An escape time algorithm for Kleinian group limit sets

[Sabine]

@C-JR

[utak3r]

Ok, my turn on Jos' "escape time", this time with some traps.
And ShaderToy's version with some zooming:
https://www.shadertoy.com/view/MdfcRr

[Imagyx]

I had a look at the very first .frag
(http://www.fractalforums.com/index.php?action=dlattach;topic=24728.0;attach=13852)
and the Java code I wrote from that works well.
Therefore I'm not totally stupid  
But I must have misinterpreted something in the later used glsl style code
(http://www.fractalforums.com/index.php?action=dlattach;topic=24728.0;attach=13853)
But I don't know yet what exactly....

https://imagyx.files.wordpress.com/2017/02/p3d_2017-02-10_18-55-29.png

[3dickulus]

@utak3r I converted your ShaderToy script to Fragmentarium

[utak3r]

Great    I haven't looked at Fragmentarium yet, unfortunately. Probably will have to do it finally 

Anyway, here's a 3D version, with some fake ambient occlusion and very fake environment mapping.
Fullsize can be seen here or here.
BTW, I have really big problems with a gallery here in our forum... many images just don't show (404). Strange...  Also, most of the times I'm unable to attach images.

[Crist-JRoger]

Tried add this coloring  
2 archives: DE-Kn2 and mine DE-Kn10 (slower)

[mclarekin]

@ crist-JRoger.


This image looks GREAT .

I love the circles amongst the standard  klienian formations

[Efoia]

Looks very ornate, thanks for the DE!!  (Also managed to figure out sphere inversion thanks to that frag)

[Sabine]

@C-JR Fantastic frag , I will take a closer look!

@Efoia Very nicely done render! Which program did you use?

[Efoia]

@Efoia Very nicely done render! Which program did you use?

Thanks!  I used my own software I'm developing.

[Sabine]

@Efoia Good luck then, looks very promising!

[DarkBeam]

Efoia I remember your program pls finish it 

[Crist-JRoger]

Played some with Kleinian 2D here above, added some colors, and then desided to convert Jos Leys shader by myself ) So add more colors too. Thanks to Jos Leys and Kali for great shaders and fractals!

[ericr]

if A=mat(t,-i,-i,0) and B=mat(1,2,o,1)
then tr(A^n*B^p)=2  give us a polynome p(t)
if I find t a have a cuspid

I use  wxMaxima a free software like "maple" formal cacul
It is a god think ??

[JosLeys]

I can send you a list of 19.000 values for t that generate cusps if you are interested.
No need to calculate them yourself.
Mind you, the current state of the algorithm as you find it in Fragmentarium or M3d will not allow to draw 'cusped' situations correctly as the 'separation line' gets very complicated.