Ideas on 3d Apfelmännchen

  • 21 Replies
  • 240 Views

0 Members and 1 Guest are viewing this topic.

Offline jukzi

  • *
  • Fractal Freshman
  • *
  • Posts: 9
« on: May 22, 2020, 10:12:29 PM »
Hi,
As far as i know its proven to be impossible to calculate a Mandelbrot in 3D as in 2D.
However it should be possible construct a solid that looks like the inner set by replacing circles with spheres. The circles in the 2d mandelbrot look like they are placed like Ford circles projected on a circle (or cardioid for the root). So i tried it using Ford spheres projected on a sphere (/extruded cardioid). And of cause recursivly subsituting any sphere with the same.
I did not find similar work like that. What do you think about the idea?
The main task to get a more beautiful picture would be to get an idea how to draw the spheres:
1. The spheres are not dense enough to look like a solid surface.
2. The main beauty of a Mandelbrot are the colors outside the actual set. In 3d one could calculate a color value for each voxel based on the distance to the next sphere. But the outside of a 3d solid is solid so one could not see it anyway.
3. One can also simply add satellite cardioids above every sphere however i have no idea how to place them so that beautiful spiral forms appear
Any Ideas how to improve?

Linkback: https://fractalforums.org/fractal-mathematics-and-new-theories/28/ideas-on-3d-apfelmannchen/3510/

Offline jukzi

  • *
  • Fractal Freshman
  • *
  • Posts: 9
« Reply #1 on: May 22, 2020, 10:27:50 PM »
another picture with spheres colored by coordinate on the parent surface

Offline hgjf2

  • *
  • Fractal Friar
  • *
  • Posts: 111
« Reply #2 on: May 23, 2020, 08:12:37 AM »
Fine 3D Mandelbrot!! Great!
 :thumbs_up_by_craig_m: :wow:
Can you show whick is the formula for this fractal?
I yet searching formulas for true 3D Mandelbrot set

Offline mclarekin

  • *
  • Fractal Freak
  • **
  • Posts: 710
« Reply #3 on: May 23, 2020, 09:40:28 AM »
super cool O0 O0 O0

it looks a bit like a juliabulb, but it is clearly different

Offline jukzi

  • *
  • Fractal Freshman
  • *
  • Posts: 9
« Reply #4 on: May 23, 2020, 10:06:31 AM »
Can you show whick is the formula for this fractal?

I wrote a hacky java program for it. See attachment.
You can run it with "java -jar apple3dSource.zip" or compile the source yourself

Offline mclarekin

  • *
  • Fractal Freak
  • **
  • Posts: 710
« Reply #5 on: May 23, 2020, 10:45:01 AM »
it should be possible to iterate and render this in Fragmentarium using raymarching and distance estimation. As it is just constructed from primitive spheres following a rule. 

Offline jukzi

  • *
  • Fractal Freshman
  • *
  • Posts: 9
« Reply #6 on: May 23, 2020, 11:04:44 AM »
Im not familiar to Fragmentarium. But as it sounds like a good idea - can you do it please? I dont even know how to draw a simple sphere there.

Offline mclarekin

  • *
  • Fractal Freak
  • **
  • Posts: 710
« Reply #7 on: May 23, 2020, 11:30:15 AM »
i can make a simple sphere but i would have to learn about cardinoids and the mandelbrot set. I will see if I can interest someone who is more clever than me :)

Online C0ryMcG

  • *
  • Uploader
  • *
  • Posts: 159
« Reply #8 on: May 23, 2020, 10:49:10 PM »
i can make a simple sphere but i would have to learn about cardinoids and the mandelbrot set. I will see if I can interest someone who is more clever than me :)

I was curious, so I tried out a few formulas for 3d cardioids.
If you're using ray-marching, I think this as an inside/outside test would work quite well. I looked up a polar formula for cardioids and approached that as a surface of revolution.

It can be easily modified to give distance estimates too, if that's more useful.

Code: [Select]
function isInside(x,y,z){
   var r = (x^2+z^2+y^2)^.5
   var xzR = (x^2+z^2)^.5

   var theta = atan(xzR/p.y);
   if(p.y < 0){theta = theta+3.1415} //(this part can often be replaced by atan2(x,y), when available)

   if (r <  1 - cos(theta)) return true
   else return false
}

x, y, and z may have to be swapped around to get proper orientation.

Offline jukzi

  • *
  • Fractal Freshman
  • *
  • Posts: 9
« Reply #9 on: May 24, 2020, 02:47:42 AM »
great. In Fragmentarium (glsl) that would be like
{code}
float cardioid(vec3 p){
   float r = length(p);
   float xzR = length(vec2(p.x,p.z));
   float theta = atan(xzR,p.y);
   return (r -  (1.0 - cos(theta)));
}
{code}
But the distance estimate looks wrong inside the hole. So if you can please provide a working distance formula for the hole...

Online C0ryMcG

  • *
  • Uploader
  • *
  • Posts: 159
« Reply #10 on: May 24, 2020, 02:59:47 AM »
Hm, are you sure? Other than what looks to me like rendering errors, it seems right to me... What seems wrong about it? Maybe I just can't see it from the one image.

Offline mclarekin

  • *
  • Fractal Freak
  • **
  • Posts: 710
« Reply #11 on: May 24, 2020, 06:15:05 AM »
   return 0.5 * (r -  (1.0 - cos(theta))); // where 0.5 was a guess

or

uniform float DEtweak; slider[0,0.5,1.0]

 
   return DEtweak  * (r -  (1.0 - cos(theta)));

or

reduce fudgefactor on Raytracer tab

Offline hgjf2

  • *
  • Fractal Friar
  • *
  • Posts: 111
« Reply #12 on: May 24, 2020, 07:23:21 AM »
Thanks!

Offline jukzi

  • *
  • Fractal Freshman
  • *
  • Posts: 9
« Reply #13 on: May 24, 2020, 07:53:57 AM »
   return 0.5 * (r -  (1.0 - cos(theta))); // where 0.5 was a guess
Doesnt work when looking from all angles: Near the pole the error getting too big :-(. Furthermore for a recursive definition we need exact values anyway.

Online C0ryMcG

  • *
  • Uploader
  • *
  • Posts: 159
« Reply #14 on: May 24, 2020, 08:09:24 AM »
Well, I looked up info on the main cardioid of the Mandelbrot Set specifically, it looks like it shifts to the right by exactly 0.25, leaving the cusp on the right side at positive 0.25, and its size is multiplied by exactly 0.25 so that it's left side is at -0.75. These values should extend into 3d pretty easily to get an exact position and size for the surface-of-revolution equivalent.

I wouldn't really know what to do to make it render more accurately after this. The math should be solid from this point, so maybe it's just a matter of turning up the settings and choosing an angle that hides the parts that still don't render correctly.


clip
Ich habe das Rätsel um das h�dimensionale Apfelmännchen gel�

Started by trafassel on Fractal Mathematics And New Theories

6 Replies
322 Views
Last post October 17, 2019, 06:23:31 PM
by trafassel
question
Just an ideas about Mandelbulb3D

Started by Alef on Mandelbulb3d

0 Replies
307 Views
Last post December 27, 2018, 03:41:01 PM
by Alef
xx
Mandelbulber - VFX Feature Ideas

Started by stilikon on Mandelbulber

17 Replies
1061 Views
Last post February 07, 2019, 08:45:30 PM
by stilikon
xx
feature request ideas

Started by claude on Fragmentarium

33 Replies
1317 Views
Last post February 09, 2019, 02:33:15 PM
by claude
xx
Feature ideas for Kalles Fraktaler

Started by FractalAlex on Kalles Fraktaler

6 Replies
84 Views
Last post May 27, 2020, 03:19:19 PM
by FractalAlex