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Author Topic: new 3d fractal generation method?  (Read 659 times)
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Juliadreamer
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« on: January 13, 2017, 10:26:28 AM »

i just read this article, and i am wondering if this could be used to generate 3d fractal shapes that retains all proprieties of fractal objects. Could it be implemented in some software similar to Mandelbulber or Mandelbulb3d to have a different kind of 3d fractal shapes?

https://www.quantamagazine.org/20170103-fractal-dynamics-from-3d-julia-sets/

Do someone has an opinion about their method to generate a 3d shape, compated to the ones usually used for the mandelbulb, the mandelbox, etc.?
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Chillheimer
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« Reply #1 on: January 13, 2017, 11:24:04 AM »

Hello and welcome to the forum!

the article has been posted here a few days ago.

but this reminded me to share some thoughts I had about it:

Concerning the search for the "holy grail", a real 3d mset: I think we kind of have found it already, but the problem is that there is no proper way to display it in a static 2d render.

I'd like to quote startdust4evers comment here, he really helped me understanding the limitations we are faced with:
"Since you can’t see all the layers of an onion without taking a slice, much of Mandelbulb exploration just explore the outer exterior of the fractal from different perspectives because we are limited by what we can see from within the plane."
We would have to do deep zoom videos, zooming in closer and closer into the never ending surface details.
just like the zooms into the 2d mandelbrot set.
right now we're only doing the 3d-equivalent of scrolling the x&y axis.

I also find the realization fascinating:
It is my belief that these 3D variants of the Mandelbrot contain the same amount of fractal detail as the traditional 2D Mandelbrot and ABS() variations which I helped to catalog, but the fractal iteration bands are like the layers of an union. Deep zooms create intricate patterns in a 2D plane which is visible to the eye. A deep zoom of the 3D Mandelbulb or BS fractal will have similar layers, but our perspective in 3D lies within the fractal rather than outside it.

In my opinion the buddhabrot method comes closest to any sort of holy grail as it shows the most information in a single image.


edit: actually concerning the linked article - to me it looks like this method will generate a folded plane, that again is "just" another single layer of the onion. A different approach, but a very similar result.
« Last Edit: January 13, 2017, 11:43:53 AM by Chillheimer » Logged

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Juliadreamer
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« Reply #2 on: January 13, 2017, 01:13:03 PM »

thanks!
i tried to use the search function, but the name of the researchers didn't give any result. I hadn't thought about using the magazine name as keyword.
But after you told me, i found even another thread.
http://www.fractalforums.com/new-theories-and-research/3-d-fractals-offer-clues-to-complex-systems-(quanta-magazine)/

thank you again for the insightful explanation and opinions.
I was also wondering if their method is able to generate something more than just a complementary folded plane. They write that "That algorithm analyzes features of the original polynomial, like its degree (the highest number that appears as an exponent) and its coefficients, and outputs another fractal shape" but i'm not knowledgeable enough to understand if this is enough to make it a proper 3d fractal. As you write, probably not, unfortunately.
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