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Author Topic: An escape time algorithm for Kleinian group limit sets  (Read 64249 times)
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JosLeys
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« Reply #45 on: December 24, 2016, 02:00:19 PM »

I made a version of the frag file that allows to rotate objects obtained by sphere inversions. (and eventually turn it into an animation)
The following two animations were made with this:

https://dl.dropboxusercontent.com/u/107725368/teapot01.mov
https://dl.dropboxusercontent.com/u/107725368/curls01.mov

Merry Christmas!

Jos


* teapot001.jpg (69.41 KB, 976x684 - viewed 343 times.)
* Kleinian_Jos_001.frag (8.28 KB - downloaded 198 times.)
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Crist-JRoger
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« Reply #46 on: December 24, 2016, 02:35:14 PM »

That's great! Thank you very much  wink
Another one, quick render (can't stop  grin)



Merry Christmas!
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Crist-JRoger
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« Reply #47 on: December 24, 2016, 03:14:44 PM »

Final_Iterations helps like alternative of FudgeFactor
FourGen kills shadows  :- strange



* 111.jpg (121.49 KB, 900x450 - viewed 249 times.)
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Aexion
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« Reply #48 on: December 24, 2016, 03:15:17 PM »

This Fractal is Incredible!!  smiley
Many Thanks to Jos and and Knighty for this creation!!
I toyed with it and made a little variation with the sphere inversion, rotating p by an angle in one of the axes.

Merry Christmas!

* Kleinian test1.frag (11.61 KB - downloaded 188 times.)

* KleinianTest.png (123.58 KB, 512x479 - viewed 279 times.)
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Sabine
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« Reply #49 on: December 25, 2016, 12:20:41 AM »



Gotta love this formula! Thanks again! smiley
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sabine62.deviantart.com
knighty
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« Reply #50 on: December 26, 2016, 01:08:09 PM »

Wow! So beautiful renders! Klein and Poincaré Would have loved to see such pictures by their own eyes.

@Crist-JRoger :
The shadows look like that because the spheres are very thin. Cool effect nevertheless. I guess, you are using Eiffie's shadow.

@lycium:
This is probably the most accurate view of a 3D kleinian group limit set. How much time did it take to render?

Happy holidays and new year!
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #51 on: December 26, 2016, 03:45:27 PM »

Knighty Lyc is experimenting with his own soft but idk well what it does and how it works smiley
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taurus
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« Reply #52 on: December 26, 2016, 04:58:25 PM »

Wowzzze, congrats guys! this is incredible! I was abscent some time here and now this...
Seldomly saw an innovation with that aesthetic potential.  A Beer Cup
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Crist-JRoger
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« Reply #53 on: December 26, 2016, 08:30:01 PM »

Hybrid of course  embarrass Quick render
Replaced sphere to Knighty's voxel. This fractal more natural and organic, great for hybrids )



and again  smiley

« Last Edit: December 26, 2016, 09:09:54 PM by Crist-JRoger » Logged

M Benesi
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« Reply #54 on: December 26, 2016, 11:01:46 PM »

very nice Crist!
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trafassel
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trafassel
« Reply #55 on: December 27, 2016, 10:00:33 AM »

Knighty, thank you for the spirals.


* Data111pic10028s256.jpg (253.69 KB, 1200x1200 - viewed 319 times.)
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Tim Emit
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« Reply #56 on: December 27, 2016, 12:16:51 PM »

This is fantastic, really beautiful., here was I mucking about with the Mandelcup and this was going on.. Thanks everyone, this will be fun cheesy Seasons best y'all afro
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Caleidoscope
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« Reply #57 on: December 27, 2016, 03:52:46 PM »

It is definitly if somebody opened a hidden treasurybox.  It stunningly beautiful and I enjoy each and every one of them!  Have fun wink  A Beer Cup
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JosLeys
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« Reply #58 on: December 28, 2016, 11:58:53 PM »

Here are three Shadertoy implementations:
https://www.shadertoy.com/view/XlVXzh
https://www.shadertoy.com/view/MtKXRh
https://www.shadertoy.com/view/llKXRh
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Imagyx
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Finally 3D and more... Thank you !! ;-)


« Reply #59 on: December 29, 2016, 12:14:27 PM »

Thank you for making a shadertoy implementation  smiley
This makes it a lot easier for me to look for errors in my own implementation.
There must be something I'm missing.
I'm using the code from shadertoy as well as the fragmentarium script from the Kleinian thread
instead of the mandelbox distance estimation, which works fine.
And all I get is this image with my code looking like that:

Code:
kl = new V2D(1.95, 0.03);
b_a = kl.y / kl.x;
box = new V2D(1.0);
extraIter = 5;
balls = true;
fourGen = false;
clamp = new V2D(0.3, 2.0);
doInv = false;
invCenter = new V3D(1, 0.96, 0);
invR = 1;
recenter = new V3D(0);

void DE() {
V3D p = previous.ergebnis;
V3D q = p.copy();
V3D lz = q.getAdd(V3D.V1);
V3D llz = q.getSub(V3D.V1);
DF = 1.0;
double DE = 1e10;
double f = Math.signum(kl.y);
for(int i = 0 ; i < maxIterM ; i++){
q.x = q.x + b_a * q.y;
if(fourGen){
q.x = wrap(q.x, 2.0 * box.x, -box.x);
q.x = wrap(q.y, kl.x, 0);
q.x = wrap(q.z, 2.0 * box.y, -box.y);
}else{
q.x = wrap(q.x, 2.0 * box.x, -box.x);
q.x = wrap(q.z, 2.0 * box.y, -box.y);
}
q.x = q.x - b_a * q.y;
if(q.y >= kl.x * (0.5 + f * (2.0 * kl.x - 1.95) * 0.25 * Math.signum(q.x + kl.y * 0.5) * (1.0 - Math
.exp(-(7.2 - (1.95 - kl.x) * 15.0) * Math.abs(q.x + kl.y * 0.5))))){
q.x = -kl.y - q.x;
q.y = kl.x - q.y;
q.z = -q.z;
}
q = TransA(q);
V3D tmp = q.getSub(llz);
if(tmp.dot(tmp) < 1e-5){
break;
}
llz = lz;
lz = q;
}
double y = balls ? Math.min(q.y, kl.x - q.y) : q.y;
DE = Math.min(DE, Math.min(y, clamp.x) / Math.max(DF, clamp.y));
dist = DE;
hitMat = mat;
}

private V3D TransA(V3D q) {
double r = 1.0 / q.dot(q);
q.mult(-r);
q.x = -kl.y - q.x;
q.y = kl.x + q.y;
DF *= r;
return q;
}

private double wrap(double x, double a, double s) {
x -= s;
return x - a * Math.floor(x / a) + s;
}

I have a near (10) and far (50) clipping plane which results in the same behaviour as the slice_end and start variables in shadertoy.


* P3D_2016.12.29_12.07.19.png (12.17 KB, 300x200 - viewed 1054 times.)
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