i posted earlier saying that i get an error in julia fractals sometimes that
looks like parts of them have been randomly sliced up.  i got a reply, which
i was most grateful for, saying that the putting the camera inside the
bounding sphere of the julia fractal was causing the error.  unfortunately,
when i moved it back to 20 units, i still get the error.  does anyone one
know why?  thanks in advance.  here's my code.

camera{
  location -20*z
  angle 6
}

light_source{
  <-5,0,-20>
  color rgb 1.3
}

julia_fractal{ 
  <-1.154166666666666, -0.25, 0, 0>
  max_iteration 10 
  quaternion
  sqr   
  precision 100
  pigment{rgb <1,.3,.3>}
  rotate<0,80,0>
}

michael

Post a reply to this message

Guess you mean the two ends (-x and +x) that are fragmented into mere
speckles instead of staying solid like the rest.
I really don't have any answer, just want to clarify this for others.
I rotated it 0*y instead of 80*y so it could be seen better where it goes
bad.  From what I've seen of the 'julia_fractal' it is prone to some
calculation precision errors (maybe) or more likely raytraced surface
difficulties, I guess you'd say, tending have some part appear like this,
though that doesn't mean there isn't a solution necessarily.
'iteration', if higher tends to scatter the surface more although dropping
it lower doesn't ever help since you lose the fractaling.  Raising precision
doesn't seem the anwer.
What's happening in your case must be that the sqr function is failing at
those points. Maybe the mathematically inclined will have some observations.

Bob

michael mcknight <nes### [at] ouedu> wrote in message
news:3834e8b5@news.povray.org...
> i posted earlier saying that i get an error in julia fractals sometimes
that
> looks like parts of them have been randomly sliced up.  i got a reply,
which
> i was most grateful for, saying that the putting the camera inside the
> bounding sphere of the julia fractal was causing the error.
unfortunately,
> when i moved it back to 20 units, i still get the error.  does anyone one
> know why?  thanks in advance.  here's my code.
>
> camera{
>   location -20*z
>   angle 6
> }
>
> light_source{
>   <-5,0,-20>
>   color rgb 1.3
> }
>
>
ia_fractal{ 
>   <-1.154166666666666, -0.25, 0, 0>
>   max_iteration 10 
>   quaternion
>   sqr   
>   precision 100
>   pigment{rgb <1,.3,.3>}
>   rotate<0,80,0>
> }
> 
> michael
> 
> 
>

Post a reply to this message

On Fri, 19 Nov 1999 00:07:31 -0600, "michael mcknight" <nes### [at] ouedu>
wrote:

>i posted earlier saying that i get an error in julia fractals sometimes that
>looks like parts of them have been randomly sliced up.  i got a reply, which
>i was most grateful for, saying that the putting the camera inside the
>bounding sphere of the julia fractal was causing the error.  unfortunately,
>when i moved it back to 20 units, i still get the error.  does anyone one
>know why?  thanks in advance.  

Michael,

sorry I mislead you. The problem I pointed out was the most common one
that I had with julias in the past. What you are facing now is a
completely different situation. It is definitely an algorithm flaw.

Change your scene file to this:

camera{
  location <0,0,-23>
  angle 7
  look_at 0
}

light_source{
  <100,100,-1000>
  color rgb 1
}

julia_fractal{ 
  <-1.154166666666666, -0.25, 0, 0>
  max_iteration 4
  quaternion
  sqr   
  precision 200
  pigment{rgb <1,.3,.3>}
  rotate<0,50,0>
  no_shadow
} 


And your command-line settings to this:

+sc0.839063 +sr0.354167 +ec0.959375 +er0.522917 +w4000 +h3000 -a

Notice how the problem starts right where the back, err, edge of the
fractal ends? Like a max_trace_level problem, but vice-versa? It
definitely looks like a ray-shape intersection flaw. The Julia root
finder should work fine, I just can't imagine what drives it nuts in
this case. Sorry, I can't help more without digging into the code
(which I will do now, but it will probably help nothing).

I will try to contact Pascal Massimino and see if he knows more on the
subject. And yeah, I know he's not a Team member anymore.

With that said... well, try to find other beautiful fractals that are



Peter Popov
ICQ: 15002700

Post a reply to this message

On Fri, 19 Nov 1999 03:19:41 -0600, "omniVERSE" <inv### [at] aolcom>
wrote:

>Guess you mean the two ends (-x and +x) that are fragmented into mere
>speckles instead of staying solid like the rest.
>I really don't have any answer, just want to clarify this for others.
>I rotated it 0*y instead of 80*y so it could be seen better where it goes
>bad.  From what I've seen of the 'julia_fractal' it is prone to some
>calculation precision errors (maybe) or more likely raytraced surface
>difficulties, I guess you'd say, tending have some part appear like this,
>though that doesn't mean there isn't a solution necessarily.
>'iteration', if higher tends to scatter the surface more although dropping
>it lower doesn't ever help since you lose the fractaling.  Raising precision
>doesn't seem the anwer.
>What's happening in your case must be that the sqr function is failing at
>those points. Maybe the mathematically inclined will have some observations.

Bob,

What you're seeing is not fractal dust caused by high iteration
settings. Also, the sqr function is a square, not a square root, and
it is defined for any set of numbers I can think of (from natural
numbers to octonions and 64-dimensional complex numbers). What we're
seeing in this image is a root solver problem similar to the specks
one can see on sphere_sweeps, isosurfaces, complex blobs etc.
Unfortunately, there's no 'sturm' keyword for the julia fractal
solver. I dug into the code this morning to no avail, I'll have
another dive tonight.


Peter Popov
ICQ: 15002700

Post a reply to this message

michael mcknight <nes### [at] ouedu> wrote:

> i posted earlier saying that i get an error in julia fractals sometimes
that
> looks like parts of them have been randomly sliced up.  i got a reply,
which
> i was most grateful for, saying that the putting the camera inside the
> bounding sphere of the julia fractal was causing the error.
unfortunately,
> when i moved it back to 20 units, i still get the error.  does anyone one
> know why?  thanks in advance.  here's my code.
>
> camera{
>   location -20*z
>   angle 6
> }
>
> light_source{
>   <-5,0,-20>
>   color rgb 1.3
> }
>
>
ia_fractal{ 
>   <-1.154166666666666, -0.25, 0, 0>
>   max_iteration 10 
>   quaternion
>   sqr   
>   precision 100
>   pigment{rgb <1,.3,.3>}
>   rotate<0,80,0>
> }
> 
> michael
> 

First: Thanks for the e-mail
          (you could have put it in the NG, though,
          I usually check for answers for a few days at least).

Now, when it comes to fractals
I just _have_ to get my (less than) 2 cents worth into the discussion ;)

IMHO the most probable cause of this is the distance estimator used
for quaternion fractals. As the name says, it's an estimate, and - according
to Peitgen's and Saupe's "Science Of Fractal Images" - really accurate
only for high iteration values.

Besides, I'm missing a factor of 0.5 in the implementation of the formula,
making the estimates twice as big as they should be (provided I'm right).

-- 
Gerald
ger### [at] aonat

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Sorry I even spoke about this really, all my mathematic knowledge can
balance well on the head of a pin, unless compared to others in my family or
friends but not compared to many of you here.

Bob

Peter Popov <pet### [at] usanet> wrote in message
news:J3U1OFKMRB7+SjAPKXKXnGnLGBi3@4ax.com...
> On Fri, 19 Nov 1999 03:19:41 -0600, "omniVERSE" <inv### [at] aolcom>
> wrote:
>
> >Guess you mean the two ends (-x and +x) that are fragmented into mere
> >speckles instead of staying solid like the rest.
> >I really don't have any answer, just want to clarify this for others.
> >I rotated it 0*y instead of 80*y so it could be seen better where it goes
> >bad.  From what I've seen of the 'julia_fractal' it is prone to some
> >calculation precision errors (maybe) or more likely raytraced surface
> >difficulties, I guess you'd say, tending have some part appear like this,
> >though that doesn't mean there isn't a solution necessarily.
> >'iteration', if higher tends to scatter the surface more although
dropping
> >it lower doesn't ever help since you lose the fractaling.  Raising
precision
> >doesn't seem the anwer.
> >What's happening in your case must be that the sqr function is failing at
> >those points. Maybe the mathematically inclined will have some
observations.
>
> Bob,
>
> What you're seeing is not fractal dust caused by high iteration
> settings. Also, the sqr function is a square, not a square root, and
> it is defined for any set of numbers I can think of (from natural
> numbers to octonions and 64-dimensional complex numbers). What we're
> seeing in this image is a root solver problem similar to the specks
> one can see on sphere_sweeps, isosurfaces, complex blobs etc.
> Unfortunately, there's no 'sturm' keyword for the julia fractal
> solver. I dug into the code this morning to no avail, I'll have
> another dive tonight.
>
>
> Peter Popov
> ICQ: 15002700

Post a reply to this message

all right.  thanks everyone for replying to that and actively mulling it
over.  it sounds like someone with enough knowledge could hack out a patch
to fix the errors if they cared too.  i've got the motivation but,
unfortunately, not the knowhow.  so while i wait for circumstance to pan
out, does anyone know of any other software, commercial or otherwise, that
can ray trace quaternion or hypercomplex julia sets and do other general
raytracing things like euclidean primitives and csg?
thanks a bunch.
michael

Post a reply to this message

michael mcknight <nes### [at] ouedu> wrote:

> all right.  thanks everyone for replying to that and actively mulling it
> over.  it sounds like someone with enough knowledge could hack out a patch
> to fix the errors if they cared too.  i've got the motivation but,
> unfortunately, not the knowhow.  so while i wait for circumstance to pan
> out, does anyone know of any other software, commercial or otherwise, that
> can ray trace quaternion or hypercomplex julia sets and do other general
> raytracing things like euclidean primitives and csg?
> thanks a bunch.
> michael
>

Sorry, none of the programs I know of do _both_ (quaternions and
general raytracing). Commercial rendering packages often come with
pretty "heavy" scripting or shader programming languages, but that
leaves the question if some user already has produced a script/shader for
3d fractal objects for that particular package.

Some of the freeware quaternion 3d programs
(you probably know about these):

FractalZPlot:
http://www-hs.iuta.u-bordeaux.fr/terry/
(This program is able to output WaveFront .OBJ files)

Quat:
http://wwwcip.rus.uni-stuttgart.de/~phy11733/index_e.html

Quaternion Julia Navigator:
http://www.pff-software.demon.nl/qjn/qjn.htm

Quaternion Generator:
http://www.krs.hia.no/~fgill/fractal.html

--
Gerald
ger### [at] aonat

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