In article <3A54F817.35634205@my-dejanews.com>, 
gre### [at] my-dejanewscom wrote:

> In the Mandel pattern, one setting gives a cool image at both camera 
> angle 20 and 20E-12, and both are super-quick (<< 5 sec) renders.

That is simply because the mandel pattern is fairly fast...I don't 
expect the multifractal to be as fast, so I recommended settings that 
would reduce wasted computation time.


> I keep losing this argument with Warp.  My experience is that above a 
> certain number of iterations, it is an extremely fine color_map that 
> is needed to see all of the detail in the mandel pattern. The map was 
> something like [1/250 Red][1/249 Blue]...    The rendering BTW zipped 
> by, maybe a sec or two for 320x 240 when at angle 20E-12.

I don't see what the color map has to do with this...except that you 
will require blends over a smaller range as you zoom in if you want to 
keep the same appearance of a pigment. Above a certain number of 
iterations, numeric precision of the computer isn't enough to represent 
the difference, and no color_map adjustment will ever help.


> As I got to to a camera angle of 20E-12, I started to see 
> "pixelation" of the Mandel pattern.  I was told that this was the 
> limit of the chip/PC/language or something, not a limitation of the 
> povray code, and I'll assert, not a limitation of the Mandel math. 

That is correct, processors are limited in the amount of precision they 
can use. Some fractal generation programs do very high precision 
calculations by implementing their own code and data types for 
manipulating them, but this gets extremely slow.


> With the heteromf, it is--again how do I say??-- not a recursive 
> object like a sierpinski gadget.

Not all fractals are recursive...but how is the multifractal different 
from the Sierpinski gasket, besides that? There is a random element to 
it, areas can vary a lot in appearance...is that it?
It is self-similar at different scales and has an infinite level of 
detail...to me, that qualifies it as a fractal.


> My intuition was that under some parameters I would be able to set up a
> camera zoom and magnify the heck out of it, getting cooler and cooler 
> detail.
> NOT SO with the heteromf. As you tell me, I'd need to keep fiddling 
> with the params as I zoomed deeper and deeper in.

Only so the larger scale frames don't waste computation time on 
invisible detail...that's the only reason not to just set a high value 
and use it all the way.


> Whereas in the Mandel, one setting gives a cool image at both camera 
> angle 20 and 20E-12, and both are super-quick renders. 

Well, that just gives you more detail than your pixels can represent at 
the higher scales...and those would likely be even faster if you used 
fewer iterations on the larger scale frames. The only reason for 
adjusting the octaves is to lower render time. That does not make it 
something other than a fractal.


> I was expecting heteromf to be something like a sierpinski gadget, 
> only in "crumbly sandy rock" form.

You might be able to get something like that...or you may be trying to 
get the multifractal to pretend to be a different kind of fractal. I'd 
play around with complex noise3d() based functions...
Raising the octaves will increase the level of detail, making smaller, 
higher frequency features, just like increasing the iterations on a 
Sierpinski gasket...what is the problem with understanding that?


> Mandel has infinite; I didn't claim that all fractals had infinite.

Well, actually, I think that is one part of the definition...computer 
generated fractals are finite simply because it would take an infinite 
amount of time and memory otherwise. Technically, any computer-generated 
fractal is an approximation.


> Have you seen the rendering textbook where they show zooms of an 
> island? Blue water, crumbly brown granola bar peninsulas, looking the 
> same at say 5 orders of magnitude.  Povray is so powerful that I'm 
> betting I can do it with existing Megapov code,

You probably could...but don't try to force a specific fractal to do 
that, and complain that it isn't a real fractal when you don't get the 
results you expect.


> sorry for haranguing you so much on this subject...............

I just want to know why you don't believe the multifractal is a fractal.

-- 
Christopher James Huff
Personal: chr### [at] maccom, http://homepage.mac.com/chrishuff/
TAG: chr### [at] tagpovrayorg, http://tag.povray.org/

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