A mere five years

[hobold]

A mere five years *cough* after the first idea for monopolar spherical coordinates ... and after a mere three months *cough* of computation time, here is finally a very detailed - and colorful! - look at the Riemandelettuce. It might have been new and interesting if I had presented it five years earlier, but now it is still a sixty second loop of mildly exotic eye candy:

http://vectorizer.org/rmdltc/AutumnTrappingsHD01.mp4

(It might take a while to download to 80MB from my humble virtual server, so you better save to your local disk before playback.)


The object is the Riemandelettuce (that apparently I'm still obsessed with), rendered with a heavily evolved version of Syntopia's brute force ray sampling. Color comes from two spherical orbit traps, and lighting is again based on Syntopia's description of a simple screen space fake of ambient occlusion. Furthermore, I used 3x3 supersampling to capture the detail at an iteration depth of ten (unfortunately I forgot to gamma-correct here, but only noticed it halfway through the computation; so the anti-aliasing is not as effective as it could be).

There is still a bit of flicker at the outlines of very thin structures, but that is a fundamental problem of brute force ray sampling.

[Chillheimer]

nice!
why are you obsessed with that fractal? could you explain what is so special about it for you?

[hobold]

I don't feel obsessed or compelled. As the person who first suggested monopolar spherical coordinates here, I somehow see myself as responsible for exploring and showing it around. But it is slow to render; maybe I should spend my time trying to understand the math better. If I could come up with a reasonably good distance estimation function, I could sort of delegate the exploration to everyone who is interested.

If there is any obsession, it is still with the "holy grail". The Riemandelettuce isn't it, but in my eyes, it seems more detailed and more varied than the original Mandelbulb. The Mandelbox still wins the top spot in three dimensions, though.

[quaz0r]

nice 

[mclarekin]

@ hobold.     Cool to see it in action.  I have not got this one coded properly yet, but I am getting close to understanding it .  So I am guessing there is probably  a lot of exploring still to do with this coordinate system.


this Reply #43 post was very helpful
http://www.fractalforums.com/index.php?topic=2424.msg12027#msg12027


BTW  should Ay *= 8.0 be Az .....

Code:

 // manipulate Ax, Az here
    // for example the standard emulation of an eighth power:
    Ax *= 8.0;
    Ay *= 8.0;

[hobold]

BTW  should Ay *= 8.0 be Az .....

Code:

 // manipulate Ax, Az here
    // for example the standard emulation of an eighth power:
    Ax *= 8.0;
    Ay *= 8.0;

Yes, you found a bug! You are right, it should be Ax and Az in that spot.

Fortunately, my actual rendering code does the right thing ... phew.