I took an interest in exploring order in chaos from a different
direction. I was inspired by a suggestion in a research report
that in the long run (enough iterations) clearly non-random
results appear. This first approach was simply getting the
process to work. There was no methodology in the report. 

Using the attachment as an example --

	It starts with an array 0..257 by 0..257 with all the pairs
containing 0 and 257 (the edges, boundary values) constrained to
zero. 

Step 1. Each of the other array elements, 1..128,1..128 are given
a random number between -0.5 and +0.5. 

Step 2. Then each cell is averaged with its nearest neighbors (8
neighbors + itself for 9). 

Step 3. Return to step 1, twenty times in the case of the
attached image. 

Step 4. convert the final array of numbers into triangles in mesh
object format. 

Setp 5. Render 

	It's a 19Meg POV source file if anyone is realy desperate. The
generating program is only 2k but you have to have Turbo Pascal
or download Free Pascal. (Go to Google.com and search 'free
pascal'. There are plenty places to get it.) Of course it is a
first attempt 

	All that aside, speaking of the image, the scale is linear, that
is 258 units on a side with the added increments of +/- 0.5 at
each step. Visually I see some extended patterns in the image. It
is also visually interesting but then so are the holes in
acoustic ceilings if you have nothing better to do with your
time. 

	Eventually I intend to produce an animation of this, one frame
per iteration (step 3). 

	/*Ignore the little thing in the lower left corner. I just
dropped the mesh into an existing scene file.*/

-- 
Kareoke is Japanese for tone deaf.

    -- The Iron Webmaster, 15

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Attachments:
Download 'array2.jpg' (27 KB) Download 'array2a.jpg' (21 KB)

Preview of image 'array2.jpg'

Preview of image 'array2a.jpg'

This gives me an idea that I'll never follow up ...

Among the screensavers that came with Red Hat is "Demon", by David
Bagley.
(http://www.jwz.org/xscreensaver/screenshots.html)  It's a cellular
automaton which a simple rule (that baffled me until I read about it
elsewhere): If the color next after yours appears on any neighboring
cell, change to that color.  Spirals almost always result.

So my thought is: make a moving hf, where the height is the sine of the
phase (color).  Initialize randomly, and watch lakes sloshing around,
nibbling gradually at their chaotic edges until they join to form the
spirals.

-- 
Anton Sherwood  --  br0### [at] p0b0xcom  --  http://ogre.nu/

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Anton Sherwood wrote:
> 
> This gives me an idea that I'll never follow up ...
> 
> Among the screensavers that came with Red Hat is "Demon", by David
> Bagley.
> (http://www.jwz.org/xscreensaver/screenshots.html)  It's a cellular
> automaton which a simple rule (that baffled me until I read about it
> elsewhere): If the color next after yours appears on any neighboring
> cell, change to that color.  Spirals almost always result.

	Have to look at that one. 

> So my thought is: make a moving hf, where the height is the sine of the
> phase (color).  Initialize randomly, and watch lakes sloshing around,
> nibbling gradually at their chaotic edges until they join to form the
> spirals.

	I can say this now that I have run it a few times and more
iterations. As it is a real number +/- 0.5, I have yet to find a
number that is +/- 10.0 or greater. Lots of +/- 9.xxx's. That
indicates a valid random number generator to me while I consider
the 256x256 a test of calling it. 

	Something I did not mention, I have to kill apps and 'sync' else
povray complains that it has run out of RAM at 128M of same. 

	That said, I don't quite see what you are saying. 

	But I could do the pigment {color calculated} and dark to light
blue between -10 and +10 to make a shot at waves. 

-- 
If you quit smoking now you can live long enough
to get Altzheimer's. 
           -- The Iron Webmaster, 24

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Matt Giwer wrote:
> 
[...]
> 
>         It's a 19Meg POV source file if anyone is realy desperate. The
> generating program is only 2k but you have to have Turbo Pascal
> or download Free Pascal. (Go to Google.com and search 'free
> pascal'. There are plenty places to get it.) Of course it is a
> first attempt
> 

Looks interesting, btw you should try a heightfield for that, it's much faster
and occupies less HD space. 

Christoph

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

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Christoph Hormann wrote:
> 
> Matt Giwer wrote:
> >
> [...]
> >
> >         It's a 19Meg POV source file if anyone is realy desperate. The
> > generating program is only 2k but you have to have Turbo Pascal
> > or download Free Pascal. (Go to Google.com and search 'free
> > pascal'. There are plenty places to get it.) Of course it is a
> > first attempt
> >
> 
> Looks interesting, btw you should try a heightfield for that, it's much faster
> and occupies less HD space.

	But how do I get the date into an image file? 

-- 
If you quit smoking now you can live long enough
to get Altzheimer's. 
           -- The Iron Webmaster, 24

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Matt Giwer wrote:
> 
>         But how do I get the date into an image file?
> 

Maybe i missed something in your description but IMO it's much easier to write
an array of numbers into a heightfield file than to a povray mesh definition. 

Christoph

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

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Christoph Hormann wrote:
> 
> Matt Giwer wrote:
> >
> >         But how do I get the date into an image file?
> >
> 
> Maybe i missed something in your description but IMO it's much easier to write
> an array of numbers into a heightfield file than to a povray mesh definition.

	I look at the docs for heightfield. 

HEIGHT_FIELD: 
     height_field{ HF_TYPE "filename" [HF_MODIFIER...] } 
HF_TYPE: 
     gif | tga | pot | png | pgm | ppm | sys <<<<<<<<
HF_MODIFIER: 
     hierarchy [Boolean] | 
     smooth [Boolean] | 
     water_level Level | 
     OBJECT_MODIFIER 

	All the HF_TYPEs are image formats. I have hacked the
uncompressed .tga format but haven't tried to implement it yet.
Is there an easier way? 

-- 
There is never any reason to be angry with the
enemy because whatever they do they are doing
it because the believe it is the right thing
to do. -- Marcus Aurelius
	-- The Iron Webmaster, 33

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Matt Giwer wrote:
> 
> 
>         All the HF_TYPEs are image formats. I have hacked the
> uncompressed .tga format but haven't tried to implement it yet.
> Is there an easier way?
> 

uncompressed tga is the simplest IMO, pgm is quite simple too.  

Christoph

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

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Christoph Hormann wrote:
> 
> Matt Giwer wrote:
> >
> >
> >         All the HF_TYPEs are image formats. I have hacked the
> > uncompressed .tga format but haven't tried to implement it yet.
> > Is there an easier way?
> >
> 
> uncompressed tga is the simplest IMO, pgm is quite simple too.

	One can always hope for simpler. Thanks. 

-- 
In WWII Britain used the old "start a world war to prevent
a world war" trick. Some say it worked better than could 
have been imagined.
	-- The Iron Webmaster, 28

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Matt's approach is probably brilliant for other fractal problems, but methinks
this is really a duplication of one of the noise functions.  An isosurface scene
file with 19 lines, instead of 19 MB,  could do the same thing, no?

Christoph Hormann wrote:

> Matt Giwer wrote:
> >
> >         But how do I get the date into an image file?
> >
>
> Maybe i missed something in your description but IMO it's much easier to write
> an array of numbers into a heightfield file than to a povray mesh definition.
>
> Christoph
>
> --
> Christoph Hormann <chr### [at] gmxde>
> Homepage: http://www.schunter.etc.tu-bs.de/~chris/

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