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Limited Mandelbar Sets

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step
6
threshold
2
exponent
2
conjugation
mesh
Consider the mapping
f
c
:z↦
2
z
+c
. The Mandelbrot set consists of those complex numbers
c
such that the iterates of
(n)
f
c
(0)
do not tend to infinity as
n∞
. 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
z
and arbitrary powers
n
z
until the result exceeds an arbitrary value w. The mapping is then
f
c
:z↦
n
z
+c
. 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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