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Author Topic: False Mandelbrot Byways No. 2  (Read 744 times)
Description: An exiled Mandelbrot with simple colouring
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element90
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« on: May 31, 2013, 05:34:40 PM »


https://copy.com/pMDzYilUtH1A

An exiled Mandelbrot island in a fractal other than the standard Mandelbrot set. Coloured using iteration of minimum magnitude.
« Last Edit: May 23, 2014, 12:26:48 PM by element90, Reason: Replaced file links. » Logged

Elelemt90 Fractals blog www.element90.wordpress.com
cKleinhuis
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« Reply #1 on: May 31, 2013, 06:19:36 PM »

Great find
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divide and conquer - iterate and rule - chaos is No random!
matsoljare
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« Reply #2 on: May 31, 2013, 08:26:05 PM »

And what is the entire fractal like, then?
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element90
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« Reply #3 on: May 31, 2013, 09:43:43 PM »

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).
« Last Edit: May 23, 2014, 12:32:48 PM by element90, Reason: Replaced file links. » Logged

Elelemt90 Fractals blog www.element90.wordpress.com
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