True 4d M extension: Search for the Holy Grail(s) goes on...

[fracmonk]

Asdam- Thanx for your interest.  I am more and more interested in the function of numbers in our natural reality, and the properties they themselves have.  It gives me kind of a bias though.  I find that my formula here does create a redundancy in complex results, just projecting the same ones off the plane, so I lately tend to stick to 2d.  Never be discouraged, though.  Mandelbulb uses an actual 3d system that makes geometric sense, but my bias is against the inability to apply all properties when sticking to the 4 basic (binary)operations.  Not even sure if I'm making sense in that...

[Alef]

I think, if mandelbulbs would be mathematicaly correct, they too would be smooth rotation surface. Could be that having some manual rotations creates all the bubles and surface pattern, but realy they have just XY plane turned all around. Mandelbulbs alsou do not have elaborate zoom in pattern of mandelbrot.

What you think about this: http://www.fractalforums.com/new-theories-and-research/few-steps-behind-perfect-3d-mandelbrot/

[fracmonk]

Yes, saw it before.  I think what a lot of people are looking for are treatments that don't stretch and smear, to put it maybe too simply.  But depending on what your 3rd D is, that elongation of edge detail may be inevitable and true.

[Alef]

Simple, but almoust like using trigonometry. If there could be something simple making 2D formulas working in 3D, there would be much more different quaternions. I tried to iterate that manualy, but didn't got, what the formula realy do. Maybe something like tricorn aka mandelbar in zx axis.

I think, swirls and tentacles going to all sides (perfect 3D) would be pretty imposible unless someone will find some new numbers with square value different than i.

[fracmonk]

Asdam-  M & Tricorn can be intersected on the real axis.  I've done it in slices in 2d, as I always do, set up so the 2 planes cross each other @ 90 degrees.  A bit blobby...

[Alef]

That in 3D turned out different then were expected. Mandelbrot in XY and tricorn in ZX axis were fractal which moving or rotating completely changes geometry, and looks pretty strange. Could be the 3D engine;)

Maybe no (true) 3D mandelbrot. But in searching for this forum folks foung hudge number of other fractals. Hmm, maybe they should be convinced to search fork some Ark of Covenant of fractal world, some true 3D/4D Milk Way galactic fractal or true 3D/4D equation based dragon curve.

[fracmonk]

Since many 3d progs use unary trig. funcs AND may have been written w. other formulae in mind, I've never been inclined to trust results either.  That DOESN'T, however, mean that you can't...