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Divergence from the Mandelbrot Set

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Consider the mapping . The Mandelbrot set consists of those complex numbers such that the iterates of do not tend to infinity as . Points with an iterate greater than 2 in absolute value diverge.

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In the left-hand image, the norms of red points reach 2 in the fewest number of iterations, followed by the other colors in order of wavelength. The initial image only takes "step size" number of iterations. Check "run" to let the number of iterations increase.

In the right-hand image, white points have iterates with norms less than 2. These are the remaining candidates for membership in the Mandelbrot set.

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Contributed by: Michael Schreiber (March 2011)
Open content licensed under CC BY-NC-SA

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The default center is in the sea horse valley.

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