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In mathematics, the term chaos game, as coined by Michael Barnsley,[1] originally referred to a method of creating a fractal, using a polygon and a random point inside it.[2] The fractal is created by finding the point a given fraction of the distance between the previous point and one of the vertices, chosen at random, a large number of times. Using a regular triangle and the factor 1/2 will result in the Sierpinski triangle. The term has been generalized to refer to a method of generating the attractor, or the fixed point, of any iterated function system (IFS). Starting with any point x0, successive iterations are formed as xk+1 = fr(xk), where fr is a member of the given IFS randomly selected for each iteration. The iterations converge to the fixed point of the IFS. Whenever x0 belongs to the attractor of the IFS, all iterations xk stay inside the attractor and, with probability 1, form a dense set in the latter. The "chaos game" method plots points in random order all over the attractor. This is in contrast to other methods of drawing fractals, which test each pixel on the screen to see whether it belongs to the fractal. The general shape of a fractal can be plotted quickly with the "chaos game" method, but it may be difficult to plot some areas of the fractal in detail. The "chaos game" method is mentioned in Tom Stoppard's 1993 play Arcadia.[3] [edit] See also[edit] References
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