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Home > Anne M. Burns :: Gallery of "Mathscapes"
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Mountains in Spring4363 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
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Circle Picture 53789 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
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Circle Picture 103721 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
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"Fractal Scene II," by Anne M. Burns (Long Island University, Brookville, NY)2047 views"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)
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Circle 51678 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.
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"Lilacs--an Imaginary Inflorescence," by Anne M. Burns (Long Island University, Brookville, NY)1593 views"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)
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Circle 41517 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.
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"Fractal Scene I," by Anne M. Burns1345 views"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)
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"Imaginary Garden," by Anne M. Burns (Long Island University, NY)1261 views"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)
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Circle 11254 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.
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Circle 31241 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.
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"Persian Rug (Recursian I)," by Anne M. Burns (Long Island University, Brookville, NY)1091 viewsAn 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)
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"Tile 7," by Anne M. Burns, Long Island University, Brookville, NY550 viewsHere 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. Burns
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"Summertime," by Anne M. Burns, Long Island University, Brookville, NY543 views"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
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"Circle D," by Anne M. Burns, Long Island University, Brookville, NY392 viewsThe 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. Burns
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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.