
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 awardwinning sculptors have used topology as the
basis for their pieces. Dutch artist M.C. Escher represented
infinity, Möbius ands, 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 mathematicsorigami, computergenerated
landscapes, tesselations, fractals, anamorphic art, and
more.
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"And how is your husband Mrs. Escher?" by Nada KringelsNada (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 existedâ€”in fact she did, Jetta Umiker, with whom Maurits Cornelius Escher had three children. Ah, by the way, how is your husband, Mrs. Escher?Mar 07, 2007


"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, Damienâ€™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 coloringâ€”austere, mournful, and at times apocalypticâ€”often produces an emotional response in the viewer of the art.Mar 07, 2007


"20040402," by Samuel MonnierThe title of this picture does not involve any mathematical riddle, but is simply the reference number by which Samuel Monnier identifies his pictures. This young Swiss man, who is preparing for his Ph.D. in Theoretical Physics, does not like to put titles on his pictures as he feels it interferes with the sensations his work can produce in the viewer. The basic concept on which this image rests is to begin with a more or less repetitive initial design and superimpose various layers with this design at different scales. This procedure generates an image that shows structures with a wide range of scales, although from a strict point of view one cannot consider it to be fractal.Mar 07, 2007


"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.Mar 07, 2007


"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 "MMF3Turning 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 fivepointed star). With the second algorithm, "MMF3Orbital 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, "MMF3Alternative 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.Mar 07, 2007


"Spiral with opaque lines," by Andreas LoberThis image belongs to a simple Julia set, but the refined technique of Andreas Lober, who graduated from the University of Heidelberg with a degree in mathematics, converted it entirely into a creative prodigy. The coloring algorithm is simple: find the minimum value of â”‚zâ”‚ during the iteration, deflecting lightly the values pseudorandomly; this produces the sine waves that heighten the composition. The values are trapped during the calculation in discrete intervals; this produces the peculiar coloring that appears to be done with colored pencils. Other preferences of Andreas Lober include designing tilings that cover the plane with squares containing geometric shapes, so that they fit perfectly with the adjacent eight squares. These experiments produce tesselations of great visual impact and, in this case, variations have been used to obtain the frames contained in the image.Mar 07, 2007


"Indra Family," by Jos LeysJos Leys is a Belgian mechanical engineer who has always shown a special interest for mathematics in general and fractal art in particular since he programmed his first fractal image 25 years ago. "Indra Family" is a tribute to the professors David Mumford, Caroline Series and David Wright, the authors of the book "Indraâ€™s Pearls: The Vision of Felix Klein." The iterative calculation techniques of the Kleinian Groups described in this book reveal new fractal images that until then had remained unexplored. The name "Indra's Pearls" is a Hindu and Buddhist concept that represents a network of silk strings that extend to infinity in all directions, and contains at each intersection a very bright and luminous pearl that reflects each of the pearls of the network, that then reflect the others and so on, without end, like mirrors reflecting to infinity.Mar 07, 2007


"Sanctuary," by Nicholas Rougeux"Sanctuary" consists of 19 layers, each one of which contains variations of the orbit trap algorithm. The traps are geometric shapes placed in the complex plane that end iteration of a point when its orbit falls within the shape, hence the name. The shape, size, and location of the traps permit Nicholas Rougeux to control the appearance of each of the layers, which are then combined together as if they were transparencies held up to light. Nicholas Rougeux, a North American web developer, reinforces in this picture the idea of a sanctuary by including smooth curves on the sides that simultaneously create sensations of protection and welcome. The mild colors also help to obtain the objective of evoking a comfortable place where spirits are free.Mar 07, 2007


"Enmpperaltta," by Inigo QuilezInigo Quilez is an engineer born in the Basque Country, Spain, who actually works in Belgium designing virtual reality tools. The word that titles the picture, Enmpperaltta, signifies nothing; it is simple a permutation of the French word "L'Appartement." The reason is the obsession shown by the author while trying to buy the perfect apartment in Brussels; that goal was finally achieved and he celebrated with this image. Enmpperaltta is in fact a still frame from an animation calculated by means of proprietary software written in the C language from a variant of the wellknown Pickover algorithm, a formula that generates shapes resembling those produced by mixing fluids, for example liquids of different colors. To generate the image, the formula was repeated three times with slightly altered parameters, each in a separate process, and applied to the three basic components of color in the image: red, green and blue, that are combined together to produce the final result.Mar 07, 2007


"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, "IFSBarnsleyJockIII," 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.Mar 07, 2007


"Asundriana," by Janet ParkeJanet Parke, born in Memphis (USA), has passed the major part of her life as a ballet dancer, choreographer, and dance professor. In 1999 she began to exhibit and sell her fractal art, characterized by an extraordinary sensitivity and coloring style unknown until then. Janet Parke replaces the characteristic loud and bright colors of the first generations of fractal art with smooth, rich tones and delicate shades. Her style will be imitated by a new generation of fractal artists. "Asundriana" is based on a variant of the Julia set ( z > zsquared + c ) such that the parameters c and z are manipulated to produce distortions in the typical spiral structures of this set. The name of the image comes from the word asunder, since the structure of the image seems to fold into and separate from itself.Mar 07, 2007


"Eifiona," by Tina OloyedeTina Oloyede left her profession as a medical doctor to become a selftaught fractal artist, a passion and obsession since 1999. Residing in England, she balances her artistic activity with the care of her young family. She is actually one of the most versatile and publiclyappreciated fractal artists. For this picture she used 13 different formulas: 7 for building the basic structure of the image, 3 for adding different textures, and another 3 for controlling the coloring of the image. The name of the picture, "Eifiona," is the Welsh name of a friend of the artist, who ordered the image with one condition, that it be of "The Autumn" and in return granted absolute freedom to make the design and finish of the image. Tina Oloyede's capacity for artistic expression is unquestionable; it is impossible to see this picture without an autumnal image appearing in our mind.Mar 07, 2007


"Fingers Holding Secrets," by Joe ZazulakJoe Zazulak retired at the age of 55 from the United States Department of Veterans Affairs in order to dedicate himself from then on to fractal art, to which he is a certified addict. This picture is called "Fingers Holding Secrets," and the name came to his mind while the image appeared slowly on his computer. From then he only worked in providing the delicate and smooth pearlescent texture that characterizes the image. Joe Zazulak never plans his images in advance, nor intuits what they will be after the creative process. He begins his works with a very simple structure, with hardly any color, and adds variations to the shape parameters intuitively until he obtains a pleasing result.Mar 07, 2007


"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.Mar 07, 2007


"Untitled," by Mark TownsendMark Townsend is a complete fractal artist who combines a refined technique with a marvelous creativity. This versatile Australian programmer has designed dozens of formulas for the program Ultra Fractal, but also gets part of his fame as the author of the popular software Apophysis. Mark Townsend is one of the authors who has contributed much to the recognition of fractal art, providing a work that is both innovative and at the same time personal. For this image, he tried to create shapes that did not appear to be made with a computer. The lines were included to emphasize the twodimensional nature of the image.Mar 07, 2007


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