Logo by Pauldelbrot - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Did you know ? you can use LaTex inside Postings on fractalforums.com!
 
*
Welcome, Guest. Please login or register. September 23, 2020, 07:26:58 PM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Pages: 1 2 3 [4] 5 6 ... 9   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: An escape time algorithm for Kleinian group limit sets  (Read 18748 times)
0 Members and 1 Guest are viewing this topic.
JosLeys
Strange Attractor
***
Posts: 258


WWW
« 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 228 times.)
* Kleinian_Jos_001.frag (8.28 KB - downloaded 123 times.)
Logged
Crist-JRoger
Fractal Fertilizer
*****
Posts: 389



WWW
« 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!
Logged

Crist-JRoger
Fractal Fertilizer
*****
Posts: 389



WWW
« 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 156 times.)
Logged

Aexion
Conqueror
*******
Posts: 116


The Fractal Hermit


WWW
« 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 125 times.)

* KleinianTest.png (123.58 KB, 512x479 - viewed 184 times.)
Logged

Fractals all the way..
Incendia for 3D Fractals
Aural for Musical Fractals
Sabine
Fractal Fertilizer
*****
Posts: 373



WWW
« Reply #49 on: December 25, 2016, 12:20:41 AM »



Gotta love this formula! Thanks again! smiley
Logged

sabine62.deviantart.com
knighty
Fractal Iambus
***
Posts: 819


« 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!
Logged
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2512


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
Logged

No sweat, guardian of wisdom!
taurus
Fractal Supremo
*****
Posts: 1175



profile.php?id=1339106810 @taurus_arts_66
WWW
« 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
Logged

when life offers you a lemon, get yourself some salt and tequila!
Crist-JRoger
Fractal Fertilizer
*****
Posts: 389



WWW
« 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
Fractal Schemer
****
Posts: 1075



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

very nice Crist!
Logged

trafassel
Fractal Bachius
*
Posts: 531


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

Knighty, thank you for the spirals.


* Data111pic10028s256.jpg (253.69 KB, 1200x1200 - viewed 206 times.)
Logged
Tim Emit
Conqueror
*******
Posts: 111



https://www.facebook.com/
WWW
« 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
Logged
Caleidoscope
Fractal Fertilizer
*****
Posts: 365



WWW
« 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
Logged

"Today you create the memory for tomorrow, be sure to make it a good one"
JosLeys
Strange Attractor
***
Posts: 258


WWW
« 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
Logged
Imagyx
Navigator
*****
Posts: 72


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 727 times.)
Logged

During difficult times, keep steady and play the match.
Pages: 1 2 3 [4] 5 6 ... 9   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
Kleinian Limit Sets Images Showcase (Rate My Fractal) gandreas 9 2820 Last post December 06, 2008, 09:11:43 PM
by _db_
Kleinian Limit Sets Other types fractalrebel 12 5405 Last post December 27, 2009, 09:34:27 PM
by fractalrebel
three more pictures, mandelbrot set, escape time algorithm Images Showcase (Rate My Fractal) Eric B 0 1080 Last post October 23, 2012, 02:03:32 AM
by Eric B
Escape time kleinian (sort of) Other types knighty 8 2650 Last post January 30, 2015, 06:04:50 PM
by knighty
Escape time algorithm defined using the Quotient and remainder functions. (new) Theories & Research mancoast 1 1002 Last post December 06, 2017, 09:50:05 PM
by mancoast

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.215 seconds with 27 queries. (Pretty URLs adds 0.016s, 2q)