Limited Mandelbar Sets
Limited Mandelbar Sets
Consider the mapping :z↦+c. The Mandelbrot set consists of those complex numbers such that the iterates of (0) 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.
f
c
2
z
c
(n)
f
c
n∞
Now consider taking the complex conjugate and arbitrary powers until the result exceeds an arbitrary value w. The mapping is then :z↦+c. The resulting sets are called Mandelbar sets because of the bar denoting conjugation.
z
n
z
f
c
n
z
The image plots the region of points having iterates with norms less than w.