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Limited Mandelbar Sets

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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 and are thus excluded from the Mandelbrot set.

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Now consider taking the complex conjugate and arbitrary powers until the result exceeds an arbitrary value w. The mapping is then . The resulting sets are called Mandelbar sets because of the bar denoting conjugation.

The image plots the region of points having iterates with norms less than w.

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

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