• May 22, 2022, 10:05:36 AM

Author Topic:  Rendering Kleinian limit sets in blender  (Read 707 times)

0 Members and 1 Guest are viewing this topic.

Offline xenodreambuie

  • Fractal Feline
  • **
  • Posts: 190
Re: Rendering Kleinian limit sets in blender
« Reply #15 on: February 17, 2022, 07:20:17 AM »
Here's how I think it works. You have six images, one for each Moebius transform, and they are initialized to constant dark grey.
At each iteration, each image gets a different combination of transforms, and what is plotted is some combination of images. I can't decipher the specifics. As usual with an IFS, the density at each pixel converges to where the set is, so it stabilizes after some number of iterations, unless the combination of parameters is unstable. You don't have to worry about inverting circles because circle inversion is part of the Moebius transforms. So you need to be doing something like that, but with the right details.

Offline JosLeys

  • Fractal Friend
  • **
  • Posts: 10
Re: Rendering Kleinian limit sets in blender
« Reply #16 on: February 17, 2022, 05:52:05 PM »
Well I have no idea how things work in Blender, so I cannot help you there, sorry!

Offline shapeweaver

  • Fractal Fanatic
  • ***
  • Posts: 37
Re: Rendering Kleinian limit sets in blender
« Reply #17 on: February 22, 2022, 07:07:47 AM »
So, blender's procedural texture nodes let you make loops? How?


Online claude

  • 3f
  • ******
  • Posts: 2202
    • mathr.co.uk
Re: Rendering Kleinian limit sets in blender
« Reply #19 on: February 22, 2022, 08:58:54 PM »
or use cube-map textures for the Riemann sphere...

Offline IgorZdrowowicz

  • Fractal Friend
  • **
  • Posts: 10
  • computable consciousness
Re: Rendering Kleinian limit sets in blender
« Reply #20 on: February 23, 2022, 05:37:34 PM »
So, blender's procedural texture nodes let you make loops? How?

There are no loops implemented but if you implement a function/transformation of initial uv coordinates (used mainly to align textures, normal maps etc) in math nodes than you can simply copy it n times. In my case i just dont know how to make setup for mobius transforms that converges to anything. I get some results by applying modulus before or after the transformation but i get discontinuity along the fractals. I know that there has to be some way of transforming simple xy coordinates to crteate kleinian fractal. My research will not stop untill i get it. Im even ready to pay a good money just to have setup for double cusp.

or use cube-map textures for the Riemann sphere...

Im not sure exactly what You mean. Blender does not support cube maps as far as im aware. It would not change anything in my case as i can simply take input called "reflection" instead of uv coord and i get similar effect to a cubemap but it still won't allow me to iterate mobius to create any limit set :(

This may help:
Lawlor, Orion. (2012). GPU-Accelerated Rendering of Unbounded Nonlinear Iterated Function System Fixed Points. ISRN Computer Graphics. 2012. 10.5402/2012/825782.
 :educated:  :lol:

I will definitely take a look with hopes to understand this :D But im a simple man and if there is no xy formula - i will fail xD

Offline IgorZdrowowicz

  • Fractal Friend
  • **
  • Posts: 10
  • computable consciousness
Re: Rendering Kleinian limit sets in blender
« Reply #21 on: May 08, 2022, 09:17:47 AM »
Problem solved! I used the Jos Leys method and it works perfectly!



clip
3D limit sets of Kleinian groups webpage

Started by JosLeys on UltraFractal

3 Replies
651 Views
Last post September 26, 2017, 07:57:07 PM
by timemit
clip
found another precision limit issue

Started by Mr Rebooted on Kalles Fraktaler

6 Replies
630 Views
Last post October 16, 2021, 03:55:54 PM
by claude
xx
Gallery Upload limit time interval calculation?

Started by Anon on Forum Help And Support

0 Replies
262 Views
Last post March 12, 2018, 01:35:49 PM
by Anon
xx
Resolution limit?

Started by ThunderboltPagoda on Forum Help And Support

7 Replies
568 Views
Last post November 01, 2018, 12:08:12 AM
by ThunderboltPagoda
clip
3D Kleinian animated gif

Started by JosLeys on UltraFractal

3 Replies
533 Views
Last post November 20, 2017, 11:28:10 AM
by JosLeys