mandelbrot set

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Definitions of mandelbrot set words

noun Technical meaning of mandelbrot set (mathematics, graphics) (After its discoverer, Benoit Mandelbrot) The set of all complex numbers c such that | z[N] | < 2 for arbitrarily large values of N, where z[0] = 0 z[n+1] = z[n]^2 + c The Mandelbrot set is usually displayed as an Argand diagram, giving each point a colour which depends on the largest N for which | z[N] | < 2, up to some maximum N which is used for the points in the set (for which N is infinite). These points are traditionally coloured black. The Mandelbrot set is the best known example of a fractal - it includes smaller versions of itself which can be explored to arbitrary levels of detail. 1
noun mandelbrot set a set of points in the complex plane that is self-replicating according to some predetermined rule such that the boundary of the set has fractal dimensions, used in the study of fractal geometry and in producing patterns in computer graphics 0
noun mandelbrot set (mathematics) the set of complex numbers c for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn2 + c remains bounded. The boundary of this set is a fractal. 0

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This term is known only to a narrow circle of people with rare knowledge. Only 7% of English native speakers know the meaning of this word.

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