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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:


...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... ?

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?

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???

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.