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Welcome to Fractal Forums > Fractal Art > Images Showcase (Rate My Fractal) > Mandelbrot Rings
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Author Topic: Mandelbrot Rings  (Read 734 times)
Description: Rings of connected Mandelbrots
0 Members and 1 Guest are viewing this topic.
element90
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« on: July 01, 2013, 01:29:22 PM »

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.
« Last Edit: May 22, 2014, 05:29:48 PM by element90, Reason: Replaced file links. » Logged
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cKleinhuis
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« Reply #1 on: July 01, 2013, 01:31:54 PM »
nice!
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divide and conquer - iterate and rule - chaos is No random!
Dinkydau
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« Reply #2 on: July 01, 2013, 01:51:27 PM »
cool!
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Kalles Fraktaler
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« Reply #3 on: July 01, 2013, 02:28:24 PM »
Cool, I first thought it was a cut and paste in paintbrush smiley

Nice marble feeling
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element90
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« Reply #4 on: July 03, 2013, 10:46:42 AM »
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
« Last Edit: May 22, 2014, 05:35:32 PM by element90, Reason: Replaced file links. » Logged
Elelemt90 Fractals blog www.element90.wordpress.com
element90
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Posts: 298



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« Reply #5 on: July 03, 2013, 11:03:27 AM »
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
« Last Edit: May 22, 2014, 05:39:10 PM by element90, Reason: Replaced file links. » Logged
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element90
Strange Attractor
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Posts: 298



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« Reply #6 on: July 03, 2013, 11:10:06 AM »
Zooms into the main ring from the last entry:


https://copy.com/hiJEGFm401Ab

https://copy.com/LNFdJu4CSx4G
« Last Edit: May 22, 2014, 05:41:30 PM by element90, Reason: Replaced file links. » Logged
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