ok, fernandez, this is my five cents:
+ because the quadratic iteration is not as intricate as expected and eighth power iteration is a peculiar sweet spot as mentioned by Daniel White?the eight power has just been producing the most intricating results, especially the formations of the bulbs are visible self-similar, even in 3d, because
those bulbs are clearly conststing of smaller copies of itself, the quadratic iteration is intricate as well, but it does not show the self similarity as in the
power8 version
the power2 variant clearly provides a method for creating a 3d object that is not just an extrusion or rotating of the plane, and shows visual advances
directly compared to the quaternion mandelbrot2 variants
+ because it has 'whipped cream' regions?the whipped cream is something we have to concentrate on, although it already has been shown that the surface of the bulbs exhibit a fractal
dimension of 3, which basically means that the surface (area) already IS infinite, the border of the mandelbrot in 2d has as well a fractal dimension
of exactly 2, which basically means that the surface (border) of the mandelbrot is infinite as well
ok, now let us look at a cut through a slice of the mandelbulb exhibiting a whipped cream area
first we need to clarify that those "whipped cream" areas are not because a too low iteration used for displaying, as a mandelbrot at low iterations
e.g. just 10 or so looks really like a whipped cream area, but this is not meant, the whipped cream areas of the mandelbulb do not exhibit more
complexity when increasing iteration count
so, as far as i know the definition of a space filling curve (->fractal dimension =2) is that every cut of such a curve must exhibit equally infinite
lengthes, so, each 2 points of the mandelbrot border are connected with an infinite long line, this property would not apply to a sliced mandelbulb
exhibiting the whipped cream, some parts of the slice may have complex parts that when connecting them together is as well an line of infinite length
but there are parts that would just be connected through a curved line, such a curved line with no extra detail exhibiting on each sub-slice is
not what we call a fractal
so, in my words i am formulating a mandelbrot holy grail as this:
every slice of any cut of a holy grail candidate's border has to be a complete space filling curve, with that i mean that every 2 points connected on such a
slices border MUST have infinite distances between them ( in theory when iterating an infinite amount of times )
+ because the two hypercomplex axes in addition to the real axis are not quite symmetrical?what do you mean by this ?! all of the axes are symetrical orthogonal
i was thinking of a triplex method defined
by non-orthogonal axis just incorporating another parameter to play with, but this would in my eyes just produce weird results