|
 The connection between mathematics and
art goes back thousands of years. Mathematics has been
used in the design of Gothic cathedrals, Rose windows,
oriental rugs, mosaics and tilings. Geometric forms were
fundamental to the cubists and many abstract expressionists,
and award-winning sculptors have used topology as the
basis for their pieces. Dutch artist M.C. Escher represented
infinity, Möbius bands, tessellations, deformations,
reflections, Platonic solids, spirals, symmetry, and
the hyperbolic plane in his works.
Mathematicians and artists continue to
create stunning works in all media and to explore the
visualization of mathematics--origami, computer-generated
landscapes, tesselations, fractals, anamorphic art, and
more.
Jump to one of the galleries
|
|
| Last additions |
"Fractal Scene II," by Anne M. Burns (Long Island University, Brookville, NY)"Mathscapes" are created using a variety of mathematical formulas. The clouds and plant life are generated using fractal methods. The mountains are created using trigonometric sums with randomly generated coefficients; then, using 3-D transformation, they are projected onto the computer screen. Value and color are functions of the dot product of the normal to the surface with a specified light vector. See the Gallery of "Mathscapes and find citations for my articles on modeling trees, plants and mountains, and on "blending and dithering," at http://myweb.cwpost.liu.edu/aburns/gallery/gallery.htm. --- Anne M. Burns (Long Island University, Brookville, NY)Jun 01, 2007
|
|
"Eights," by George W. Hart (www.georgehart.com)This six-inch diameter paper sculpture is made of sixty identically shaped parts. Parts of any one color form a type of tetrahedron, and there are five such, deeply interlocked. No glue is used; they parts just hook into each other. I call this type of design "modular kirigami". It took me about four hours to assemble after several hours of false starts and figuring out how to do it. I generated a computer-rendered view down a five-fold axis. The "8"-shaped parts each link with many others. So they could not be made as single pieces of paper unless they were glued or taped together after being linked. But I wanted to be a purist and use no glue or tape, so I designed the parts as two overlapping "3"-shaped pieces.
--- George W. Hart (www.georgehart.com)May 17, 2007
|
|
"Star Corona," by George W. Hart (www.georgehart.com)This 8-inch, diameter, one-of-a-kind, acrylic sculpture consists of an inner red star surrounded by a yellow corona. It is designed to hang and the two components do not touch each other. The star has twelve large 5-sided spikes and twenty smaller 3-sided spikes, all assembled from sixty identical angular components. The corona is assembled from twenty identical curved components, which give the effect of swirling motion. If you look straight down on a spike, you see that arms from five of the yellow parts combine to make a circle around the spike. Both components are based on stellations of the icosahedron. The outer corona is based on the first stellation and the inner star shape is based on number 53 in the list by Coxeter et al. To understand it well, make a paper model from the instructions on my website.
--- George W. Hart (www.georgehart.com)May 17, 2007
|
|
"The Susurrus of the Sea," by George W. Hart (www.georgehart.com)Soft waves, suggestive of both sky and water, travel around the globe along six different criss-crossing equators. The susurrus (murmur) of the sea is suggested as a sense of harmony in this sphere. Technically difficult, the 60 transparent blue acrylic plastic components had to be made very precisely to fit together. Heat-formed, the components were formed and assembled on special jigs which imparted the proper dimensions and angles. Mathematically, the blue spirals are helixes that follow the edges of an icosidodecahedron. This is a polyhedron that was known to the ancient Greeks, but the oldest known drawing of it is by Leonardo da Vinci. Formally constructed of triangles and pentagons (which show up here as the openings) it can also be seen as an arrangement of six equatorial regular decagons. Each equator makes ten twists in a complete path, crossing the other five equators at two opposite points. If one "walks along" a dark blue edge, making right-angle turns where edges meet, one traces a large five-pointed star before returning to one’s starting point.
--- George W. Hart (www.georgehart.com)May 17, 2007
|
|
"Three Link Chain," by Jarke J. van Wijk (Technische Universiteit Eindhoven). Image courtesy of Jarke J. van Wijk.This knot consists of three similar links, and is threefold-symmetric. The surface shown is a Seifert surface, an orientable surface bounded by the links. Considering only the links, it is hard to imagine that such a surface does exist. However, in the 1930's, the German mathematician Herbert Seifert presented an algorithm to find such surfaces for any knot or link. This image was made with a tool called SeifertView.
--- Jarke J. van WijkMar 13, 2007
|
|
"Borromean Rings," by Jarke J. van Wijk (Technische Universiteit Eindhoven). Image courtesy of Jarke J. van Wijk.The Borromean Rings consist of three links. Take one link away and the other links fall apart, but together they are inseparable. Because of this, they are popular as a symbol for strength in unity. Here they are shown from an unusual point of view, and also a Seifert surface is shown. This is an orientable surface, bounded by the links. This image was made with a tool called SeifertView.
--- Jarke J. van WijkMar 13, 2007
|
|
"(1,3,5) Pretzel Knot," by Jarke J. van Wijk (Technische Universiteit Eindhoven). Image courtesy of Jarke J. van Wijk.The yellow tube is a (1, 3, 5) pretzel knot. Such a pretzel knot or link consists of a sequence of angles, where each tangle has a number of twists. The brown surface is a Seifert surface: an orientable surface bounded by the knot. Here the surface is easy to understand; for arbitrary knots such surfaces often have strange and difficult shapes. However, for any knot or link such surfaces can be found, as shown by Herbert Seifert in the 1930's. This image was made with a tool called SeifertView.
--- Jarke J. van WijkMar 13, 2007
|
|
"Bonhomme de Neige (Snowman)," by Sylvie GalletSylvie Gallet is a mathematics professor at a secondary school near Paris. With 20 years of experience in writing fractal formulas and algorithms, she is an expert in the handling of color gradients. In fact, Sylvie avoids complex and postprocessed images, in preference to designs with little elaboration, whose value resides in the intelligent and creative use of color. "Bonhomme de Neige" is a good example of Sylvie's art. It is a conceptually simple image, but the careful use of color transports us immediately to an image of Christmas and winter countryside. Few fractal artists are capable of transmitting such direct visions and sensations.Mar 07, 2007
|
|
"Encore," by Paul DecellePaul DeCelle is a mechanical engineer in Michigan (USA). His image for this exhibition is a very handsome composition based on a portion of the Mandelbrot set (magnified approximately 10 to the 13th times). The artist has used techniques known for more than 10 years, but can still surprise the viewer by its majesty, especially in large-scale reproductions. If we imagine the Mandelbrot set as an extensive mountain range, the composition relies on two basic principles. The "Slope" algorithm assigns the same color to those regions with the same height, like in a topographical map. The "Lighting" algorithm colors towards white those regions of the surface illuminated by an imaginary sun sitting on the horizon, while the shadows partially obscure the surface. The result is a three-dimensional effect that enriches and enhances the detail in the original fractal.Mar 07, 2007
|
|
"Ebony and Ivory," by Bill BeathBill Beath is an Australian photographer specializing in depicting nature, the countryside and architecture. His photographic work combines raditional film processes with the most modern digital techniques. His first contact with fractals was a photograph of a Nautilus shell, which led to the Fibonacci sequence, which led to his discovery of fractals and fractal art. Since then, Bill Beath has been permanently immersed in fractal art, as much as an art form as an integral part of his photographic work. For that reason this image is based on the "Fibonacci Julia" algorithm, developed by Kerry Mitchell. It shows a fascinating shape somewhere between a natural design and an exquisite man-made design. The name of the image, "Ebony and Ivory," refers to the palette used, based on elegant tones of black and white.Mar 07, 2007
|
|
"Fractal Effervescence," by David AprilThis image comes from the fusion of the three separate image files generated with the software Apophysis, designed by Mark Townsend. Each one of the files contains different types of transformations-linear, polar, and spherical-that produce a curious dialog between the vertical lines, the sinuous curves with the appearance of smoke, and the bubbling circular shapes. In this type of fractal there is only one method of coloring. Sometimes a tiny change to the color gradient can distort the image dramatically. Fractal artists, hunting for treasure, can tease out unexplored forms, but a slight difference in this or that parameter can make them pass by that secret treasure without seeing its hidden beauty. David April lives in Illinois (USA). His interest in fractals is relatively recent, but he compensates for that with an enormous enthusiasm and fascination for finding new forms.Mar 07, 2007
|
|
"Different Strokes," by Linda AllisonThis image, like most of those selected for this exhibition, is generated with Ultra Fractal, designed by Frederik Slijkerman. "Different Strokes" consists of 10 layers, using Julia and Mandelbrot fractal formulas with other formulas and algorithms for coloring. The layers are merged into a unique image using different techniques and transparencies for each layer in the composition. The author, Linda Allison, is a disabled housewife living in Florida. Since 1994, Linda has dedicated part of her free time to designing fractal images. Having no formal mathematical training, Linda possesses an incredible ability to represent the concept of infinity in images with smooth and delicate color palettes. Her shapes blend and separate in absolute harmony, with balanced framing that combines the classicism of the first fractals with the latest advances of fractal art.Mar 07, 2007
|
|
"Polished," by Heather LambHeather Lamb was born and lives in Scotland. From an early age she has developed a strong interest for mathematics that strengthened by her studies at the Open University, where she became familiar with fractal geometry and the Mandelbrot set. A strong association exists between nature and fractal geometry and Heather Lamb exploits this, creating images that evoke the real world while at the same time transforming mathematics into something that can be understood and visualized. For this image she was inspired by her childhood experiences with polished stones, in which the true beauty of their colors is only discovered during the process of polishing. The colors were chosen to reproduce the appearance of stone, but also to be harmonious with each other and produce a balanced image. Masks with black and white gradients were used to precisely place the shadows and lights and provide a realistic sensation of polish and a tangible, three-dimensional effect that accentuates the image.Mar 07, 2007
|
|
"Mateko," by Dan KuzmenkaDan Kuzmenka is a North American researcher in the field of chemistry. Like many other scientists, Dan discovered fractal geometry in 1985 reading an article in the magazine Scientific American, although it wasn’t until 1999 that he began to create his first fractal images. Mateko is a word invented by its author, who maintains a personal challenge to find new ways of expressing spirals—the most important fractal icon—without showing the same shape time and time again. For this image he experimented with different color palettes and ways to combine them before the colors we now see appeared; these colors are unusual for Dan Kuzmenka, who usually uses warmer colors and earth tones.Mar 07, 2007
|
|
"Grey Moon Rising," by Klaus-Peter KubikMany fractal formulas and algorithms produce conventional geometric figures with certain parameters. For example, the Julia set iterated using the origin as its parameter produces a circle. The style of Klaus-Peter Kubik is focused on producing conventional geometric figures using fractal techniques. He likes to explore the combinations of the simple figures of circles and squares with attractive shapes for the viewer. He also exploits the possibilities of fractal geometry to create textures. The rough, grey texture of the circle symbolizes the surface of the moon while the vertical and horizontal lines, similar to those made with a pencil, emphasize the geometric structure of the image. Klaus-Peter Kubik works for the German government in the public health field and has participated in nearly a dozen exhibitions since 1994.Mar 07, 2007
|
|
| 435 files on 29 page(s) |
 |
|
|
|
25 | |
|
|
|
|
