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.
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