amazing surf

[Kali]

just tried. this is the spot (i measured). as expected with zero rotations it is a flat disc. I think your parameter has no equivalent here. I don't even understand, why the julia set is 3d. Sorry!  Maybe Kali can explain.

Not always Mandelbrot version shows a consistent map of Julia versions of the fractal. I learned this when I discovered the 2D Kaliset formula, as you can see in this post: http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/
I guess it's because of how julias are positioned and how it's position changes with the different values.

It's something to take into account when researching new formulas 

[bib]

Not always Mandelbrot version shows a consistent map of Julia versions of the fractal. I learned this when I discovered the 2D Kaliset formula, as you can see in this post: http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/
I guess it's because of how julias are positioned and how it's position changes with the different values.

It's something to take into account when researching new formulas 

Kali, I read that thread and your discussion with Sam but I did not see any clear conclusion...Did I miss something?

[taurus]

I thought about this "anomaly" a little while. As Asurf is tight related to Abox, my investigations on Abox might be useful for this.
My expierience with the Mandelbox says following:

• For every Point on the mset surface (and solid spaces too), there is a correlated julia set, with graphically identical properties, BUT
• there are (non zero) julia sets, that are not mapped in the mset as their constants are outside the mset

There seem to be a (narrow) coordinate space outside the box mset, where juliaset constants lead to not empty juliasets. when they are far enough away from surface, they have graphically no equivalent struchture on the mset. Most significant example i found for such jset is this.



I think with bib's parameter it is similar. the mset is a flat disc in xy plane. every jset with non zero z constant is not mapped on the mset.
ps be indulgent with this attempt of a declaration. I am neither programmer nor mathematician. 

[bib]

Mmmh, could that have anything to do with iteration count and bailout? Those "ghost" Julias are not real, I mean, we see them because of the DE stop, but in reality they are "empty". So what we see is a kind of "solid iteration fog". Don't know how to explain better, sorry

Just my 2 cents...

[taurus]

I mean, we see them because of the DE stop, but in reality they are "empty". So what we see is a kind of "solid iteration fog".

I think you got it!
The one below is very sensitive on changes of de stop. Decreasing it makes the arms thinner and thinner.

(terms like "in reality" are quite strange and funny in this context...)

[Kali]

Kali, I read that thread and your discussion with Sam but I did not see any clear conclusion...Did I miss something?

No, you missed nothing, we noticed this fact but couldn't find why it happens... I pointed to that thread only to show an example of another mset "not working properly".

Now, my theory on your params is: When calculating a mset, for every point in space, the formula is iterated adding the same coordinate values of the point to be drawn.
I didn't test it in specifically in your params, but what could be happening is that for every Julia set calculated outside the x-y plane, the point located at the position matching the Julia constants, is empty. So in mandelbrot version, for every point x,y,z is like extracting that specific point from the Julia using same x,y,z as constant, and is the only part of the Julia that will be shown, so the result is mostly empty space excepting the flat surface when z=0.
Something like this should be happening with taurus example.

I hope I made myself clear, I don't know how to explain it better, at least in english 

[Kali]

Also, I forgot to mention, about the DE stop thing... that happens because it's really a surface (hence the formula's name), so the fractal's volume is zero.
It's the DE approximation what makes it solid, but they are in fact 2D surfaces on a 3D space.