(To the right group this time ;)

One way of making fractals: you have a region of space where the fractal
will be. You then have rules for making copies of that region
(translate, scale, rotate etc) within itself. Do the same thing within
each of those smaller copies. When you get down to the smallest level
you fill in the tiny copy of the original region. In two dimensions this
can be used to make the classic sierpinsky triangle or fern. I tried it
in three dimensions with an arbitrary set of rules for copying the
region, and placing a blob component whenever the macro got below a box
of width .005 (the original region being from <-1,-1,-1> to <1,1,1>). I
can easily define different rules to get different fractals.

The full-size render (1152x864) has some artifacts, black pixels, in the
blob. What causes that?

32768 blob components, 19880794 bytes, 40m 05s render time.

Comments/criticisms please

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

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Attachments:
Download 'iterated01.jpg' (163 KB)

Preview of image 'iterated01.jpg'

Wow!!!

Mick

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Lovely!

"David Fontaine" <dav### [at] faricynet> wrote in message
news:3AB1B2B9.A87FF859@faricy.net...
> (To the right group this time ;)
>
> One way of making fractals: you have a region of space where the fractal
> will be. You then have rules for making copies of that region
> (translate, scale, rotate etc) within itself. Do the same thing within
> each of those smaller copies. When you get down to the smallest level
> you fill in the tiny copy of the original region. In two dimensions this
> can be used to make the classic sierpinsky triangle or fern. I tried it
> in three dimensions with an arbitrary set of rules for copying the
> region, and placing a blob component whenever the macro got below a box
> of width .005 (the original region being from <-1,-1,-1> to <1,1,1>). I
> can easily define different rules to get different fractals.
>
I've been thinking of using this self similar scaling technique you
described for Apolloniian packing. In 2d if you have 3 large circles that
are not the same size but in a certain proportion that would result in
fitting exactly with sides touching when iterated at smaller sizes. Almost
the same way that when you cut an A0 size pare in half you get A2 and so on
until you get A4, A5 etc.  As far as I know appolonian packing has only been
done starting with 3 equally sixed circles. The next step would be to do
this in 3d.

Nekar

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> The full-size render (1152x864) has some artifacts, black pixels, in the
> blob. What causes that?
>

I can't see them here. Does it still show if you push up the maximum trace
level? Unless you're talking about the shadow in the background.

Nekar

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this is one of those magic render that the more you look the more you see

if you get the 1152x864 sorted out, post it somewhere as it would make
execellent desktop wallpaper


--
Rick

POV-Ray News & Resources - http://povray.co.uk
Kitty5 WebDesign - http://kitty5.com
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TEL : +44 (01625) 266358 - FAX : +44 (01625) 611913 - ICQ : 15776037

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Nekar Xenos wrote:

> > The full-size render (1152x864) has some artifacts, black pixels, in the
> > blob. What causes that?
> >
>
> I can't see them here. Does it still show if you push up the maximum trace
> level? Unless you're talking about the shadow in the background.

They don't show up because this has been resized (and cropped). I don't think
it'd be max_trace, since the blob is opaque and nonreflective. Must be some
sort of math accuracy thing? I attached a clip of the large version to show
the spots.

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

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Attachments:
Download 'blobartifacts.jpg' (12 KB)

Preview of image 'blobartifacts.jpg'

David Fontaine wrote:

> Must be some sort of math accuracy thing?

Looking closely the blob has platelette-like structures that get very thin in the
middle. It could very well be an accuracy issue. These kinds of aritfacts do show
up in isosurface...

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

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Mick Hazelgrove wrote:

> Wow!!!

A "Wow!!!" from Mick Hazelgrove? Oxygen! I need oxygen! :)
Thanks! I'll probably churn out some more. As usual, simple iterated
math makes for a great image. Chaos, anyone?

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

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Nekar Xenos wrote:

> Lovely!

Thank you!


> I've been thinking of using this self similar scaling technique you
> described for Apolloniian packing. In 2d if you have 3 large circles that
> are not the same size but in a certain proportion that would result in
> fitting exactly with sides touching when iterated at smaller sizes. Almost
> the same way that when you cut an A0 size pare in half you get A2 and so on
> until you get A4, A5 etc.  As far as I know appolonian packing has only been
> done starting with 3 equally sixed circles. The next step would be to do
> this in 3d.

I did a search for it and found, Start with a boundary and three circles tangent
to the boundary and each other. Then every gap left, make a maximum dimatere
circle in the middle, tangent to the three sides bounding the gap.
I've seen stuff like this before. Quite interesting patterns. I don't know how
you'd do it in 3d though. Every sphere would be tangent to 4 surfaces I would
think, but you wouldn't be able to make them close off areas of empty space like
in 2d. Maybe it can't be done... :(

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

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"Rick [Kitty5]" wrote:

> this is one of those magic render that the more you look the more you see

Yeah! It kinda looks random, then patterns start to emerge and you see that
it is in fact very rigidly organized.


> if you get the 1152x864 sorted out, post it somewhere as it would make
> execellent desktop wallpaper

If you don't care about the artifacts (not much worse than in this one), I
can post the 1152 at my site for ya.

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

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David Fontaine wrote:
> 
> They don't show up because this has been resized (and cropped). I don't think
> it'd be max_trace, since the blob is opaque and nonreflective. Must be some
> sort of math accuracy thing? I attached a clip of the large version to show
> the spots.
> 

Have you tried adding 'sturm' to the blob object?  I remember i had
similar problems once, but i am not sure if it helped.

Nice picture BTW, any chance to see your IFS code?  An universal include
file for such fractals would be quite useful...

Christoph

-- 
Christoph Hormann <chr### [at] gmxde>
IsoWood include, radiosity tutorial, TransSkin and other 
things on: http://www.schunter.etc.tu-bs.de/~chris/

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Christoph Hormann wrote:

> Have you tried adding 'sturm' to the blob object?  I remember i had
> similar problems once, but i am not sure if it helped.

I didn't know blob had such a thing. That could very well fix it. Thanks. (note to
self: RTFM)


> Nice picture BTW, any chance to see your IFS code?  An universal include
> file for such fractals would be quite useful...

There's probably more I can do to make it more versatile and readable. It should be
up eventially, once I feel like it.

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

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> They don't show up because this has been resized (and cropped). I don't
think
> it'd be max_trace, since the blob is opaque and nonreflective. Must be
some
> sort of math accuracy thing? I attached a clip of the large version to
show
> the spots.

try scaling your whole scene up by a factor of 10 or 100, it probably is
math accuracy

--
Rick

POV-Ray News & Resources - http://povray.co.uk
Kitty5 WebDesign - http://kitty5.com
Hi-Impact web site design & database driven e-commerce
TEL : +44 (01625) 266358 - FAX : +44 (01625) 611913 - ICQ : 15776037

PGP Public Key
http://pgpkeys.mit.edu:11371/pks/lookup?op=get&search=0x231E1CEA

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> Comments/criticisms please
>

'tis beautiful.

--John

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In article <3AB28A11.FF99E2B5@faricy.net>, David Fontaine 
<dav### [at] faricynet> wrote:

> They don't show up because this has been resized (and cropped). I don't 
> think it'd be max_trace, since the blob is opaque and nonreflective.

Maybe adjust the max_intersections value...it affects the number of 
intersections found when testing against an object. If it simply isn't 
finding the front surfaces of the blob because it's tested as many as it 
can, it might cause this artifact.

4.10.7  Max_Intersections
POV-Ray uses a set of internal stacks to collect ray/object intersection 
points. The usual maximum number of entries in these I-Stacks is 64. 
Complex scenes may cause these stacks to overflow. POV-Ray doesn't stop 
but it may incorrectly render your scene. When POV-Ray finishes 
rendering, a number of statistics are displayed. If you see I-Stack 
Overflows reported in the statistics you should increase the stack size. 
Add a global setting to your scene as follows:
global_settings { max_intersections  Integer }
If the I-Stack Overflows remain increase this value until they stop.

-- 
Christopher James Huff
Personal: chr### [at] maccom, http://homepage.mac.com/chrishuff/
TAG: chr### [at] tagpovrayorg, http://tag.povray.org/

<><

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Thanks Christoph Rick and Chris for tips on the aritfacts. I'll have to check
into those.

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

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This is the set of transforms that was used to make this fractal...

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

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Attachments:
Download 'determrule01.gif' (9 KB)

Preview of image 'determrule01.gif'

"David Fontaine" <dav### [at] faricynet> wrote in message
news:3AB28F0D.DAFE0512@faricy.net...
> Nekar Xenos wrote:
>
> > Lovely!
>
> Thank you!
>
>
> > I've been thinking of using this self similar scaling technique you
> > described for Apolloniian packing. In 2d if you have 3 large circles
that
> > are not the same size but in a certain proportion that would result in
> > fitting exactly with sides touching when iterated at smaller sizes.
Almost
> > the same way that when you cut an A0 size pare in half you get A2 and so
on
> > until you get A4, A5 etc.  As far as I know appolonian packing has only
been
> > done starting with 3 equally sixed circles. The next step would be to do
> > this in 3d.
>
> I did a search for it and found, Start with a boundary and three circles
tangent
> to the boundary and each other. Then every gap left, make a maximum
dimatere
> circle in the middle, tangent to the three sides bounding the gap

The only problem is that it isn't always self similar in proportion. What I
want is a spcific proprtion of the circles that will make it self imilar
proportionally as well.

>I don't know how
> you'd do it in 3d though. Every sphere would be tangent to 4 surfaces I
would
> think, but you wouldn't be able to make them close off areas of empty
space like
> in 2d. Maybe it can't be done... :(
>
It's been done...
 I got this from Greg M Johnson
news://news.povray.org/3a4e9ea8@news.povray.org. It'll fill any objct with
spheres but it takes some time to parse. But the equal proportions would be
another story...

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

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> The only problem is that it isn't always self similar in proportion. What
I
> want is a spcific proprtion of the circles that will make it self imilar
> proportionally as well.

 Ugh! Major blunder! If it stayed the same proportion it would be a
sierpinski triangle...

Nekar

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David,

Cool pic. I shall have to download it and stick it on a
floppy and look at it properly on me other box.

16 colors doesn't do justice to anything but The Simpsons.

I hobble off...

Peter

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>I shall have to download it and stick it on a
>floppy and look at it properly on me other box.
Done. Woo. That's wicked wierd. I see another post
down a bit. I will check that.
Seriously. There is some funky as* sh*t  in their.
(Or maybe not. Perhaps it was all that pot I smoked in the '70s.)

Peter Warren

+++disclaimer+++
Drugs are bad. Drinking is (mostly) bad. Do good things. Do 'right.'

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Peter Warren wrote:

> Done. Woo. That's wicked wierd. I see another post
> down a bit. I will check that.
> Seriously. There is some funky as* sh*t  in their.

Word up. I'm all about fractals an' sh*t.


> (Or maybe not. Perhaps it was all that pot I smoked in the '70s.)

That would explain a lot. j/k :)


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

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