40” x 15” - 2010

This work is a better representation of Sierpinski Triangle pattern. The generator tile of this piece has a simple pattern, two side-by-side triangles the central part of which is taken and put inside the other one. The property of this tessellation, in spite of its simplicity, is the upside down triangular shapes which it presents in large scales. Besides triangular Sierpinski patterns which are constructed, in a converse orientation, there appear some other semi-triangular Sierpinski patterns.

Garousi, Mehrdad #4 - Multi-Layered Tessellation

40” x 15” - 2010

The exclusive property of this work is its colorfulness and to be seen multi-layered. Over those numerous small triangles, different sorts of forms can be found.

Garousi, Mehrdad #5 - Blooms

40” x 15” - 2010

This tessellation containing many properties of other same works, due to its coloring, has a more flat feel and inspires combinations of more classic Euclidean patterns.

Gondos, Gábor #1

Gondos, Gábor #2

Gondos, Gábor #3

Gondos, Gábor #4

Gondos, Gábor #5

Hiigli 1 (6" X 6") : (12" X 18")

Origin: Chrome 035 : VIRUS XIII (NESTING OF OCTAHEDRA AND CUBOCTAHEDRA): VIRUS PAINTING SERIES. 1980-86. Opaque Oil on canvas, 132 x 163 in (335.28 x 414.02 cm)

Description: The basic tile (1-1) is a rhombus displaying three cuboctahedra and parts of several octahedra. The rhombus is then rotated to make a circle enclosing an elongated four pointed star (1-2).

Hiigli 2 (6" X 6") : (12" X 18")

Origin: Chrome 035 : VIRUS XIII (NESTING OF OCTAHEDRA AND CUBOCTAHEDRA): VIRUS PAINTING SERIES. 1980-86. Opaque Oil on canvas, 132 x 163 in (335.28 x 414.02 cm)

Description: The basic tile in this case is half of a similar rhombus. To form the tessellation a second tile is rotated 180 degrees so that the the whole rhombus so formed is oriented standing upright, three a row.

Hiigli 3 (6" X 6") : (12" X 18")

Origin: Cr157 FOUR CUBES - THREE SPHERES (III): FRONT VIEW TETRANET SERIES. 2002. Transparent Oil on Canvas, 65 X 65 in (165 X 165 cm)

Description: Chrome 157 (Tile 3-1) shows a transparent painting with four cubes. The smallest of the four cubes is obliterated (not visible) as it is obscured by three layers of transparent white. Each cube has an edge length of 1/2 the preceding cube and 1/8 of its volume. The second, third and fourth cube each have a sphere. The diameter of each sphere is equal to the diagonal of the face of its respective cube. The series of cubes manifest a regular change in scale. This is matched and mirrored by the scale change for spheres.

Hiigli 4 (6" X 6") : (12" X 18")

Origin : Chrome159 : HYPERCUBE VIII: TRANSFIGURATION PAINTING SERIES. 2002. Transparent Oil on Canvas, 72 X 72 in (182,8 X 182.8 cm)

Description: This tile (4-1) is an image of the transparent painting Chrome 159, which I called a hypercube. However it is really a series of cuboctahedra mapped onto a series of squares in geometric progression. The superimposition in geometric progression suggests an emphatic center of energy and a third dimension, or depth. The growth rate suggested in this case is a doubling of the squares and therefore of the cuboctahedra.

Hiigli 5-1 (6" X 6") : (12" X 18")

Origin: Cr 173 : FOURTH DIMENSION MODEL: MATHEMATICA SERIES. 2003-04. Transparent Oil on Canvas, 66 X 66 in (168 X 168 cm)

Description: This tile (5-1) is a detail of the transparent painting Chrome 173, The detail is actually the central space of the fourth dimension model, or hypercube. The hypercube is well known as a four-dimensional cube consisting of eight cube cells, twenty-four square faces, sixteen vertices (each made up of four mutually perpendicular lines), and thirty-two edges all the same length.

Hiigli 5-2 (6" X 6") : (12" X 18")

Origin: Cr 173 : FOURTH DIMENSION MODEL: MATHEMATICA SERIES. 2003-04. Transparent Oil on Canvas, 66 X 66 in (168 X 168 cm)

Description: I have included one extra set, alternate set 5-3, 5-4 since I could not decide which would make the most interesting and satisfying tessellation, 5-1 or 5-3. This tile (5-3) is a slightly larger detail of the same painting : the hypercube. I like the fact that its tessellation makes a more complex but somehow softer tiling.

Kaplan, Craig S. #1 - TI-LE (2010)

Two tiles, each 6"x6" (15.25 cm x 15.25 cm)

I was interested in the idea of forming non-repeating patterns by allowing the tiles to be re-oriented arbitrarily, and thought of expressing this idea via words split in half. The two tiles contain four beginnings (TI,FI,MI,MA) and four endings (LE,NE,RE,LL) of four-letter words. They are chosen so that all sixteen combinations are common English words, including the special word TILE. The only requirement is the the two tiles strictly alternate in a checkerboard pattern. These prefixes and suffixes are not necessarily easy to find; I used a computer search to identify a set of possibilities.

Kaplan, Craig S. #2 - Rectified hexes (2010)

8"x6.93" (20.3 cm x 17.6 cm)

In thinking about decorative tiles, it occurred to me a pattern with hexagonal symmetry might be broken down into rectangular tiles that are laid out in a running bond brick pattern, and that the rectangularity of the tiles might then provide a compelling visual counterpoint to the symmetry of the pattern. Thus in this design the grout is not intended to be invisible; rather, its shape is intended to play off against the pattern. I chose a simple two-point Islamic star pattern as a basis. I also observed the curious fact that the pattern can be reconstructed with the tiles laid out in a strict grid (see Kaplan2-3.jpg), giving the user freedom to pick a pleasing layout.

Kepner, Margaret #1 - PÉCS Logo

6-inch square tile - 2010

Description: This design is based on the letters in PÉCS using a visual form of Morse code. Working inward, the element in the tile’s upper-left-corner “reads” as circle, square, square, circle. This corresponds to dot-dash-dash-dot, which is the Morse code for P. Moving clockwise, the other three elements represent E (dot), C (dash-dot-dash-dot), and S (dot-dot-dot). The four elements are overlapped halfway and the colors derived from the PÉCS 2010 logo, with É “accented” in grey. Four-fold rotation around the “C” corner of the tile produces a virtual combo-tile, which is then tessellated in a brick-like pattern.

Kepner, Margaret #2 - PÉCS C&C

6-inch square tile - 2010

Description: This design is based on the letters in PÉCS using a visual form of Morse code – see Submission1. For the basic tile, the shapes are colored, overlapped, and shifted to produce visual elements: a light-blue crescent (the É) and a purple backward-L shape (lower-right). When combined in groups of four tiles, as shown below the basic tile, a cross-shape and swirling crescent moons are suggested. These symbols relate to the cultural history of Pécs: Christian and Islamic. The Kepner2-2 tessellation balances both symbols, while Kepner2-3 shows one tessellation emphasizing the cross-shape and another featuring the swirling crescents.

Kepner, Margaret #3 - Roman Arch

6-inch square tile - 2010

Description: The starting shape for this tile is a circle centered within a square. The proportions are such that the area of the circle equals that of the residual square-minus-circle. The shape is cut into quadrants, which are rearranged to suggest arches, alluding to the history of Pécs as a Roman colony. The shades of green relate to the area’s many vineyards. The first tessellation shown (Kepner3-2) is based on a 180-degree rotation and half-drop pattern, and has the appearance of climbing vines. The Kepner3-3 file demonstrates how this simple tile generates a surprising variety of tessellation patterns.

Kepner, Margaret #4 - Origami 3,4

6-inch square tile - 2010

Description: In honor of 2010, this design begins with 10-by-10 grid in a square. One corner has coordinates (0,0) and the opposite one has coordinates (10,10). A point is selected at (3,4). Lines are drawn to the four corners of the square, generating four non-congruent triangles. The triangles are colored with transparent shades, and the square is superimposed on a copy of itself rotated 90-degrees. This produces an origami-like image with nine colored regions. This is repeated four times with various reflections, forming a compound square -- the basic tile. The tessellation shown is a four-fold rotation pattern.

Kepner, Margaret #5 - Vasarely

6-inch square tile - 2010

Description: This design is based on a silkscreen print from the 1960s by Victor Vasarely. The basic tile is composed of a 4-by-4 grid of squares, each of which has a smaller square, diamond, or circle inside it. The forms and colors are similar to those found in the print, but are not exact copies. The tile is assembled into a four-tile grouping, which is shown below the basic tile in Kepner5-1. Using four-fold symmetry, this compound unit can be used to generate the tessellation seen in Kepner5-2.

Láng, Eszter 1 - Korond I.

Digital print on paper - 60x68,5 cm - 2010

In this work the repetition of the motif effect a rhythm. I use an element of a painted door in my home town, Korond. The mathematical harmony is perceptible. I designed the border tile using a Korond folk element likewise, his feature the symmetry, the mathematical harmony, the proportionality.

Láng, Eszter 2 - Korond II.

Digital print on paper - 70x60 cm - 2010

In the second variation I use the element of thesame painted door in my home town, Korond. The used motif is rotated with 45 degrees, that is how the final composition was created. I designed the border tile using a Korond folk element likewise, his feature the symmetry, the mathematical harmony, the proportionality.

Láng, Eszter 3 - Korond III.

Digital print on paper - 60x68,5 cm - 2010

In this work the repetition of the motif effect a rhythm. I use an element of a painted door in my home town, Korond. The mathematical harmony is perceptible. I designed the border tile using a Korond folk element likewise, his feature the symmetry, the mathematical harmony, the proportionality.

Láng, Eszter 4 ** - **Ovalia

Digital print on paper - 60x60 cm - 2010

In this work the motive is the egg, with distortion. The repetition of the motive emphasize the rhythm.

Láng, Eszter 5 - Hommage à Sándor Torok

Digital print on paper - 90x60 cm - 2010

prepared this work to the memory of my hausband ( Sandor Torok, painter, 1936-2006). The motive is one of his picture. The method is the multiplication.

Muzsai, István #1 - NIMRÓD tile

12"x12" - 2009

An equilibrated constructivist composition, colour dynamically based on simultane and quantitative contrast.

Permits only periodic tiling.

Muzsai, István #2 - CITYLIGHT tile

12"x12" - 2009

A really flowing colourful composition, colour dynamically based on simultane and quantitative contrast.

Permits only periodic tiling.

Muzsai, István #3 - ONDULA tile

12"x12" - 2009

A tricolor waveing composition, intervowen pulsating lines

Permits only periodic tiling.

Muzsai, István #4 - MARAGHA tile

12"x12" - 2010

Adaptation of the mosaic from the tomb-tower Gunbad-e Qabud in Maragha, the first known quasicrystalline Islamic pattern ( B.C.1196-1197)

Permits aperiodic tiling, having 10-fold symmetry. My set contains 8 basic elements, but it is could be transformed in 6 pieces ( 3 fundamentals, 2 composite, 2 derived )

In execution using of the famous Zsolnay invented eosin enamel, red (bullblood) and green colours are required.

Muzsai, István #5 - DIMGRID tile

12"x12" - 2010

A result of my DLA research about "Golden Mean & Pythagorean Scale " beside others was a decagonal quasicrystalline tiling, based on the LSLSLLSL Fibonacci pentagrid. As we know ' Nihil nove sub sole", of course this grid was publicated before ( Ref.: R. Ingalls: Decagonal

quasicrystal tilings, Acta Cryst. A 48 (1992) 533-541, Fig 7, pattern t_c. )

BUT: Inflating the black-white coloured pattern, results the attached set of 9 pieces and it's inverses.

Permits aperiodic tiling, having 10-fold symmetry.

Prof. Newman, Rochelle # 1 6" tile, tessellation 12" x 18", 2010

"Purple Cut"

A motif was developed using Golden Cuts of the square. Shapes were developed within each area so that edges could connect. The motif was rotated four times in order to create the unit. This unit was then translated to build the tiling.

Prof. Newman, Rochelle # 2 4" tile, tessellation 12" x 12", 2010

"Crossroads"

Using graph paper interlocking crosses were constructed playing with the high contrast of black and white. Color was added to the edges. The grouping became the tile which was then translated.

Prof. Newman, Richard # 1 6" tile, tessellation 12" x 18", 2010

"Spatial Twist"

The unit was built out of visually contradictory information, the push and pull of back and forth in space. Gradients of tone were added to provide more spatial ambiguity. This unit was then translated to build a tiling that had even more spatial ambiguity.

Raedschelders, Peter #1 - Peace

15cm x 15 cm

2000

The tile is 15 x15 cm. It was created starting from a square. The 8 orientations of the square are used. But for making the tile you only need the tile and his mirror-images. It is possible to make a tiling with the 8 different orientations. It is like a Sudoku: on each row and each columns each orientation occurs only once!! It is a semi-magical square!

Raedschelders, Peter #2 - Space

Edges of triangle +/- 15cm

1996

The tile is +/- 15 cm. The tile is a equilateral triangle with a lot of straight lines on it. It look quite simple.

But if you tile the plane with it, you see infinity, circles, perhaps some kind of visualization of a higher dimension.

(Of course you need several types of tiles if you also want the “animals”, due to the deadline of the competition I did not found the time to remake the tiling without animals)

Sarhangi, Reza #1

Each side 6”. Tessellation: 16”X20” - 2008

The tessellation in this artwork is based on two different tiles. Except for the corners with constant color, the two compound triangle tiles (modules) are in a positive-negative color relationship with respect to each other. Using these two tiles in a rotational fashion, results in the pattern in the tessellation. The “Modularity” concept has been presented in an article by Reza Sarhangi, Modules and Modularity in Mosaic Patterns, the Journal of the Symmetrion (Symmetry: Culture and Science), Volume 19, Numbers 2-3, 2008. Another article in this regard would be Sarhangi, R., S. Jablan, and R. Sazdanovic, Modularity in Medieval Persian Mosaics: Textual, Empirical, Analytical, and Theoretical Considerations, 2004 Bridges Proceedings.

Sarhangi, Reza #2

Each side 6”. Tessellation: 16”X20” - 2008

The tessellation in this artwork is based on only one compound tile (module). However, using different colors on the corners of the tiles and erasing lines on some tiles will create an opportunity for the tile maker to make more interesting patterns.

Saxon-Szász, János

Galaxy Tiles

Séquin, Carlo H. #1 - “Celtic Rainbows”

8” x 8” - May 2010

Rainbows form attractive, luminous patterns, whether they occur in the sky or on a light table in the laboratory. Here crisscrossing rainbow bands have been interwoven to form Celtic knot patterns. The challenge was to create only one asymmetrical tile that could be connected in arbitrary ways with itself, always leading to a seamless fit around its border, while overall creating many different irregular, but pleasing tiling patterns.

Séquin, Carlo H. #2 - “Poincaré Undulations”

8” x 8” - May 2010

The tile geometry is based on the Poincaré disk for the regular hyperbolic {4,6} tiling. The geometry in the region between the two quarter disks has been obtained by a conformal distortion of the basic hyperbolic tiling pattern. There is only one tile type, but it comes in two different complementary colorings. This allows one to form ever new undulating patterns. It also raises the puzzling question, which color is the foreground and which one is the background?

Séquin, Carlo H. #3 - “Impossible Tangles”

9″ diameter - May 2010

This work was inspired by many artists, but especially by M.C. Escher, Oscar Reutersvärd, and Tamas Farkas. Inside the one hexagonal tile, I kept the parallel projection of the pseudo-3D corners consistent. Thus half of all the possible ways of joining two abutting tiles will maintain that consistent orientation in space globally. However, if some of the tiles are rotated by an odd multiple of 60 degrees, a Necker-cube like inversion is forced onto the viewer’s perspective when the gaze travels from one tile to the next.

Séquin, Carlo H. #4 - “Green Earth”

8″x 8″-
May 2010

A collection of these tiles form a depiction of a luscious green jungle in the style of Henri Rousseau, celebrating a healthy green Earth. Again, I tried to use only a single tile to create a jungle scene as varied as possible; thus asymmetry and irregularity were important attributes. After some experimentation, I found a structure that keeps the snake body as well as the vines seamlessly connected across tile boundaries, and which creates many different leaf bundles by connection half-bundles across the tile boundaries. With this one tile, jungle scenes of arbitrary sizes can be composed.

Stewart, Sean R. #1 - heterotic string theory no 12

size 6"x4" - March 2010

Created using mandelbrot fractal mapping of a photograph of graffiti, then (using polar coordinate mapping) bending the image.

The fractal portion is used mainly to simplify the photograph and mathematically select the colour palate.

Stewart, Sean R. #2 - incongruent paths no 1

size 6"x4" - March 2010

Created using mandelbrot fractal mapping of a photograph of graffiti, then (using polar coordinate mapping) bending the image.

The fractal portion is used mainly to simplify the photograph and mathematically select the colour palate.

Stewart, Sean R. #3 - incongruent paths no 2

size 6"x4" - March 2010

Created using mandelbrot fractal mapping of a photograph of graffiti, then (using polar coordinate mapping) bending the image.

The fractal portion is used mainly to simplify the photograph and mathematically select the colour palate.

Szuhay, Márton #1

Szuhay, Márton #2

Szuhay, Márton #3

Szuhay, Márton #4

Szuhay, Márton #5