(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

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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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