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.


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.


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



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