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Author Topic: Transformation of a sphere to make 3D julia? Possible to do?  (Read 940 times)
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KRAFTWERK
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« on: February 26, 2015, 07:08:03 PM »

I copied my comment from this thread http://www.fractalforums.com/philosophy/where-are-all-these-forms-coming-from!/ , thrilled to hear what you have to say about my question, would it be possible? - laser blaster posted this video:

This video helps me to understand how the shapes of Julia spirals arise.

<a href="https://www.youtube.com/v/R1gpm7WsNhg&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/R1gpm7WsNhg&rel=1&fs=1&hd=1</a>

Each Julia set can be visualized by repeatedly iterating a transformation on a circle....

...which made me wonder:
Hmmm,  looking at this way to produce a julia shape... would it be possible to do the same thing in 3D starting with a sphere... you beautiful minds of mathematics... ?
« Last Edit: February 26, 2015, 07:27:11 PM by KRAFTWERK » Logged

laser blaster
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« Reply #1 on: February 27, 2015, 04:34:57 PM »

Yes, it would be possible to do it in 3D. It won't give us any grails, as this inverse transform method isn't fundamentally different from the escape time method, just a different way of visualizing it. But it would make a really cool animation for sure. It should even work for Tglad's tetrahedral transforms.
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youhn
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« Reply #2 on: February 27, 2015, 07:10:31 PM »

I've got the feeling there _IS_ something fundamentally different. I'm no mathwiz, so I can't really explain it good enough. But it has something to do with the properties of complex numbers in 2D versus 3D. When you look at the first iteration of the julia sphere folding, you notice that the horizontal offset caused by the translation becomes vertical after folding. Each step all direction are involved and most importantly intertwined. The grail probably needs a 3D method which intertwines ALL directions in the same way that the mandelbrot iterations do with complex numbers in the 2D world.

Maybe start with a sphere and use the 2D method, but rotate the whole thing 90 deg around each axis:
1. translate, fold, square root, quarter turn around x
2. translate, fold, square root, quarter turn around y
3. translate, fold, square root, quarter turn around z
4. translate, fold, square root, quarter turn around x
5. etc

How would this look?
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KRAFTWERK
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« Reply #3 on: February 28, 2015, 10:17:59 AM »

I've got the feeling there _IS_ something fundamentally different. I'm no mathwiz, so I can't really explain it good enough. But it has something to do with the properties of complex numbers in 2D versus 3D. When you look at the first iteration of the julia sphere folding, you notice that the horizontal offset caused by the translation becomes vertical after folding. Each step all direction are involved and most importantly intertwined. The grail probably needs a 3D method which intertwines ALL directions in the same way that the mandelbrot iterations do with complex numbers in the 2D world.

Maybe start with a sphere and use the 2D method, but rotate the whole thing 90 deg around each axis:
1. translate, fold, square root, quarter turn around x
2. translate, fold, square root, quarter turn around y
3. translate, fold, square root, quarter turn around z
4. translate, fold, square root, quarter turn around x
5. etc

How would this look?

Now, THIS sounds a lot like what I visualized when I asked myself the question...
I hope someone could try this out... Luca?  wink
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flexiverse
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« Reply #4 on: March 15, 2015, 01:21:16 AM »

This is exactly the kind of contemplation that led to the creation of the mandelbox.

Naturally in the same way iterating these transformations will lead to interesting 3d fractals.

But I don't see anyone really trying and playing with new sets of transformations to create new 3d fractals.

We seem to be stuck at the mandelbox and mandelbulb.

FOR EXAMPLE this super cool dude is the only person on the planet that had tried to explain the mandelbox transformations in video form:

<a href="http://www.youtube.com/v/FspAvR42E54&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/FspAvR42E54&rel=1&fs=1&hd=1</a>

It's always struck me, well, why hasn't anyone tried just a collection of other transformations?huh???

I guess you can probably count on one hand the number of people here on this forum that have the skills to do this and write the code for distance estimators to plot the fractal in 3D!!!


I'm still trying to understand the code behind the distance estimator for a mandelbox!!!

Never mind new sets of transformations.  There  must be a super clever way to create a 3d distance estimator for messing with any set of made up transformations.

But honestly it's takes serious maths chops.
« Last Edit: March 15, 2015, 01:35:29 AM by flexiverse » Logged
1990winfractal
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« Reply #5 on: April 11, 2015, 02:54:22 AM »

sounds fun and would look good on my desk if it is possible   Spiral Thingy MiniBrot A Star
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I am new to this form but not to fractals I love them I wish to fly in one with out a computers help one day
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