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.
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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"Eifiona," by Tina OloyedeTina Oloyede left her profession as a medical doctor to become a self-taught 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 publicly-appreciated 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.
"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 -> z-squared + 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.
"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.
"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 well-known 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.
"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.
"Potemkine," by Etienne Saint-AmantEtienne Saint-Amant is a Canadian scientist passionate for art and mathematics. He has had various exhibitions both individual and collective, he has presented conferences on art and mathematics and he has appeared in numerous programs on radio and television. His work can be seen on CD and book covers, calendars and web pages. "Potemkine" is a pseudo-abstract composition that portrays the intense emotion lived during the rebellion of the battleship Potemkin in the port of Odessa, Ukraine, in 1905. It brings to mind the ship enveloped in smoke, the flying projectiles, the din of the battle: a scene of the terrible emotional conflict of the Russian troops brought about by the orders to quash the rebellion and those sentiments confronted by compassion towards their compatriots. The image was created to commemorate, a century later, these events.
"Spellbinder," by Richard SpixThis image was formed with no less than 105 fractal layers composed of a large number of different coloring algorithms applied to a Phoenix set. It is the kind of image in which the composition enjoys much importance and in which many of the formulas are used to correct or emphasize small details, at times almost imperceptibly. The name of the image comes from the idea of representing an ancient artifact, enigmatic, bound to legend and secret mysteries. The author of this complex picture, Richard Spix, has created fractal art since 1996 in Florida (USA) where he works as a technical engineer.
"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 two-dimensional nature of the image.
"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.
"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.