Following on from Warp's lovely julia set from a few days ago, I decided
that I would have a go at animating it. The results of the animation are
in povray.binaries.animation, but here is a large still from the
sequence.

Cheers,
Ian Shumsky
http://www.outerarm.demon.co.uk/graphics/graphics.html

PS. I've also attached the code as Warp did in his original post. The
code is mostly his with only some very minor modifications.

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Attachments:
Download 'julia.jpg' (48 KB) Download 'julia.pov.txt' (2 KB)

Preview of image 'julia.jpg'

Is there infinite complexity in the forest?

Ian Shumsky wrote:

> Following on from Warp's lovely julia set from a few days ago, I decided
> that I would have a go at animating it. The results of the animation are
> in povray.binaries.animation, but here is a large still from the
> sequence.
>
> Cheers,
> Ian Shumsky
> http://www.outerarm.demon.co.uk/graphics/graphics.html
>
> PS. I've also attached the code as Warp did in his original post. The
> code is mostly his with only some very minor modifications.
>


>

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"Greg M. Johnson" wrote:
> 
> Is there infinite complexity in the forest?
> 

:-) 
probably not.

The only infinite things in Povray are infinites and rendering times.


Nice picture BTW.

Christoph

-- 
Christoph Hormann <chr### [at] gmxde>
Homepage: http://www.schunter.etc.tu-bs.de/~chris/

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Until you hit some kind of wall w/ precision of the calculation, the
mandel pattern ought to have unending complexity as you zoom and zoom.
I'm wondering if the Julia forest has the same property.  I guess the
only way to answer is to do the rendering.

Christoph Hormann wrote:

> "Greg M. Johnson" wrote:
> >
> > Is there infinite complexity in the forest?
> >
>
> :-)
> probably not.
>
> The only infinite things in Povray are infinites and rendering times.
>
> Nice picture BTW.
>
> Christoph
>
> --
> Christoph Hormann <chr### [at] gmxde>
> Homepage: http://www.schunter.etc.tu-bs.de/~chris/

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I'm running a 3500x2650 render of the image at the moment - hopefully
this will be finished by the weekend!

Cheers,
Ian.

http://www.outerarm.demon.co.uk/graphics/graphics.html

"Greg M. Johnson" wrote:
> 
> Until you hit some kind of wall w/ precision of the calculation, the
> mandel pattern ought to have unending complexity as you zoom and zoom.
> I'm wondering if the Julia forest has the same property.  I guess the
> only way to answer is to do the rendering.
> 
> Christoph Hormann wrote:
> 
> > "Greg M. Johnson" wrote:
> > >
> > > Is there infinite complexity in the forest?
> > >
> >
> > :-)
> > probably not.
> >
> > The only infinite things in Povray are infinites and rendering times.
> >
> > Nice picture BTW.
> >
> > Christoph
> >
> > --
> > Christoph Hormann <chr### [at] gmxde>
> > Homepage: http://www.schunter.etc.tu-bs.de/~chris/

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Greg M. Johnson <"gregj;-()"@aol.c;-()om> wrote:
: Is there infinite complexity in the forest?

  Since it uses an iteration amount of 30 then the answer is no.

  To get infinity complexity you should use infinite iterations. This is,
of course, not possible.

  Note that increasing the iterations amount will flatten the shape of the
object (but you can someway compensate that by increasing the power of the
function, which was in this case .25, although you'll not get an identical
result, but something similar at least).

-- 
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):_;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/

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Warp wrote:

> Greg M. Johnson <"gregj;-()"@aol.c;-()om> wrote:
> : Is there infinite complexity in the forest?
>
>   Since it uses an iteration amount of 30 then the answer is no.
>
>   To get infinity complexity you should use infinite iterations. This is,
> of course, not possible.

No, the iteration amount of 30 means your trees are demarcated into 30
different possible heights.
It does nothing for the complexity of structure in x-z plane.
I've got test renders that demonstrate this with mandel, may post or make web
page later.

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Greg M. Johnson <gre### [at] my-dejanewscom> wrote:
: No, the iteration amount of 30 means your trees are demarcated into 30
: different possible heights.
: It does nothing for the complexity of structure in x-z plane.

  Sorry, but I have to disagree. And this is easy to prove:

  Calculate a regular mandel with 1 iteration. You get a black (or
interior-colored) circular shape and one color in the exterior (the shape
is exactly circular because every point that is inside your threshold
radius will be considered "inside" and all the other points will be
"outside").

  Calculate the mandel with 2 iterations.
  Now you get a band of different color (supposing you are using a color
map that allows you to distinguish well between two adjacent colors)
inside the abovementioned circle and a black shape which is less
circular, but still with a smooth edge.

  Calculate the mandel with 3 iterations.
  Another color band will appear inside the previous one and the black
"inside" area will be smaller and less circular-shaped, but still quite
smooth.

  In no way can you say that that black area has infinite complexity in
its border. It's quite smooth.

  With more iterations (tens, hundreds...) the black "inside" area will
"twist" more and more and its border will be less smooth with each increased
iteration amount, but if you zoom it large enough, you will always find
that the border is smooth, without infinite complexity.

  To get the true mandelbrot fractal, with infinitely complex border
(and infinitely long), you'll have to make an infinite number of
iterations. This is also its mathematical definition.
  Since we can't calculate infinite iterations we have to calculate a
finite number of them. Fortunately, since the resolution of our screens
is limited, after going up to certain iterations amount, the lack of
complexity will be buried in the pixel resolution of the image and thus
we will not notice the difference.
  That's why a finite number of iterations is enough to get a good-enough
approximation.
  But it also means that if we zoom the fractal enough, we have to increase
the iterations amount.

-- 
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):_;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/

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This is quite neat! I wonder what an integrated version would look like...

--
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/

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