| Search results - "mandelbrot" |
Mandelbrot SetA striking aspect of this image is its self-similarity: Parts of the set look very similar to larger parts of the set, or to the entire set itself. The boundary of the Mandelbrot Set is an example of a fractal, a name derived from the fact that the dimensions of such sets need not be integers like two or three, but can be fractions like 4/3. See more at the 3D-XplorMath Fractal Gallery.
--- Richard Palais (Univ. of California at Irvine, Irvine, CA)
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"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.
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"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.
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"Overwrought," by Damien JonesDamien Jones is a respected artist and fractal expert. His Internet domain fractalus is one of the most complete sources to start with for fractal art. Through years of explorations of the mathematics for aesthetic reasons, Damien’s work has appeared in numerous books, magazines, posters, calendars, and international exhibitions. Born in the United Kingdom, he currently resides in Florida (USA) with his wife Michelle, whom he married while collaborating on the organization of this exhibition. The image "Overwrought" belongs to the Mandelbrot set, although it is difficult to see because of the use of "turbulence," which distorts the calculations before the application of the fractal coloring. After the image is colored, the turbulence is removed and the calculation continues. The process produces a cloudy texture but keeps the underlying shapes unaltered. The coloring—austere, mournful, and at times apocalyptic—often produces an emotional response in the viewer of the art.
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"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.
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"Warm Glow," by Kerry MitchellKerry Mitchell is an aeronautical engineer born in Iowa (USA) who since 1984 has occupied diverse positions related to NASA. At the same time he is a computational artist of great technical resources that he uses to represent fractal images and visualize mathematical relationships. A subject that always accompanies the work of Kerry Mitchell is to show the complexity and beauty that flows through extremely simple mathematical rules. The metaphorical idea of the complexity of nature associated with the simplicity of deterministic mathematical formulas is a constant in his work. For this image Kerry Mitchell has applied to a zoom of the Mandelbrot set a coloring algorithm named "Buddhabrot," invented by Melinda Green (see
"The Buddhabrot Technique" at www.superliminal.com/fractals/bbrot/bbrot.htm). The result is an image of mystical character that suggests a seated Buddha at different scales.
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"Xolis," by Jaroslaw Wierny"Xolis" is an abstract word for an abstract picture. Each person can give to it the significance they want, as the author does not pretend to predispose the viewer. The image was generated with Ultra Fractal and consists of 10 layers containing the two most famous fractal sets, the Julia set and the Mandelbrot set. Six different coloring algorithms are applied to these. Jaroslaw Wierny is a Polish graphic designer profoundly interested in the Buddhist philosophy, which he relates to the fractal structure of the world.
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"Pulse," by Jeanette Powers, Rockhurst University, Kansas City, MO (2008)Acrylic, 6" x 24". "This piece explores Hausdorff Dimension. Chaos and dynamical systems collapse in ordered ways. A nebula coalescing into a galaxy, a frozen molecule tossing through the tumult and falling as a six-sided crystal, the Mandelbrot Set. As an artist, I've tried to use chaotic interactions as a tool to express the limitations of our control and the beauty of chaos. This painting uses cellophane crushed into wet pigment to create the random patterning of the surface. The result is a chaotic landscape reminiscent of leaves, cells, rivulets, the cracked dirt of arid lands. All chaotic processes which leave a recognizable mark. The pattern is not exact, but exhibits self-similarity." --- Jeanette Powers, Student, Physics and Math Department, Rockhurst University, Kansas City, MO
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