- published: 14 Feb 2014
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A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers. Fractals are typically self-similar patterns, where self-similar means they are "the same from near as from far" Fractals may be exactly the same at every scale, or as illustrated in Figure 1, they may be nearly the same at different scales. The definition of fractal goes beyond self-similarity per se to exclude trivial self-similarity and include the idea of a detailed pattern repeating itself.
As mathematical equations, fractals are usually nowhere differentiable, which means that they cannot be measured in traditional ways. An infinite fractal curve can be perceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.
The mathematical roots of the idea of fractals have been traced through a formal path of published works, starting in the 17th century with notions of recursion, then moving through increasingly rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century, and on to the coining of the word fractal in the 20th century with a subsequent burgeoning of interest in fractals and computer-based modelling in the 21st century. The term "fractal" was first used by mathematician Benoît Mandelbrot in 1975. Mandelbrot based it on the Latin frāctus meaning "broken" or "fractured", and used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature.
Benoît B. Mandelbrot (20 November 1924 – 14 October 2010) was a French American mathematician. Born in Poland, he moved to France with his family when he was a child. Mandelbrot spent much of his life living and working in the United States, and he acquired dual French and American citizenship.
Mandelbrot worked on a wide range of mathematical problems, including mathematical physics and quantitative finance, but is best known as the father of fractal geometry. He coined the term fractal and described the Mandelbrot set. Mandelbrot also wrote books and gave lectures aimed at the general public.
Mandelbrot spent most of his career at IBM's Thomas J. Watson Research Center, and was appointed as an IBM Fellow. He later became a Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure. Mandelbrot also held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Centre National de la Recherche Scientifique.
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Genres: Comedy, Short,Actors: Mike Kovac (actor), Jesse Wheeler (actor), Scott Wallis (actor), Scott Mainwood (producer), Scott Mainwood (actor), Jon Anctil (editor), Jon Anctil (writer), Jon Anctil (director), Justin Sproule (actor), Michael Fenske (actor), Malcolm Oliver (producer), Malcolm Oliver (editor), Ian Ronningen (actor), Courtney Shields (actress), Jacqueline Breakwell (actress),
Genres: Comedy, Short,Actors: Mike Kovac (actor), Jesse Wheeler (actor), Scott Wallis (actor), Scott Mainwood (producer), Scott Mainwood (actor), Jon Anctil (editor), Jon Anctil (writer), Jon Anctil (director), Justin Sproule (actor), Michael Fenske (actor), Malcolm Oliver (producer), Malcolm Oliver (editor), Ian Ronningen (actor), Courtney Shields (actress), Jacqueline Breakwell (actress),
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