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Math ImageryThe 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.

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Home > Anne M. Burns :: Gallery of "Mathscapes"

Last additions - Anne M. Burns :: Gallery of "Mathscapes"
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"Circle D," by Anne M. Burns, Long Island University, Brookville, NYThe Unit Circle Group is a subgroup of the group of Mobius Transformations. Read about how this and other circle images are created and view more examples at http://www.anneburns.net/circles/unitcircle.html. --- Anne M. BurnsJul 23, 2010
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"June wreath," by Anne M. Burns, Long Island University, Brookville, NYThis circle image is made by iterating systems of Mobius Transformations. Read about how this and other circle images are created and view more examples at http://www.anneburns.net/circles/unitcircle.html. --- Anne M. BurnsJul 23, 2010
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"Kaleidoscope," by Anne M. Burns, Long Island University, Brookville, NYThis circle image is made by iterating systems of Mobius Transformations. Read about how this and other circle images are created and view more examples at http://www.anneburns.net/circles/unitcircle.html. --- Anne M. BurnsJul 23, 2010
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"Tile 7," by Anne M. Burns, Long Island University, Brookville, NYHere is a fractal tiles created with Geometer's Sketchpad. I start with a single "tile" designed using Geometer's Sketchpad. Then, using Flash Actionscript I place that "tile" in the center of the screen and surround it with 12 copies of the tile that are half the size of the original, then surround those with 36 "tiles" half the size of the second set of "tiles"; the process is continued until the tiles are too small to see. Thus we obtain a "fractal" tiling. See more fractal tiles at http://www.anneburns.net/tiles/tiles.html. --- Anne M. BurnsJul 23, 2010
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"Summertime," 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 May 05, 2009
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"Persian Rug (Recursian I)," by Anne M. Burns (Long Island University, Brookville, NY)An applet uses a recursive (repeatedly applied) procedure to make designs that resemble Persian rugs. You may choose 3 parameters a, b and c, and one of 6 color palettes each consisting of 16 colors numbered 0 through 15. The parameter c ( 0 through 15) represents an initial color. A 257 by 257 square is drawn in the color numbered c. Label the 4 corner colors c1, c2, c3 and c4 (at the initial stage they will all be c). then a new color is determined by the formula a + (c1+c2+c3+c4)/b mod 16 and a horizontal and vertical line that divide the original square into 4 new squares are drawn in the new color. The procedure is repeated recursively until all the pixels are filled in. Read more about "Persian" Recursians, enter the parameters and click on Draw rugs, and download a Windows Program that makes "Persian" rugs, at http://myweb.cwpost.liu.edu/aburns/persian/persian.htm. --- Anne M. Burns (Long Island University, Brookville, NY)Jun 01, 2007
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"Fractal Scene I," by Anne M. Burns"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
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"Imaginary Garden," by Anne M. Burns (Long Island University, 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
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"Lilacs--an Imaginary Inflorescence," by Anne M. Burns (Long Island University, Brookville, NY)"Inflorescence" is the arrangement of flowers, or the mode of flowering, on a plant--sometimes simple and easily distinguishable, sometimes very complex. "Lilacs" is an example of an imaginary inflorescence that I have created using computer graphics techniques. Two Java applets allow users to see and draw purely imaginary inflorescences at various stages using the recursive (repeatedly applied) functions. Download the code from either applet, and see photographs of real inflorescences several imaginary inflorescences, at http://myweb.cwpost.liu.edu/aburns/inflores/inflores.htm. --- Anne M. Burns (Long Island University, Brookville, NY)Jun 01, 2007
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"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
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Circle 1Computers 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. Sep 26, 2006
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Circle 3Computers 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. Sep 26, 2006
CIRCLE4.jpg
Circle 4Computers 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. Sep 26, 2006
CIRCLE5.jpg
Circle 5Computers 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. Sep 26, 2006
CIRPIC5.jpg
Circle Picture 5Computers 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
Mar 28, 2006
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