Hi folks.

OK, maybe not totally POV-related, but... I'm curiose to know how POV-Ray's
"random" textures work. Textures like bozo...

If you pick two distant points in space, the value at each of those points
is random. And yet, if you pick to near-by points, you get similar values.
I'm curiose to know how on earth they managed to do that...

I can't think of a single way you could use a traditional PRNG to create a
3D texture like this without building the entire texture in memory and
referring to it. But that would require a stupid amount of RAM. But if you
were to try to compute the function at individual points, surely you'd have
great difficulty with seeding issues...

The documentation says these functions are fractal noise. Well, I know about
fractals, but I know nothing about fractal noise functions. (Last time I
read such a book - when I was 17, I believe - the statistics was WAY over my
head!) Can anyone enlighten me?

Thanks.
Andrew.

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Andrew Coppin wrote:
> 
> Hi folks.
> 
> OK, maybe not totally POV-related, but... I'm curiose to know how POV-Ray's
> "random" textures work. Textures like bozo...
> 
> [...]

A fairly good introduction can be found on:

http://freespace.virgin.net/hugo.elias/models/m_perlin.htm

Christoph

-- 
POV-Ray tutorials, include files, Sim-POV,
HCR-Edit and more: http://www.tu-bs.de/~y0013390/
Last updated 28 Feb. 2003 _____./\/^>_*_<^\/\.______

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> A fairly good introduction can be found on:
>
> http://freespace.virgin.net/hugo.elias/models/m_perlin.htm

Thanks. This was helpful.

So, essentially, the Perlin noise function is built on a normal random
function where a point (in whatever dimensionallity of space) is the seed,
yielding the randomness between distant points. Then interpolation is used
to make points nearby have similar values. Oh, and the fractal bit - several
different interpolated random functions of different wavelengths and
amplitudes are added together for extra "natralness". Is that about how it
works?

Andrew.

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The perlin-noise function itself has got nothing to do with fractals 
(correct me if I'm wrong :-)

You get something that's called "Fractal Brownian Motion" (FBM) when you 
add "turbulence" to the pigment. The POV-Documentation explains how 
turbulence works.

-Sascha

Andrew Coppin wrote:
> A fairly good introduction can be found on:
> 
> http://freespace.virgin.net/hugo.elias/models/m_perlin.htm
> 
> 
> Thanks. This was helpful.
> 
> So, essentially, the Perlin noise function is built on a normal random
> function where a point (in whatever dimensionallity of space) is the seed,
> yielding the randomness between distant points. Then interpolation is used
> to make points nearby have similar values. Oh, and the fractal bit - several
> different interpolated random functions of different wavelengths and
> amplitudes are added together for extra "natralness". Is that about how it
> works?
> 
> Andrew.
> 
>

Post a reply to this message

sascha wrote:
> 
> You get something that's called "Fractal Brownian Motion" (FBM) when you
> add "turbulence" to the pigment. The POV-Documentation explains how
> turbulence works.

'fBm' stands for 'fractional Brownian motion'.

Christoph

-- 
POV-Ray tutorials, include files, Sim-POV,
HCR-Edit and more: http://www.tu-bs.de/~y0013390/
Last updated 28 Feb. 2003 _____./\/^>_*_<^\/\.______

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You're right, of course.

Christoph Hormann wrote:
> 
> sascha wrote:
> 
>>You get something that's called "Fractal Brownian Motion" (FBM) when you
>>add "turbulence" to the pigment. The POV-Documentation explains how
>>turbulence works.
> 
> 
> 'fBm' stands for 'fractional Brownian motion'.
> 
> Christoph
>

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On Sat, 10 May 2003 19:06:21 +0200, sascha
<sas### [at] userssourceforgenet> wrote:

>The perlin-noise function itself has got nothing to do with fractals 
>(correct me if I'm wrong :-)

I think what "fractal" stands for in this context is that is
inherently self-similar in different scales (to a limited extent
though, unlike "true" fractals)


Peter Popov ICQ : 15002700
Personal e-mail : pet### [at] vipbg
TAG      e-mail : pet### [at] tagpovrayorg

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Peter Popov <pet### [at] vipbg> wrote:
> I think what "fractal" stands for in this context is that is
> inherently self-similar in different scales (to a limited extent
> though, unlike "true" fractals)

  No, the word "fractal" does not imply self-similarity. The origin of
the word is related to mathematical calculations of the dimensions of
a fractal shape, which is fractional in a mathematical sense.

-- 
#macro N(D)#if(D>99)cylinder{M()#local D=div(D,104);M().5,2pigment{rgb M()}}
N(D)#end#end#macro M()<mod(D,13)-6mod(div(D,13)8)-3,10>#end blob{
N(11117333955)N(4254934330)N(3900569407)N(7382340)N(3358)N(970)}//  - Warp -

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In article <3ebf872c@news.povray.org>, Warp <war### [at] tagpovrayorg> 
wrote:

>   No, the word "fractal" does not imply self-similarity. The origin of
> the word is related to mathematical calculations of the dimensions of
> a fractal shape, which is fractional in a mathematical sense.

Actually, it has nothing to do with that. The words "fractal" and 
"fraction" have a common root, but "fractal" is more closely related to 
"fractured" and "fragment". Mandelbrot coined the word "fractal" from 
the Latin "fractus", which means rough, irregular, or broken, and it 
does refer to the self-similarity aspect: if you were to break a fractal 
into pieces ("fracts"?), each fragment would appear similar to the 
others.

Here's a quote from Mandelbrot himself: "I coined fractal from the Latin 
adjective fractus. The corresponding Latin verb fragere means 'to 
break': to create irregular fragments...how appropriate for our needs!"

-- 
Christopher James Huff <cja### [at] earthlinknet>
http://home.earthlink.net/~cjameshuff/
POV-Ray TAG: chr### [at] tagpovrayorg
http://tag.povray.org/

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In article <q7lubvcvspu6h4f1sabho2niej44dcp26q@4ax.com>,
 Peter Popov <pet### [at] vipbg> wrote:

> >The perlin-noise function itself has got nothing to do with fractals 
> >(correct me if I'm wrong :-)
> 
> I think what "fractal" stands for in this context is that is
> inherently self-similar in different scales (to a limited extent
> though, unlike "true" fractals)

Perlin noise is not self-similar at different scales, though. It is 
self-similar at one scale only.
Now, things like sum 1/F-noise are fractal. (wrinkles, granite)

http://astronomy.swin.edu.au/~pbourke/texture/perlin/

-- 
Christopher James Huff <cja### [at] earthlinknet>
http://home.earthlink.net/~cjameshuff/
POV-Ray TAG: chr### [at] tagpovrayorg
http://tag.povray.org/

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