An escape time algorithm for Kleinian group limit sets

[pupukuusikko]

..
Below is another view (with occasional overstepping due to inadequate DE)...and it's not extruded!

This is absolutely wonderful, congrats on the great discovery!

[knighty]

After a little (long) discussion with Jos Leys, some results:





Still not perfect, but It is wonderful!

[quaz0r]

DAMN those are great!   

[hobold]

Breathtaking!

I'm curious how this works.

[3dickulus]

Awesome, like watching a butterfly emerge from it's cocoon.

[DarkBeam]

Oh nooo too awesome... I am having a heart attack gimmegimme 

[knighty]

All the merit goes to Jos Leys. He did all the hard work.

[KRAFTWERK]

HOLY.... Stuff!  Fantastic work! 

[knighty]

Here are the fragmentarium shaders:
The first is from Jos Leys which don't work on my PC for unknown reason. I put it here especially for darkbeam in order to make a formula for MB3D and  mclarekin to include it in mandelbulber. 
The second one was "rewritten" in order to look better as glsl code. It may look obfuscated or better .

It is still work in progress. There are some ideas to try in order to make it faster / have better DE.

The algorithm is very simple. The main idea is to use a "line of separation" in order to choose the transformation to apply. In those shaders, the line is approximated by a simple sinusoid. IMHO, it is related to "Schottky blobs" as described in this article (see for example figure 2). The drawback of this method is that in most cases the fractal will have cuts... but the cases where it works well is already huge.

[M Benesi]

Wow!@#!@# 

[JosLeys]

Well, the title of this series of posts has become a bit of a misnomer, as the actual algorithm that produces these 3D type images is not of the escape type.
Points do not escape outside some bailout, and in fact the distance estimate is a bit peculiar.

In parallel with the Fragmentarium code that Knighty and myself worked on, I also have an implementation in Ultrafractal, which of course is much slower. On the other hand it is stable, which cannot be said of the frag code. Overdoing the number of iterations there can easily run into trouble with the responsiveness of the graphics card. Having said that, further improvements are certainly possible.

The images below were done in Ultrafractal. The first shows the basic configuration. The second shows what can be achieved by a sphere inversion.

[JosLeys]

Here is a small animation :  https://plus.google.com/+josleys/posts/QtfH3gjyXpg

[M Benesi]

Elephants... 

[KRAFTWERK]

I
AM
SPEACHLESS...

LUCA!!!!!  


Great work Knighty & Jos!

[knighty]

LUCAAAA!!!!!!!!