So I decided to play with the julia set this time, these are all from the fractal type 8 (4D "Variation" julia set.)
It took me time to find the values that produce something interesting, as the default ones did not produce anything very amusing.
I have set the iteration level to 20, lowering it might produce more minetest friendly shapes that one can actually play on. All the mapgen decorations, caves and dungeons are removed here in order to better observe the fractal.
I managed to get something that resembles an overall spherical object, by setting all of the values to 0 (I am here adjusting mgfractal_julia_x, y, z and w values). I scaled the fractal to 128, and set the offsets to 0. This one appears when the x value is around 0.3 - 0.33 (y = 0, z = 0, w = 0), I have never gone beyond that though.
Now, there is this mgfractal_slice_w value that does some very interesting stuff to the 4D fractals (only), they eventually get smaller and smaller. But I am not going to demonstrate that as it requires me to raise/lower that value a lot. But by increasing it as much as 0.1 I got:
And that fractal changes more and more, rotates the line of symmetry (not even a straight line anymore, this happens a lot with this fractal) and starts vanishing into nothingness.
w = 0.2
Anyways thats where I lost the point from where I was originally screenshotting.
w = 0.3
You get the idea of what happens.
After that I experimented with raising the y along with x (which I left at 0.3 as it seemed to be nice).
Raising y made the hollow sphere become filled inside by growing those noticeable formations on the sides towards the inside.
I also observed the change that happens when raising the z and w values. Raising each of these will break the fractal's symmetry. Raising both will not make the fractal symmetrical again, actually it will make it as asymmetrical as it can get. Raising each of these individually with the rest of the values being 0 each will change the fractal differently each (I haven't noticed any similarity in these changes).
After the y value raises at around 0.017 - 0.02 (x = 0.3, z = 0, w = 0) you get this nice shape that is filled with differently sized tunnels.
The shape in the center of the screenshot is one of those objects on the sides that has changed beyond recognition. It has merged with the object on the other side forming this land where I stood. (they are actually disconnected at y = 0.017 and below, also at the larger scales)^
This is another one of those side objects that got even smaller than their discs (the disc structure that can be seen in the middle of the objects on the 1st screenshot). And a pillar has grown below it.^
Anyway, there is just too much to be explored here. And the fact that these fractals are rarely usable as a terrain for minetest makes them even less popular. Also the fact that I probably have no idea what I am doing, but its fun so I don't really care :)