Riemandelettuce

[hobold]

To break my death grip on Timeroot's thread about alternate coordinate systems (http://www.fractalforums.com/theory/alternate-co-ordinate-systems/), I decided to start a new thread here. Not sure if I should have stayed in the sub-forums of the Mandelbulb department. But the fact remains that this fractal isn't quite the Mandelbulb, despite stealing all of those ideas. :-)

For explanations, formulas and even a few first tantalizing images, refer to Timeroot's linked thread above.

Now on to the new information. As I was debugging my own rendering code, I stumbled upon an odd and interesting image of what seems to be the inside of the riemandelettuce. The image itself doesn't have a straight forward meaning as an inside view, but is more of a weird kind of volume rendering, so take the appearing shapes with a grain of salt.

I found it noteworthy to see that there is a very large amount of "dust" filling the space between the minibulbs, obscuring the shape of the solid inside. A relatively high number of iterations is required to get sharply defined outlines of the solid inside (more than 100 in this case).

[kram1032]

Looks promising, however, it needs a non-Zdepth-only render

[hobold]

Oh, I can render the usual outside views by now. They are not as pretty as the pictures done already by other people, but they suffice as evidence that at least three different rendering algorithms agree on essentially the same shape. (With a shifted coordinate origin in this particular example, which is why it isn't perfectly symmetrical.)

But I need to extend my distance transform to a signed distance transform, and I need to somehow isolate the solid from the dust in order to render surface views of the solid core of the riemandelettuce.

[hobold]

Okay, at long last, here is the first animation of the riemandelettuce. No artistic value, and the lighting is more of a bug rather than a feature.

http://www.vectorizer.org/riemandel1.mpg   (3 megabytes)


The underlying voxel cube was sampled with 1000^3 voxels, with an iteration depth of 1000 iterations. The coordinate origin was slightly offset to break the perfect symmetry. I guess sampling missed thin sheets and filaments, which is why the north pole looks quite different than Jesse's renderings. Still, there are a lot of bits and pieces, and the overall feel is more solid than dusty. The arches between the 'bulbs are a nice touch.

[kram1032]

I actually meant, that volume/inside/whatever-render should not only be a Z-depth-like render which doesn't show that many details...
The animation looks nice

[hobold]

The same in "high definition": http://www.vectorizer.org/riemandel1hd.mp4  (12 megabytes)

[kram1032]

looks really good

[hobold]

Okay, here's the promised "too high definition" version.

The rotation is a bit slower, and the object tumbles so that you can take a close look at the pole and the antipole. The underlying volume was sampled on a 1600^3 grid. The 2d views were rendered with 4x4 supersampling on a jittered grid (to reduce the aliasing caused by the high voxel resolution). The lighting is still buggy, and no concern has been given to aesthetics. The bit rate is rather high, because some of my local friends complained about compression artifacts.

http://www.vectorizer.org/riemandeltumble2hd.mp4   (WARNING! 99 megabytes for an 1m20s loop)

This is pretty much the resolution limit for my brute force approach. As much as I would like to do close-ups and fly-bys, I cannot really do that with my current code base.


BTW, to those of you who are hunting for formulas with their own programs: if you are interested in doing quick and dirty animations (like the ones I have shown here), I would be willing to share my code. I am not particularly proud of it, but with a bit of cleaning up, I could probably let it loose upon the world without causing too many headaches ...

My code consists of a number of command line tools written for a unix environment, with the only "user interface" to speak of being a makefile. There are probably a few BSDisms in there that need fixing for Linux, but nothing too major.

If you are interested in toying with this kind of thing, drop me a note or a reply.

[KRAFTWERK]

Really nice render Hobolt!

I see what you mean, that this thing is really noisy and it would be interesting to see the shapes of the inside...

There seems to be a lot of unconnected parts, is it so or are they really connected?

[hobold]

I suspect that all the chunks are connected by thin sheets or filaments. But my algorithm cannot capture such structures, they are lost between the sampled grid points.

[hobold]

I must apologize that I cannot uphold the artistic standards that many other fractal explorers are setting. But my first glimpse on the back side of the antipole was just too surprising to withhold it. This is part of the riemandelettuce as seen from outside and inside. Reminds me of classical architecture, but without columns to carry the dome.

http://www.vectorizer.org/insideAntipole.mp4 (15 megabytes)

[Jesse]

I must apologize that I cannot uphold the artistic standards that many other fractal explorers are setting.

Hobold, that is absolutely not true, its a different thing to display such details in comparison to the DE thresholded images.
If i would try to get this informations, i wouldnt get as good results as you!

But my first glimpse on the back side of the antipole was just too surprising to withhold it. This is part of the riemandelettuce as seen from outside and inside. Reminds me of classical architecture, but without columns to carry the dome.

http://www.vectorizer.org/insideAntipole.mp4 (15 megabytes)

Great, are these little dots caves inside the bulb?

[hobold]

Great, are these little dots caves inside the bulb?

Some of the little bubbles should be cavities (not all of them; some are clearly an artifact of cutting the shape open). That's if my code is free of bugs. But I personally would not bet on it.

I have done a similar animation of the polar region, but that one looks less interesting. And it exhibits some very obvious render bug, where apparently some rays overshoot and miss the surface. In theory, it should be impossible for my algorithm to overstep, but obviously theory and practice are the same thing only in theory. :-)

[kram1032]

A very nice video

[hobold]

its a different thing to display such details in comparison to the DE thresholded images.
If i would try to get this informations, i wouldnt get as good results as you!

Well, most of what I present here are drafts. You and others put a lot more energy into finding good view points than I do. Instead of fixing the bugs in my renderer, I breathlessly throw more half-baked animations at you.

My renderer doesn't even provide any good depth cues. Except movement, that is. But if you halt one of my animations, the image immediately falls flat. Nor did I try to use colour to emphasize structures, like most of you are doing. So I am quite sure that I can objectively prove that my production of flickering pixels so far is just not in the same ballpark, with regards to the quality of visualization.

Maybe I am just too lazy, but I don't feel like I can ever catch up with the intuition for beauty that other fractal explorers have achieved. And so I set another goal for myself: produce images that are just good enough to pique the curiosity of you guys. If I can provide you with some inspiration for your work, the net result will be more numerous and more interesting imagery than if I strive to do it all perfect by myself.