• October 16, 2021, 05:54:05 PM

Author Topic:  Imaginary Mandelbrot Set (Z^I+C)  (Read 333 times)

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Offline DeusDarker

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Imaginary Mandelbrot Set (Z^I+C)
« on: June 30, 2020, 02:19:43 AM »
I was messing around and 'discovered' this fractal by putting in ^I+C instead of ^2+C
i also made a exploration/zoom in video with more details, if you want to see such a thing the link is https://www.youtube.com/watch?v=WfLmBgAksQw

Linkback: https://fractalforums.org/index.php?topic=3629.0

Offline C0ryMcG

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Re: Imaginary Mandelbrot Set (Z^I+C)
« Reply #1 on: June 30, 2020, 03:06:34 AM »
Interesting! I'm surprised I've never encountered this before... it doesn't act like I'd expect.

What is your coloring method in that? It turns out different than my methods. Also, does this formula have a name??

This makes interesting Julia images, as well!
Here's one with Lagrangian Descriptor coloring


Offline DeusDarker

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Re: Imaginary Mandelbrot Set (Z^I+C)
« Reply #2 on: June 30, 2020, 03:31:16 AM »
Interesting! I'm surprised I've never encountered this before... it doesn't act like I'd expect.

What is your coloring method in that? It turns out different than my methods. Also, does this formula have a name??

This makes interesting Julia images, as well!
Here's one with Lagrangian Descriptor coloring
Yeah its very strange! im using XaoS 4.0 with outcoloring mode iter+real+imag+real/imag
Ive looked on the internet and this fourm site and have not found any references to this exact fractal/formula, so who knows maybe im the first with the idea to put in ^I instead of ^2 (probably not, but it never hurts to dream  :P) so no official name for this formula as far as i know. very cool julia sets! something i noticed is that they only become filled near/around the center and the bottom 'seashell valley' and nowhere else, which is kind of odd as i was expecting a distribution of places but nope. what software are you using to generate btw?

Offline DeusDarker

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Re: Imaginary Mandelbrot Set (Z^I+C)
« Reply #3 on: June 30, 2020, 03:35:59 AM »
another picture

Offline C0ryMcG

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Re: Imaginary Mandelbrot Set (Z^I+C)
« Reply #4 on: June 30, 2020, 04:15:49 AM »
Interesting! I've gotten somewhat close to your details with that hint you gave there. But this thread isn't about the coloring method, I just get distracted by such things.
To answer your question, I have a javascript program that I've been building as a way to learn about fractals. So when I find cool new formulas, I can just type them in and hit 'go', then try out the various coloring methods I've collected, too.

Offline marcm200

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Re: Imaginary Mandelbrot Set (Z^I+C)
« Reply #5 on: June 30, 2020, 12:15:49 PM »
Is there a theoretically derivable valid escape criterion for z^i+c?

As it's not a polynomial (with natural degree, the coefficients allow for computing a valid enclosement), this would probably be implemented as complex exp/log. For exp, there is no escape radius (as values can get arbitrarily large and then come back), but maybe the log-part removes that problem?


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