Mandelbrot Rings

[element90]

https://copy.com/j9xL1xYxWL4c

Inner rings:


https://copy.com/nQkLdlkAbiqq

The fractal is a modification of this fractal:


https://copy.com/INbRMEOelPVC

The formula is:

z = transform(z)
z = alpha(beta*z^gamma + delta*z^epsilon)

initial z = 1
alpha = 1
beta = 1
gamma = 2
delta = 1
epsilon = -2

Two transform sets:

A - empty
B - inverse reflect (circle diameter = 1)

Transform sequence AB i.e. the transform sets are applied on alternate iterations.

[cKleinhuis]

nice!

[Dinkydau]

cool!

[Kalles Fraktaler]

Cool, I first thought it was a cut and paste in paintbrush

Nice marble feeling

[element90]

There is an error in the settings for the fractal that started this thread, the value of alpha should be:

alpha = location in the complex plane

Changing the transform sequence from AB to ABA and the image becomes:


https://copy.com/fkilWgD7dm9X

[element90]

Changing the B transform set to contain this transform:

circle reflect, diameter 0.1

with a transform sequence of AB.

The result is deformed Tricorns (or Mandelbars).


https://copy.com/0Cvx8ajNOATg

Circle reflect produces a fractal that features Tricorns and Mandelbrots. Zooming in on barely visible ring at the centre:


https://copy.com/A91eSTjb3qKx

https://copy.com/sBmf4PKLFRdc

[element90]

Zooms into the main ring from the last entry:


https://copy.com/hiJEGFm401Ab

https://copy.com/LNFdJu4CSx4G