Fractal From Wikipedia, the free encyclopedia Jump to: navigation, search The boundary of the Mandelbrot set is a famous example of a fractal. Another view of the Mandelbrot set.In colloquial usage, a fractal is "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole".[1] The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured". A fractal as a geometric object generally has the following features: It has a fine structure at arbitrarily small scales. It is too irregular to be easily described in traditional Euclidean geometric language. It is self-similar (at least approximately or stochastically). It has a Hausdorff dimension that is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve). It has a simple and recursive definition.[2] Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, and snow flakes. However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics. http://en.wikipedia.org/wiki/Fractal

A fractal is a structure which is similar at various scales. Wikipedia gives you a lot of info: http://en.wikipedia.org/wiki/Fractal The famous "Mandelbrot Set" fractal has a very simple definition. Starting at z = 0, where z is a complex number, replace z with z^2 + c, where c is another complex number. That's it. If the magnitude of z increases to infinity (in practical terms, say, two!) after an infinite number of steps (say 100) then plot the pixel corresponding to c in white, it is outside the fractal. Otherwise plot it in black. You can color the pixel by the number of steps it takes to hit "infinity". The formula in terms of real numbers is x_old = x, y_old = y x_new = x_old * x_old - y_old * y_old + pixel_x_value y_new = 2 * x_old * y_old + pixel_y_value x becomes x_new y becomes y_new

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