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Author Topic: An escape time algorithm for Kleinian group limit sets  (Read 8718 times)
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pupukuusikko
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« Reply #15 on: October 31, 2016, 11:57:05 AM »

..
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!
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knighty
Fractal Iambus
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Posts: 818


« Reply #16 on: December 18, 2016, 03:48:20 PM »

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





Still not perfect, but It is wonderful!
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quaz0r
Fractal Molossus
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« Reply #17 on: December 18, 2016, 04:29:22 PM »

DAMN those are great!   shocked
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hobold
Fractal Bachius
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Posts: 570


« Reply #18 on: December 18, 2016, 04:32:29 PM »

Breathtaking!

I'm curious how this works. smiley
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3dickulus
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Posts: 1555



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« Reply #19 on: December 18, 2016, 06:26:38 PM »

Awesome, like watching a butterfly emerge from it's cocoon.
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Resistance is fertile...
You will be illuminated!

                            #B^] https://en.wikibooks.org/wiki/Fractals/fragmentarium
DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #20 on: December 18, 2016, 07:33:18 PM »

Oh nooo too awesome... I am having a heart attack cry gimmegimme  embarrass kiss
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No sweat, guardian of wisdom!
knighty
Fractal Iambus
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Posts: 818


« Reply #21 on: December 18, 2016, 07:58:30 PM »

All the merit goes to Jos Leys. He did all the hard work.
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KRAFTWERK
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Posts: 1439


Virtual Surreality


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« Reply #22 on: December 19, 2016, 07:56:43 PM »

HOLY.... Stuff!  afro Fantastic work!  A Beer Cup
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knighty
Fractal Iambus
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Posts: 818


« Reply #23 on: December 19, 2016, 08:41:22 PM »

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.  praying
The second one was "rewritten" in order to look better as glsl code. It may look obfuscated or better grin.

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. smiley

* Kleinian_test.frag (8.54 KB - downloaded 87 times.)
* Kleinian_test15-bis.frag (13.87 KB - downloaded 85 times.)

* Kleinian-jos-Inv-20.jpg (102.61 KB, 1280x720 - viewed 86 times.)
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M Benesi
Fractal Schemer
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« Reply #24 on: December 19, 2016, 11:29:23 PM »

Wow!@#!@#  cheesy
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JosLeys
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Posts: 258


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« Reply #25 on: December 19, 2016, 11:52:20 PM »

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.


* atest_hybrid025L.jpg (152.38 KB, 1024x768 - viewed 102 times.)

* atest_hybrid027L.jpg (101.77 KB, 1024x768 - viewed 98 times.)
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JosLeys
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« Reply #26 on: December 20, 2016, 12:15:41 AM »

Here is a small animation :  https://plus.google.com/+josleys/posts/QtfH3gjyXpg
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M Benesi
Fractal Schemer
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Posts: 1074



WWW
« Reply #27 on: December 20, 2016, 03:20:06 AM »

Elephants... 
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KRAFTWERK
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Posts: 1439


Virtual Surreality


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« Reply #28 on: December 20, 2016, 08:33:16 PM »

I
AM
SPEACHLESS...

LUCA!!!!!  

horsie riding run over sweet music
Great work Knighty & Jos!
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knighty
Fractal Iambus
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Posts: 818


« Reply #29 on: December 20, 2016, 08:37:20 PM »

LUCAAAA!!!!!!!!  grin
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