| Most viewed |
Mountains in Spring3487 viewsComputers make it possible for me to "see" the beauty of mathematics. The artworks in the gallery of "Mathscapes" were 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.
--- Anne M. Burns
|
|
Circle Picture 103251 viewsComputers make it possible for me to "see" the beauty of mathematics. This image and all of the Circle Pictures are made by iterating systems of Mobius Transformations.
--- Anne M. Burns
|
|
Circle Picture 53227 viewsComputers make it possible for me to "see" the beauty of mathematics. This image and all of the Circle Pictures are made by iterating systems of Mobius Transformations.
--- Anne M. Burns
|
|
"Hilbert Cube 512"3182 views"Hilbert Cube" is a space-filling recursive curve in 3 dimensions in analogy to the famous Hilbert curve in the plane. Special care has been taken never to place more than 3 coplanar line segments in sequence. At the largest recursion step the geometry has been slightly altered so as to obtain a closed loop. In the proper parallel projection one can see that the 2 halves of this sculpture are connected by only 2 tube segments. This piece of art gives me the association of an abstract, constructivist model of the human brain. See more views of the
"Hilbert Cube 512". --- Carlo Sequin
|
|
Five Intersecting Tetrahedra2848 viewsThis is a version of the Ow-Hull "Five Intersecting Tetrahedra." The visually stunning object should be a familiar sight to those who frequent the landscapes of M.C. Escher or like to thumb through geometry textbooks. Read about the object and how it is constructed on the Origami Gallery.
--- Thomas Hull. Photograph by Nancy Rose Marshall.
|
|
Nested Hexogonal Collapse2563 viewsThis model is a series of concentric hexagons with "zig-zag" creases coming from the center-most hexagon out to the midpoints of the paper's sides. It can be collapsed in many different ways and twisted into interesting shapes, as done here. See more geometrics and tesselations on the Origami Gallery.
--- Thomas Hull. Photograph by Nancy Rose Marshall.
|
|
Spiked Rhombic Enneacontahedron2518 viewsThis structure was conceived by taking a 90-sided polyhedron, whose faces are made from two types of rhombi, and placing a pyramid on each face. The construction uses 180 small squares of paper, all folded and interlocked together without glue. See more models on the Origami Gallery.
--- Thomas Hull. Photograph by Nancy Rose Marshall.
|
|
"Poincare FishDish," by Carlo Sequin, University of California, Berkeley2369 viewsA tiling with regular heptagons does not fit into the Euclidean plane, since 3 times the dihedral angle of the heptagon exceeds 360 degrees. But if we are willing to introduce a progressive scale factor, then the whole hyperbolic plane can be fit into the Poincaré disc. Here is a visualization of a {7,3} tessellation where 3 heptagons join at every vertex, using a tiling motif inspired by the famous Dutch artist M.C. Escher. Each heptagon is cut into 7 identical pizza slices with irregular boundaries in the shape of fish that properly interlock with one another. See more tiling patterns on the Poincare disc. --- Carlo Sequin
|
|
"Fractal Effervescence," by David April2297 viewsThis 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.
|
|
"Lizard Tetrus," by Carlo Sequin and Pushkar Joshi, University of California, Berkeley2269 views24 Lizard tiles, inspired by one of the many planar tilings by M.C. Escher, are mapped around a rounded tetrahedral frame of genus 3. This tiling is a contorted version of the pattern of 24 heptagons displayed on the surface of the marble sculpture "Eight-fold Way" by Helaman Ferguson. That sculpture celebrates Felix Kelin's famous "Quartic Curve" which achieves the maximal symmetry of 168 automorphisms possible on a genus-3 surface. Read more about patterns on the Tetrus surface.. --- Carlo Sequin
|
|
"Different Strokes," by Linda Allison2176 viewsThis 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.
|
|
"And how is your husband Mrs. Escher?" by Nada Kringels2044 viewsNada (Brigitte) Kringels is a German expatriate who has been living in Spain for 14 years, where she learned to use Ultra Fractal. This image consists of 25 layers using basically two algorithms designed by Kerry Mitchell, "Gaussian Integer" for the background and "Rose Range Lite" for the top layers. During the composition phase of the image, Nada Kringels discovered various shapes that immediately resembled some of the work of M.C. Escher, so she decided to introduce geometric impossibilities into the design. To finish the background, in marked feminine character according to the author, she began to imagine that it had been made by Mrs. Escher. Fascinated with this possibility, Nada Kringels began to consider in her image the idea of Mrs. Escher as an artist, without even knowing if this Mrs. Escher existed—in fact she did, Jetta Umiker, with whom Maurits Cornelius Escher had three children. Ah, by the way, how is your husband, Mrs. Escher?
|
|
"Bonhomme de Neige (Snowman)," by Sylvie Gallet2022 viewsSylvie 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.
|
|
Kleinian Pearls1993 viewsPeople have long been fascinated with repeated patterns that display a rich collection of symmetries. The discovery of hyperbolic geometries in the nineteenth century revealed a far greater wealth of patterns, some popularized by Dutch artist M. C. Escher in his Circle Limit series of works.
This cover illustration portrays a pattern which is symmetric under a group generated by two Möbius transformations. These are not distance-preserving, but they do preserve angles between curves and they map circles to circles. The image accompanies "Double Cusp Group," by David J. Wright (Notices of the American Mathematical Society, December 2004, p. 1322).
|
|
"Knot divided" (snow sculpture), by Carlo Sequin (University of California, Bekeley), Stan Wagon (Team Captain), John Sullivan, Dan Schwalbe, and Rich Seeley1909 viewsCan a DIVIDED KNOT be NOT DIVIDED? When carving this sculpture out of a 10x10x12 foot block of hard compacted snow, we started with the simplest possible knot: the overhand knot, also known as the trefoil knot. We then split lengthwise the whole ribbon forming the three big loops. But there is a twist that may lead to surprises: The original knotted strand was actually a triply twisted Moebius band! Thus the question: Does our cut separate the structure into two pieces, or does it form a single, highly knotted twisted strand? Read more about this snow sculpture. --- Carlo Sequin
|
|
|
|
