Limited Mandelbar Sets
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.[more]
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.[less]