| Search results - "ii," |
symmetry3.jpg"Symmetry Energy Image III," by Rob Scharein (Centre for Experimental and Constructive Mathematics, Simon Fraser University, B.C., Canada)
This example illustrates the SE rendering mode in KnotPlot, which visualizes the symmetric energy distribution. KnotPlot is a program to visualize and manipulate mathematical knots in three and four dimensions, and the website includes a wealth of resources and pictures. This picture is a direct screen capture from KnotPlot, rendered entirely in OpenGL, an environment for portable, interactive graphics applications.
--- Rob Scharein
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symmetry2.jpg"Symmetry Energy Image II," by Rob Scharein (Centre for Experimental and Constructive Mathematics, Simon Fraser University, B.C., Canada)
This example illustrates the SE rendering mode in KnotPlot, which visualizes the symmetric energy distribution. KnotPlot is a program to visualize and manipulate mathematical knots in three and four dimensions, and the website includes a wealth of resources and pictures. This picture is a direct screen capture from KnotPlot, rendered entirely in OpenGL, an environment for portable, interactive graphics applications.
--- Rob Scharein
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"Rhombic Triacontahedron III," by Vladimir Bulatov (2007)Metal sculpture, 4.0" diameter. "Stellation of rhombic triacontahedron with 30 identical rhombic faces makes base for this sculpture. All internal intersections of rhombic faces were carefully eliminated by cutting away parts of rhombuses. The resulting 3D body was given organic shape by replacing straight faces with smooth subdivided surface. My artistic passions are purely mathematical images and sculptures, which express a certain vision of forms and shapes, my interpretations of distance, transformations and space. In my opinion, mathematics is not simply a profession, but rather a way of thinking, a way of life." --- Vladimir Bulatov, Independent Artist, Corvallis, OR
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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)
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"Starfruit," by David MakinDavid Makin is a British computer programmer born in North Wales, who loves fractal geometry and science fiction. The majority of his work comes from his investigations into the use of coloring algorithms. In this case he employed three algorithms applied to a Julia set. The first of his algorithms, named "MMF3-Turning Points," generated the starred forms that characterize the image and suggested the title of the shape immediately to him (the starfruit is a tropical fruit whose cross section produces a five-pointed star). With the second algorithm, "MMF3-Orbital Waves," he used the idea of complementing the first layer with the handsome curved lines that accentuate the set. At this point he proceeded to include the third algorithm, "MMF3-Alternative fBm II," which provides a more organic texture. Finally, David Makin took considerable time in combining the three layers with color palettes and the algorithms described that produced the final result.
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"Tribute to Zemela," by Joseph PresleyJoseph Presley has worked with traditional art forms since he was a child, but discovered his favorite form of expression in fractal art, which produces the sensation of painting with the same tools that make nature beautiful. This image was generated by means of a variant of the Barnsley formula, "IFS-Barnsley-JockIII," written by Jock Cooper, and colored basically with the algorithm "fBm Popcorn Traps," written by Mark Townsend. The name of the picture, Tribute to Zemela, refers to an artist friend of the author, Lisa Thallauer, for whom Joseph Presley designed the image, being inspired by an imaginary wooden object.
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