In 2009 some guys (Daniel White, Paul Nylander and others) developed a kind of
3-space version of the mandelbrot set by trying to simulate the operations
within the (two dimensional) complex numbers with polar coordinates. As I
understood their approach so far.

At the end of this year (2009) David Wagner (waggy) proposed an implemtation
with POV with isosurfaces using (illegal, but still working) recursive function
calls at the newsgroups. Tor Olav Kristensen was so kind, to give an iterative
alternative to the recursive algorithm. Both sources can be found at:

http://news.povray.org/povray.binaries.scene-files/thread/%3C4b2c7b3f%40news.povray.org%3E/

Now I found this old treasures and played a little bit around with them. The
main parameters I changed was the iteration depth and the treshhold of the
isosurface used, which proved the more interesting issue. Here is a first close
up. I hope you enjoy it like me. I used Tor Olav's (POV-legal) version for this
images.

The texture is a very simple slope-pattern so far. The direction of the slope
pattern is choosen as the direction from  camera position to camera look at
which happens to be z in this case. red violet marks areas with normals opposing
z (slope=0), cyan marks areas perpendicular to z (slope=0.5), dark cyan is in
the middle of both (slope=0.25). In this situation slope values
above 0.5 are not visible.

Best regards,
Michael

Post a reply to this message

Attachments:
Download 'tok_mjf_03_01.png' (2055 KB)

Preview of image 'tok_mjf_03_01.png'

Fascinating indeed. I wonder: has the mandelbulb code as used by Sam 
Benge in particular ever been posted here? And how about those by Scott, 
James Holsenback, or PM2Ring? Possibly those were not pure POV-Ray codes 
but only rendered here. I don't remember.

-- 
Thomas

Post a reply to this message

Thomas de Groot <tho### [at] degrootorg> wrote:
> Fascinating indeed. I wonder: has the mandelbulb code as used by Sam
> Benge in particular ever been posted here? And how about those by Scott,
> James Holsenback, or PM2Ring? Possibly those were not pure POV-Ray codes
> but only rendered here. I don't remember.
>
> --
> Thomas

Thank you Thomas. I'm just playing around. Works about mandelbulbs by James
Holsenback or Samuel Benge are unknown to me and Google (the search engine
within the newsgroups) yields nothing about mandelbulbs and their names. The
only other POV-code I've noticed so far is using df3-files as function pattern
within an isosurface (PM2Ring and others). But their df3 is generated outside of
POV. In fact I'm searching for a special view but I fear I can only tell after
I've found it.

Here is a fifth order mandelbulb using the positive z-component method as Paul
Nylander (a.k.a. bugman) put it. Lighting and background adopted from Tor Olav
Kristensen. I added only a little bit of radiosity. The texture is very simple
in this case (color Cyan).

Best regards,
Michael

Post a reply to this message

Attachments:
Download 'mb_pow5.png' (842 KB)

Preview of image 'mb_pow5.png'

On 8-4-2015 7:38, MichaelJF wrote:
> Thomas de Groot <tho### [at] degrootorg> wrote:
>> Fascinating indeed. I wonder: has the mandelbulb code as used by Sam
>> Benge in particular ever been posted here? And how about those by Scott,
>> James Holsenback, or PM2Ring? Possibly those were not pure POV-Ray codes
>> but only rendered here. I don't remember.
>>
>> --
>> Thomas
>
> Thank you Thomas. I'm just playing around. Works about mandelbulbs by James
> Holsenback or Samuel Benge are unknown to me and Google (the search engine
> within the newsgroups) yields nothing about mandelbulbs and their names. The
> only other POV-code I've noticed so far is using df3-files as function pattern
> within an isosurface (PM2Ring and others). But their df3 is generated outside of
> POV. In fact I'm searching for a special view but I fear I can only tell after
> I've found it.

I have a collection of images made over the years by the POV community. 
Unfortunately, I did not save the dates, only the maker's names, so I 
cannot tell you /when/ mandelbulb explorations took place here. Maybe 
Yadgar knows. He is a more complete collector than I am :-) However, my 
feeling is that the mandelbulbs were not generated by POV-Ray.

>
> Here is a fifth order mandelbulb using the positive z-component method as Paul
> Nylander (a.k.a. bugman) put it. Lighting and background adopted from Tor Olav
> Kristensen. I added only a little bit of radiosity. The texture is very simple
> in this case (color Cyan).
>
Ah yes, the familiar shape. I like it.

-- 
Thomas

Post a reply to this message

Hi(gh)!

On 08.04.2015 09:23, Thomas de Groot wrote:

> I have a collection of images made over the years by the POV community.
> Unfortunately, I did not save the dates, only the maker's names, so I
> cannot tell you /when/ mandelbulb explorations took place here. Maybe
> Yadgar knows. He is a more complete collector than I am :-)

The earliest Mandelbulb posting in my collection dates from November 19, 
2009 - a scene rendered by Scott...

See you in Khyberspace!

Yadgar

Post a reply to this message

On 08/04/2015 15:28, Jörg 'Yadgar' Bleimann wrote:
> Hi(gh)!
>
> On 08.04.2015 09:23, Thomas de Groot wrote:
>
>> I have a collection of images made over the years by the POV community.
>> Unfortunately, I did not save the dates, only the maker's names, so I
>> cannot tell you /when/ mandelbulb explorations took place here. Maybe
>> Yadgar knows. He is a more complete collector than I am :-)
>
> The earliest Mandelbulb posting in my collection dates from November 19,
> 2009 - a scene rendered by Scott...
>

I remember some discussion around about the time I was playing with the 
code for a cubic Mandelbrot that Andrew posted. That was in 2005 and 
2007/8. Going by the file dates.

As an aside. I thought that off topic posts expired after a short while. 
But I can find posts as early as 2006 on the web interface.

-- 

Regards
     Stephen

Post a reply to this message

Stephen <mca### [at] aolcom> wrote:
> On 08/04/2015 15:28, Jörg 'Yadgar' Bleimann wrote:
> > Hi(gh)!
> >
> > On 08.04.2015 09:23, Thomas de Groot wrote:
> >
> >> I have a collection of images made over the years by the POV community.
> >> Unfortunately, I did not save the dates, only the maker's names, so I
> >> cannot tell you /when/ mandelbulb explorations took place here. Maybe
> >> Yadgar knows. He is a more complete collector than I am :-)
> >
> > The earliest Mandelbulb posting in my collection dates from November 19,
> > 2009 - a scene rendered by Scott...
> >
>
> I remember some discussion around about the time I was playing with the
> code for a cubic Mandelbrot that Andrew posted. That was in 2005 and
> 2007/8. Going by the file dates.
>
> As an aside. I thought that off topic posts expired after a short while.
> But I can find posts as early as 2006 on the web interface.
>
> --
>
> Regards
>      Stephen

Thanks to you all. So far as I learned the mandelbulb was invented around 2009.
But I think it was the end of a longer ongoing investigation labeled with this
name first in 2009. ATM I'm fascinated by this strange structures yielded from
such a very simple formula. In a way it takes me back over twenty years into the
past when I rendered the mandelbrot set with my amiga long gone.

Best regards,
Michael

Post a reply to this message

On 08/04/2015 18:03, MichaelJF wrote:
> Thanks to you all. So far as I learned the mandelbulb was invented around 2009.

And I was thinking of the Buddhabrot.

  http://en.wikipedia.org/wiki/Buddhabrot



-- 

Regards
     Stephen

Post a reply to this message