## Mathematical artMathematical artAbout mathematics in art. Photos of mathematical sculptures. Artworks of Escher's followers ## ArticlesWood work by Hans de Koning2008-03-20 17:51:00Today I received a postage with wood work by Hans de Koning (see above). The shapes of the most of his works are based on impossible figures. His works are flat, but he uses different kinds of wood to make three-dimensional effect. Wood planks with different hues imitate sides slope and opacity of the impossible figure. You can see more his work in his Picasa album and at the site Impossible More About: Work
Fractal trees2008-03-01 18:11:00Some time ago we have talked about Pythagoras tree, which represents simple fractal structure consisting of squares. Also, there are many variations of fractal trees, which are consist of lines and curves. The three-dimensional fractal tree above is constructed from lines. It belongs to L-system class of fractals. Associated as trunk and branches brown lines of the tree are elements of low More About: Trees
, Fractal
Hilbert curve2008-02-18 17:44:00Hilbert curve is a continuous fractal space filling curve, which was first described by German mathematician David Hilbert in 1891. Below you can see 5 first steps of the plane Hilbert curve. But the Hilbert curve looks more interesting if it represent in three dimensions. Carlo H. Séquin, a professor of Berkley, created a small 5" metal sculpture of Hilbert curve, which he called "Hilbert 512" More About: Curve
Jos de Mey has died2007-12-23 08:43:00With deep regret I should report that in December 22th 2007 the great man and the famous Belgian artist Jos de Mey has died. He was one of the most famous artists in imp-art. His name have always been referred along with another Holland artist M.C. Escher. Jos de Mey was the unique artist, who could organic combine detailed photo realistic Flemish landscapes with complex impossible More About: Died
Escher's creature2007-12-15 19:03:00This series of photos by Hawken King was inspired by creatures from Escher's artworks "House of stairs" and "Curl up". A small strange creature should curl to move forward.Below you can see the original Escher's image "Curl up", where moving of this created is shown in four steps. More About: Creature
Celtic Möbius strip by Paul Bielaczyc2007-12-09 20:26:00Celtic Möbiusby Paul BielaczycColored Pencil and Ink, 21" x 13". In this image by Paul Bielaczyc we see joining of aspects of artist's life. As he says Celtic knots surround him in his job, M.C. Escher who has always bee inspiring in his art and the Möbius strip as intriguing mathematical form. More About: Strip
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Tessellations by Daniel Wyllie2007-11-15 17:09:00Daniel Wyllie creates wonderful tessellations, which got First prize in Tess Contest 2006 and Grand prize in Tess Contest 2007. His tesselations are designed in classic Escher style with animals, faces a other artistic figures as main characters. Grand prize in Tess Contest 2007 CoworkersLast Laugh Mad dog First prize in Tess Contest 2006 Faces In a FlowerStork And Cougar More About: Daniel
Kaleidocycles2007-11-09 18:27:00Kaleidocycle consists of at least 6 tetrahedrons joined into chain, which head connected to it's tail. In the case of at least 8 tetrahedra it has the interesting property that it can be turned through its center in a continuous motion. In the book "M.C.Escher kaleidocycles" (1977) the mathematician Doris Schattschneider and the graphic designer Wallace Walker showed how to cover kaleidocycles Tesselation World of Makoto Nakamura2007-10-08 18:46:00Who said that there's no masters of tessellation art after Escher? Just look on artworks by Japanese artist Makoto Nakamura. Pay attention to areas of the image, which are filled with identical figures that show dolphins, sea gulls, flying fishes and other figures. Put together all these figures constitute complete image, which looks as a single whole and don't fall to pieces. Like in Escher's " More About: World
Staircase knot2007-09-27 18:09:00This strange composition of staircase reminds Möbius strip, but unlike Möbius strip this figure has two sides. So someone, who will try to rise this stairs, will continue rising infinitely returning to the starting point. The sculpture also reminds one of the famous Escher's images "Knot s". One of the them you can see below. This knot is also not a Möbius strip, because it has four sides. Escher's building in origami2007-07-19 17:11:00Some people redraw Escher 's artworks with computer, the others create woodcarvings based on Escher's lithographs, but Ingrid Siliakus crates Escher's buildings using paper. I don't know how this kind of art can be called. I think it's a branch of origami. UPDATE (thanks to lispnik):This kind of art is called kirigami that is variation of origami, where the artist is allowed to make small cuts in the paper. Below you can see some Escher-like kirigami works with respective originals.BalconyRelativityConvex and concaveThese images are close to originals by M.C. Escher. More such style origami constructions can be seen here http://haha.nu/amazing/unique-paper-cut-a rtworks/ More About: Building
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Triangle vortex2007-06-19 17:04:00A nice rendering of triangle vortex was found at forum WooYah, which was created by member Heidi. This image is interesting by shapes of triangles, which look like Penrose tribar, but they are not. If looking attentively we see that these triangles are more distorted than classic Penrose triangle. So these figures cannot be named 'impossible' because they don't make sense possible figure. It sounds paradoxically, but all impossible figures makes sense common possible object at first glance.Below you can see another rendering with the same kind of triangle. More About: Vortex
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Trigonometric art By Fergus Ray Murray2007-06-07 17:58:00Created by Fergus Ray Murray images above are not fractals. They show us beauty of trigonometry. Every such image consists of set of sine and cosine curves, which makes complex wave frozen in still image.You can see more trigonometric images and wonderful mathematical animations at the Fergus's website. Escher spheres2007-05-26 16:15:00Some Escher 's tessellated images can be adopted to spherical surface. First of all it is concerned to his lithographs which show hyperbolic space such as "Angels and Devils", "Circle limit IV" etc. Above left is the original lithograph "Angels and Devils" and above right is the wooden spherical interpretation of it.There's regular way to transformation hyperbolic geometry to spherical geometry. You can read it here http://plus.maths.org/issue18/xfile/.Othe r Escher's tessellations also can be applied to sphere. You can see some examples below.The last three images were found here. More About: Spheres
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New artwork by Jos de Mey2007-05-05 08:29:00Yesterday, I received a pack with artworks by Jos de Mey. Above you can see the latest artwork by him. As usual, there's impossible figure on his artwork. He is my favorite artist in the field of impossible art. More About: Artwork
Black cube by Gregor Schneider2007-04-22 08:30:00German sculptor Greg or Schneider was fascinated by artwork "Black square", which was created by famous russian artist Kasismir Malevich, and he decided to create an analogue of it as sculpture.Firstly, he tried to represent 15-metres high black cube in 2005 and was erected in Venice at International Art Exhibition - La Biennalle de Venezia. It was named "Cube Venice 2005". But his application was rejected by Venice authority for politic reasons because they were afraid to offend muslims who could consider it as recostruction of the holiest place of Islam - Kaaba, which is at the center of the Great Mosque in Mecca.In 2006 Gregor Schneider with his cube was invited to exhibition in Berlin Museum of Modern Art. He renaimed it to "Cube Berlin 2006". But his participation in the exhibition was rejected again at the last moment by the general director of Berlin public museums.Nadeem Elyas, the president of the central Muslim coulcil in Germany, advocated the cube, and finally, 14-metres ... More About: Lack
Rapid prototyping sculptures2007-04-15 16:48:00George Hart is active using rapid prototyping (RP) technology for modeling sculptures. Rapid Prot otyping or Solid Freeform Fabrication refers to a range of new technologies which construct physical three-dimensional objects by assembling thin layers of material under computer control. Objects can be made which are extremely accurate, complex, and beautiful, and which no other technology can produce.The image left shows he and his model of Sierpinski triangle.He also interested in four-dimensional geometry. From a 4D object, one can calculate 3D "shadows" which are often beautiful but very complex objects.The image below shows a 4D structure made of 120 regular dodecahedra. This "shadow" of it has the form of one large dodecahedron filled in with 119 smaller dodecahedra. In 4D all the dodecahedra are regular, but in this 3D shadow, angles are necessarily distorted, so only the innermost and outermost dodecahedra appear regular.Even more beautiful and intricate is the truncat... More About: Sculptures
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Structures by Rinus Roelofs2007-04-02 18:04:00Holland artist and mathematician Rinus Roelofs constructs charming mathematical structures. He constructs his structures in computer but some of them became sculptures in various Holland towns.The sculpture above was erected in Borne (Holland) in 2005. It consists of 26 tetrahedrons or 104 triangles. Triangles are just slid together. Construction is stable and need no further fixing.Bet he created a lot more computer models of three-dimensional structures. One of them (below) shows Hamiltonean path of polyhedron. Hamiltonean path is a sequence of edges that visits all vertexes of a polyhedron exactly once.Besides three-dimensional structure Rinus Roelofs created a set of two-dimensional tessellation structures for Escher Centennial Congress in Rome in 1998. They represents regular structures that constitute infinite impossible figures. He insists not to call them tessellations but joins. More About: Structures
Anamorphic art2007-03-25 17:29:00The word anamorphic is from the Greek "ana" (again) and "morphe" (form). It refers to images that are so heavily distorted that they are hard to recognize without the use of a mirror, sometimes referred to as an anamorphoscope. When viewed in the anamorphoscope, the image is "formed again", so that it becomes recognizable.Anamorphic art as known from middle ages. European painters of the early Renaissance were fascinated by linear anamorphic images, in which stretched pictures are formed again when viewed on a slant. A famous example is Hans Holbein's "The Ambassadors" (1533), which contains a stretched-out skull.Nowadays anamoprhic art is rised again because of works of such famous artists as István Orosz, Kelly M. Houle, Julian Beever and Felice Varini.Hungarian artist István Orosz is well known for his artworks with impossible figures and constructions. He also tries to renew anamorphosis art. Frequently he uses etching tecnique for his artworks. Below you can see two views of... More About: Morph
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Platonic solids with Escher's mosaics2007-03-24 07:46:00With Escher 's mosaics we can cover not only flat plane but also surfaces of platonic solids. Some Escher's tessellations can be divided into simple shapes such as triangle and square. Using these simple shapes we can cover facets of polyhedrons. Below, you can see several examples of covering of Plato nic solids with Escher's mosaics.These images was found at http://www.math-inf.uni-greifswald.de/mat hematik+kunst/polyeder.html More About: Toni
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Visage of War2007-03-19 18:36:00In 1940 Salvador Dalí created his painting Visage of War where eyes and mouth each contain a face, whose eyes and mouth each contain a face and so on. Painting this artwork Dalí thought about Spanish Civil War, and eyes are filled with infinite death. Perhaps Dali decided the infinite horrors of war were better depicted in a bounded canvas through self-similarity, though most certainly he had not been exposed to this as a mathematical concept. Analogous fractal of order four can be viewed to the right.Interestingly, a preliminary study (below) of this picture had a face within only one face within the mouth of the largest face. Sculpture of Sierpiski triangle2007-03-15 19:01:00This giant sculpture represents three-dimensional version of fractal named Sierpinski triangle. This large tetrahedron that consists of 1024 smaller tetrahedrons was created by students of Alan A. Lewis School. Order of fractal is 6. More About: Sculpture
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Pythagoras tree2007-03-09 10:24:00The Pythagoras tree is a plane fractal constructed from squares. It's named after Pythagoras because each triple touching squares encloses right triangle, traditionally used to depict Pythagorean theorem. If triangles of the tree have equal sides, the Pythagorean tree is symmetric, as you can see above, otherwise the tree is asymmetric. The illustration above shows eight iterations of tree construction progress.Below it's shown asymmetric Pythagoras tree. The shape of the tree can be used for creation of infinite impossible figure. Some parts of the fractal can be replaced to impossible triangles or squares. Illustrations below show symmetrical and asymmetrical impossible fractal tree. Flemish artist Jos de Mey created many artworks with Pythagoras tree as main motif. Below you can see his artworks.Three dimensional effect can be applied to the Pythagoras tree. Illustrations below by Koos Verhoeff shows trees with applied various parameters.Below you can bronse sculpture of Pythag... More About: Tree
Pre-fractal islamic art2007-03-04 10:50:00Representations of fractals appear in human art of the Religious and Spiritual varieties. Above left you can see an Ottoman illustration of sacrifice of Ishmael dated to 1583. Above right you can a Mandelbrot fractal image with very similar shape and proportions. More About: Islamic
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Corpus Hypercubus2007-03-01 10:12:00Crucifixion (Corpus Hyper cubus)Salvador Dalí (1954)Salvador Dalí, the master of surrealism, had a keen interest in natural science and mathematics. He was fascinated by hypercube, and it is featured in the painting Crucifixion (Corpus Hypercubus). Here Christ is crucified on figure of unfolded hypercube.Hypercube is four-dimensional analogy of three-dimensional cube. It comes in by shifting three-dimensional cube perpendicular to three axis of our space. It consists of eight cubes. Frequently it depicted in it's frontal view as you can see in the image right. As cube can be unfolded into flat figure of six squares, hypercube can be unfolded into three-dimensional construction of eight cubes. This construction we see at Dalí's artworks, in particular. Snow sculptures from Breckenridge2007-02-27 10:02:00Lately, we published snow sculpture by Bathsheba Grossman which was represented at Breckenridge snow sculpture contest. Here some other mathematical snow sculptures represented at Breckenridge in other years. Knot divided (2005) This is a triply twisted Moebius band. There is a self-referential beauty in our sculpture: If one forms a Moebius band by twisting a belt through three half-turns (instead of just one), then the band's edge forms a trefoil knot. Whirled White Web (2003) This sculpture is a 3-fold symmetrical whirl of twisted and stretched saddle shapes. Such saddles occur naturally in soap films that are spanning warped wire frames; such "minimal surfaces" are nature's way of creating strength in delicate structures. Our sculpture uses these natural ideas to create an intricate network of ribs and internal spaces suspended from a web of three mutually interwoven double loops. Turning a Snow ball Inside Out (2004) In the 1960s, mathematicians showed how to turn a sphere... More About: Sculptures
Graffiti in Barcelona2007-02-26 10:08:00Graffiti in Barcelona Rosa y DanyIn this wonderful illustration we see the same artistic effect which Escher used in his lithograph "Reptiles" where reptiles go from tessellated surface of table into three-dimensional environment, crawl by things on the table and returns into tessellated surface. Unlike, Escher's artwork here reptiles appears from mosaic. More About: Graffiti
Fractals in nature2007-02-21 09:29:00Fractals are not only mathematical abstraction, which can be used for creation of abstract or realistic images (see images by Keith Mackay). They can be found in our world in various plants, shells etc. Below you can see several examples of fractals in nature.The most known fractal is fern leaf. Every little leaf of fern repeats whole large leaf.Another interesting nature fractal is romanesco cauliflower, which is a cross between broccoli and Cauliflower, which accentuates the great fractal spiral patterns on the top.In cactus below leafs become twisted towards the center.Fractals also exists in micro world. Viruses, mould and bacterial aggregate colonies spontaneously assume fractal shapes.The best known fractal representation among animals is nautilus shell.Lightning Strikes and Electrical Discharge creates fractal formations called Lichtenberg figures on rocks, grass,wood or even people!Many symmetrical wonderful fractal shapes can be found in snowflakes.This post was created by... More About: Nature
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Temperal paradox2007-02-20 10:34:00Temperal Paradox Patrick's PicksAfter mystery of blank spot in Escher's lithograph "Print Gallery" was revealed many derived images have appeared. Very often these images are created from real photos as it was done in Stanford University with photo of Hendrik Lenstra who revealed the mystery.The image above was created by Patricks Picks from photo of clock face. He also created many other similar images. You can see them in his profile on Flickr or in Escher's Droste Print Gallery pool. More About: Rado
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Dog Dream2007-02-19 10:30:00Dog Dream In this artwork created by Kaz Maslanka we can see artistic representation of fractal like Koch snowflake. The inscription at the top is in Korean: Dog Dream = Irrationality / Importance More articles from this author:1, 2 |