Well, can ya?

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Please put the question in the body of the article, not in the subject.
You shouldn't force people to re-scale their windows/tabs in order to see
the whole question. The subject should contain a short phrase about the
topic of the article.

-- 
#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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On Fri, 2 May 2003 09:52:29 -0400, "Greg M. Johnson" <gregj:-)565### [at] aolcom>
wrote:

>Well, can ya?
>
>
The FM (as I believe it is affectionately called) only mentions the Julia Set,
6.5.1.6 
or do you mean for a pattern ?

Regards
        Stephen

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Yes, can one make a function of sorts that duplicates the fractal algorithm
so that you'd have a pattern.

<mca### [at] aolcom (S McAvoy)> wrote in message
news:3eb2cfbd.98435893@news.povray.org...
> On Fri, 2 May 2003 09:52:29 -0400, "Greg M. Johnson"
<gregj:-)565### [at] aolcom>
> wrote:
>
> >Well, can ya?
> >
> >
> The FM (as I believe it is affectionately called) only mentions the Julia
Set,
> 6.5.1.6
> or do you mean for a pattern ?
>
> Regards
>         Stephen

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On Fri, 2 May 2003 17:44:52 -0700, "Greg M. Johnson" <gregj;-)565### [at] aolcom>
wrote:

>Yes, can one make a function of sorts that duplicates the fractal algorithm
>so that you'd have a pattern.
>
That's beyond me, though as Pov supports Mandelbrot and Julia sets I would think
that It might need to be patched to get other types. What type of Fractal do you
want? If you can do something with formulas then Fractint can give you lots.
http://spanky.triumf.ca/www/fractint/fractint.html
  
Andrew Coppin has been doing something with the Mandelbrot set that's not
available at his link :-{
Simen Kvaal did a beautiful Pickover attractor as well, I sigh with envy.

Regards
        Stephen

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S McAvoy <mca### [at] aolcom> wrote:
> That's beyond me, though as Pov supports Mandelbrot and Julia sets I would think
> that It might need to be patched to get other types.

  If POV-Ray supported recursive functions, then you could do them with
those.
  In fact, I implemented the Mandelbrot pattern as a recursive function
in a prototype version of POV-Ray 3.5, and it worked ok (it was acceptably
fast).

  It's a bummer the recursion support didn't completely work out.

-- 
#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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On 2 May 2003 20:16:46 -0400, Warp <war### [at] tagpovrayorg> wrote:


>
>  It's a bummer the recursion support didn't completely work out.
>
'Tis, you can get lost in fractals :-)

Regards
        Stephen

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Warp wrote:
>   If POV-Ray supported recursive functions, then you could do them with
> those.
>   In fact, I implemented the Mandelbrot pattern as a recursive function
> in a prototype version of POV-Ray 3.5, and it worked ok (it was acceptably
> fast).

What du you need recursion for?  Most fractals I know of
(Mandelbrot included) are computed in simple iterations,
as in (pseudo-code):

FOR Y-coordinates [of the entire fractal image]
   FOR X-coordinates
     WHILE conditions (i.e.: |Z| < 4 AND num_loops < max_loops)
       Iterate function (i.e.: Z = Z*Z + C [Mandelbrot])
     END
     Draw Pixel
   END
END

Any end-recursive function can be written as an iteration.
And in most cases the iterative version will be faster.

> It's a bummer the recursion support didn't completely work out.

That is true, however. ;)

g.

-- 
++++++++++++++++ http://www.psico.ch/ ++++++++++++++++

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In article <3eb3ac4c@news.povray.org>, gimi <gim### [at] psicoch> wrote:

> What du you need recursion for?  Most fractals I know of
> (Mandelbrot included) are computed in simple iterations,
> as in (pseudo-code):

You can make an iterative version of any recursive algorithm. However, 
the recursive version is often much simpler, and most fractals are 
mathematically defined as recursive because of the self-similar nature 
of fractals. At the time this was written, POV supported function 
recursion, but it still does not support loops, though you can imitate 
it using a long string of select() calls.

-- 
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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Christopher James Huff wrote:
> In article <3eb3ac4c@news.povray.org>, gimi <gim### [at] psicoch> wrote:
>>What du you need recursion for?  Most fractals I know of
>>(Mandelbrot included) are computed in simple iterations,
>>as in (pseudo-code):
 >
> You can make an iterative version of any recursive algorithm. 

AFAIK this is only proven to be true for end-recursive algorithms
(though /many/ of the functions with a single recursion call can
be made end-recursive; but you will usually run into trouble if
the algorithm has multiple recursive calls).

> However, the recursive version is often much simpler, 

I agree, but it depends on how you look at it.  For people
not too familiar with the concept, an iterative function
is far easier to grasp. - And, as I mentioned before, it's
faster (and more efficient) in almost every case (Note that
I speak as a programmer here, not as a mathematician).

 > and most fractals are mathematically defined as recursive
 > because of the self-similar nature of fractals.

Can you elaborate on this kind of definition?
   I don't doubt this, I just think that one can as well
define them by iterative means ("As long as the conditions
are not fulfilled, do repeat...").
   However, I doubt that the relation between recursion and
self-similarity is as strong as you think.  Recursion is
often (ab-)used in order to make code look slick, when in
fact it isn't.

 > At the time this was written, POV supported function
> recursion, but it still does not support loops, though you can imitate 
> it using a long string of select() calls.

You mean "does not support loops" because there is no
proper stack to store (local) variables on?  In this
case, yes; but I'd prefer to solve (not "imitate") this
by implementing one - *if* I *really* need to... ;)


BTW, Christopher, what is your profession?


g.

-- 
9) Count the number of odd entries in the 100th row of
Pascal's triangle.
++++++++++++++++ http://www.psico.ch/ ++++++++++++++++

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