False Mandelbrot Byways No. 2

[element90]

https://copy.com/pMDzYilUtH1A

An exiled Mandelbrot island in a fractal other than the standard Mandelbrot set. Coloured using iteration of minimum magnitude.

[cKleinhuis]

Great find

[matsoljare]

And what is the entire fractal like, then?

[element90]

The full fractal looks like this:


https://copy.com/pwf8HxenE7E9

The formula is:

z = (alpha(beta*z^gamma - delta*z^epsilon) + zeta)^eta

initial z = 0.75
alpha = location in the complex plane
beta = 1
gamma = 3
delta = -1
epsilon = 4
zeta = 0.999999995

Zooming in:


https://copy.com/kJUEfUzP1YIp

and


https://copy.com/VFyc3Fk1V3Gm

Change zeta to 1 and the fractal becomes:


https://copy.com/YLYsDy3HG9vE

With zeta at 1 it starts getting a bit weird see http://www.fractalforums.com/new-theories-and-research/is-there-anything-novel-left-to-do-in-m-like-escape-time-fractals-in-2d/318/ (reply 318).