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.
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