 |
|
|
|
|
|
| |
| |
|
|
|
|
| |
| |
|
|
I have a question on how the Julia Fractal object is created. This is built in
to Povray, so I have no way of studying how it is done.
I want to draw another (fractal) object, an object that depends on an iteration.
Points in space will belong to this object if they do not leave a prescribed
bounding volume after a certain number of iterations using a specific formula.
Can somebody point me into the right direction?
Thanks..
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
"Jos leys" <jos### [at] pandora be> wrote:
> I have a question on how the Julia Fractal object is created. This is built in
> to Povray, so I have no way of studying how it is done.
> I want to draw another (fractal) object, an object that depends on an iteration.
> Points in space will belong to this object if they do not leave a prescribed
> bounding volume after a certain number of iterations using a specific formula.
> Can somebody point me into the right direction?
> Thanks..
I am totally ignorant on this subject.
However, I can redirect at this page:
http://local.wasp.uwa.edu.au/~pbourke/fractals/
Indispensable, in my opinion.
Regards
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Le Thu, 25 Sep 2008 13:55:37 -0400, Jos leys a modifié des petits morceaux
de l'univers pour nous faire lire :
> I have a question on how the Julia Fractal object is created. This is
> built in to Povray, so I have no way of studying how it is done.
Well, you can always use the source, so the previous assertion is not
right. Now, it's 4D math.. that's another story to understand the code.
> I want
> to draw another (fractal) object, an object that depends on an
> iteration. Points in space will belong to this object if they do not
> leave a prescribed bounding volume after a certain number of iterations
> using a specific formula. Can somebody point me into the right
> direction? Thanks..
Patching is one way... but first have a look at the julia documentation,
maybe your formula is already part of the 18 provided for hypercomplex.
If not, add it.
BTW, what is your specific formula ?
would it matter if your bounding volume is not a 4D-4-units sphere ?
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
> Well, you can always use the source, so the previous assertion is not
> right. Now, it's 4D math.. that's another story to understand the code.
> Patching is one way... but first have a look at the julia documentation,
> maybe your formula is already part of the 18 provided for hypercomplex.
> If not, add it.
> BTW, what is your specific formula ?
> would it matter if your bounding volume is not a 4D-4-units sphere ?
Right, I did look at the code, but I'm too unfamiliar with the language. Anyway,
I did some more homework on how this is done in general (one uses a distance
estimation method for every ray to determine an intersection point and a
surface normal)
So if I want to do something similar just using SDL code, it's like trying to
write a raytracer inside a raytracer, which is not good! :-((
The thing I want to try and do in a novel way is the Lorenz attractor, so none
of the features in Julia Fractal can be used, as what I want to do is totally
different.
My own conclusion is that want I want to do is impossible..
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Wasn't it Jos leys who wrote:
>The thing I want to try and do in a novel way is the Lorenz attractor, so none
>of the features in Julia Fractal can be used, as what I want to do is totally
>different.
Fractal surfaces, like the Julia fractals, are completely different from
Attractors.
With a fractal surface, you consider each point in space, iterate that
with some function, and determine if the function converges to some
limit or diverges to infinity. [For most suitable functions, it's
possible to prove that if the track leaves a certain bounding volume,
then it must continue to diverge to infinity.] If the function
converges, then the point is inside the surface, otherwise it is
outside.
With a Strange Attractor, the track neither converges nor diverges. It
wanders chaotically within a finite volume. The pretty patterns that the
Attractor makes aren't a surface, they're a cloud of separate points. To
model such an Attractor in POV, plot a small sphere at each of the
points.
--
Mike Williams
Gentleman of Leisure
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Mike Williams <nos### [at] econymdemoncouk> wrote:
> Wasn't it Jos leys who wrote:
>
> With a Strange Attractor, the track neither converges nor diverges. It
> wanders chaotically within a finite volume.
Sure, you are right, but what if I told you that there may be a way to treat
this attractor in a similar fashion than a Julia fractal?
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Wasn't it Jos leys who wrote:
>Mike Williams <nos### [at] econymdemoncouk> wrote:
>> Wasn't it Jos leys who wrote:
>>
>> With a Strange Attractor, the track neither converges nor diverges. It
>> wanders chaotically within a finite volume.
>
>Sure, you are right, but what if I told you that there may be a way to treat
>this attractor in a similar fashion than a Julia fractal?
I have a suspicion that anything like that would probably end up
describing a rather boring surface.
I also suspect that you might need to track a lot more iterations on
average than you would for a Julia fractal in order to decide whether
the sequence you're tracking is going to converge to the attractor or
drift off to infinity. In the case of a Julia fractal, you only need to
calculate a small number of iterations for the vast majority of starting
points.
However, it might be worthwhile to run a few low resolution
visualizations to have a quick look. Run your calculations for a grid of
points and plot a sphere if the sequence looks like it converges.
--
Mike Williams
Gentleman of Leisure
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
I ran a calculation of a slice through such a surface.
A point is white if the Lorenz Attractor with parameters Sigma=10,
Rho=28, Beta=8/3 starting at that point converges to the Attractor and
black if it diverges.
The shape has got a bit more structure than I expected, but it's not
very exciting. It took 4m 35s to calculate that one slice, so expect
several hours to calculate a complete 3D surface using SDL. If you think
it's worth pursuing, then you'd be better off doing the calculations in
a compiled language and outputting something that POV can process.
I've posted the image to binaries.images and gave it the title "Lorenz
Generator Slice". I thought that retaining the title of this thread for
the image posting would confuse readers of that group.
--
Mike Williams
Gentleman of Leisure
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
> I've posted the image to binaries.images and gave it the title "Lorenz
> Generator Slice". I thought that retaining the title of this thread for
> the image posting would confuse readers of that group.
>
Thanks for the image.
Yes, I thought putting spheres on points that belong to the attractor, but that
would not produce anything new.
The Lorenz attractor actually has enormous detail of a fractal nature.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
