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I've done a lot of playing around with the parameters of the heteromf
function. The question is: will any of the settings ever lead me to a
fractal, to something with infinite complexity, to a structure I can do
a zoom in on for a dozen orders of magnitude as I did in:
p.b.a. : Subject: Mandel fractal zoom (686 kbbu) Date: Sun, 10
Dec 2000 17:46:56 -0500
(I had to overdefine my term as some like to nitpick my terminology.
:-| )
I remember seeing in a graphics textbook where someone had zoomed in on
a 3D mountainous seascape fractal structure that looks like some of the
sandbar/granola bar structures I'm starting to see with heteromf.
Do you think that they used this function?
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In article <3A533572.364B53F8@my-dejanews.com>,
gre### [at] my-dejanews com wrote:
> I've done a lot of playing around with the parameters of the heteromf
> function. The question is: will any of the settings ever lead me to a
> fractal, to something with infinite complexity, to a structure I can do
> a zoom in on for a dozen orders of magnitude as I did in:
It *is* a fractal, though that may not be immediately obvious by the
result, and to have infinite complexity would take an infinite amount of
calculation time. That's a problem. :-)
You could probably do what you want by increasing the octaves of the
function as you zoom in. Similar to what you need to do in order to zoom
far into a mandel pattern.
--
Christopher James Huff
Personal: chr### [at] maccom, http://homepage.mac.com/chrishuff/
TAG: chr### [at] tagpovrayorg, http://tag.povray.org/
<><
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Chris Huff wrote:
> It *is* a fractal, though that may not be immediately obvious by the
> result, and to have infinite complexity would take an infinite amount of
> calculation time. That's a problem. :-)
> You could probably do what you want by increasing the octaves of the
> function as you zoom in. Similar to what you need to do in order to zoom
> far into a mandel pattern.
Thanks for taking the time to reply for my eclectic projects here and there,
but hopefully some may help spark ideas on how to further improve pov!
Actually, in my Mandel and Julia zooms, I needed an exhaustive color_map, but
*never* changed the pattern itself: only the camera angle changed in those
anims. And I keep using the term "infinite complexity" because as I
understand it, the pure math behind the concept has detail literally, ad
infinitum--it's just these finite clunky PC's that limit us to a mere 12
orders of magnitude. I once heard a precise definition of fractal as
something that has interesting detail at many orders of magnification.
I asked the question as I looked at the structures I'm making because I'm
beginning to doubt that it is fractal in the same sense or to the same degree
as the mandel. Yes, I'm thinking I'd have to keep changing parameters as I
zoomed on on it. If I have to do that, I may as well just change the scale
;-)
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In article <3A5487CE.BC74CB31@my-dejanews.com>,
gre### [at] my-dejanewscom wrote:
> Actually, in my Mandel and Julia zooms, I needed an exhaustive
> color_map, but *never* changed the pattern itself: only the camera
> angle changed in those anims.
Then the number of iterations you used was large enough that you didn't
need to change anything as you zoomed in...you might have gotten faster
rendering if you reduced it at the higher scales.
> And I keep using the term "infinite complexity" because as I
> understand it, the pure math behind the concept has detail literally,
> ad infinitum--
If you used infinite octaves in the multifractal, it would have an
infinite level of detail...and take an infinite amount of time to
compute 1 pixel.
> it's just these finite clunky PC's that limit us to a mere 12 orders
> of magnitude.
Where did you get that number? The possible orders of magnitude of
detail would depend on the fractal you are computing and the amount of
time you have to do the calculations...and sometimes on available memory.
> I once heard a precise definition of fractal as something that has
> interesting detail at many orders of magnification.
"many" != "infinite"
And that doesn't seem very precise to me...it generally has to be
self-similar as well.
> I asked the question as I looked at the structures I'm making because
> I'm beginning to doubt that it is fractal in the same sense or to the
> same degree as the mandel.
It is a fractal, in the same way the mandel pattern is a fractal. As for
the "degree", that is a matter of the default settings...iterations of
the mandel pattern or octaves of the multifractal.
> Yes, I'm thinking I'd have to keep changing parameters as I zoomed on
> on it. If I have to do that, I may as well just change the scale
Changing the scale as you zoom in is completely different from
increasing octaves...
--
Christopher James Huff
Personal: chr### [at] maccom, http://homepage.mac.com/chrishuff/
TAG: chr### [at] tagpovrayorg, http://tag.povray.org/
<><
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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.
Chris Huff wrote:
> Then the number of iterations you used was large enough that you didn't
> need to change anything as you zoomed in...you might have gotten faster
> rendering if you reduced it at the higher scales.
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.
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. So once I had completed a lot of tweaking to
find an interesting x/z location, I just set up a simple code to reduce
camera angle and voila! I've got a cool zoomin' anim. With the heteromf, it
is--again how do I say??-- not a recursive object like a sierpinski gadget.
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.
> If you used infinite octaves in the multifractal, it would have an
> infinite level of detail...and take an infinite amount of time to
> compute 1 pixel.
Whereas in the Mandel, one setting gives a cool image at both camera angle 20
and 20E-12, and both are super-quick renders. I was expecting heteromf to be
something like a sierpinski gadget, only in "crumbly sandy rock" form.
> > I once heard a precise definition of fractal as something that has
> > interesting detail at many orders of magnification.
>
> "many" != "infinite"
> And that doesn't seem very precise to me...it generally has to be
> self-similar as well.
Mandel has infinite; I didn't claim that all fractals had infinite.
> > I asked the question as I looked at the structures I'm making because
> > I'm beginning to doubt that it is fractal in the same sense or to the
> > same degree as the mandel.
>
> It is a fractal, in the same way the mandel pattern is a fractal. As for
> the "degree", that is a matter of the default settings...iterations of
> the mandel pattern or octaves of the multifractal.
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, sorry for haranguing you so much on this
subject...............
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On Thu, 04 Jan 2001 17:24:24 -0500, Greg M. Johnson wrote:
>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.
Not true. You can crank the octaves way up from the beginning, if you want.
It'll just render much more slowly for no added benefit at the lesser zooms.
--
Ron Parker http://www2.fwi.com/~parkerr/traces.html
My opinions. Mine. Not anyone else's.
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Greg M. Johnson wrote in message <3A5487CE.BC74CB31@my-dejanews.com>...
>Chris Huff wrote:
>
>> It *is* a fractal, though that may not be immediately obvious by the
>> result, and to have infinite complexity would take an infinite amount of
>> calculation time. That's a problem. :-)
>> You could probably do what you want by increasing the octaves of the
>> function as you zoom in. Similar to what you need to do in order to zoom
>> far into a mandel pattern.
>
>Actually, in my Mandel and Julia zooms, I needed an exhaustive color_map,
but
>*never* changed the pattern itself: only the camera angle changed in those
>anims
As I understand the Heteromf pattern, the "octaves" setting is the
equivalent of the iterations of a Mandel or Julia pattern.
--
Mark
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"Greg M. Johnson" <gre### [at] my-dejanewscom> wrote in message
news:3A54F817.35634205@my-dejanews.com...
>
> 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.
>
But this is almost certainly what any fractal program - that's why they get
slower the more you zoom in. I know of no reasonable definition of a fractal
that doesn't imply an infinite amount of calculations for "perfection".
>
> Mandel has infinite; I didn't claim that all fractals had infinite.
>
... but you should. They do.
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First of all everyone, when I say I want "infinite" with povray, I guess I mean
a full 12 orders of magnitude of zoom as I was able to get with Mandel. I hope
yall have understood this is what I meant.
Tom Melly wrote:
> "Greg M. Johnson" <gre### [at] my-dejanewscom> wrote in message
> news:3A54F817.35634205@my-dejanews.com...
> >
> > 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.
> >
>
> But this is almost certainly what any fractal program - that's why they get
> slower the more you zoom in. I know of no reasonable definition of a fractal
> that doesn't imply an infinite amount of calculations for "perfection".
> > Mandel has infinite; I didn't claim that all fractals had infinite.
> ... but you should. They do.
I did some reading on a fractals textbook last night. If someone were to say
write an INC to make a Sierpinski sponge--truly a fractal object, a recursive
object. I would have to put in a parameter for "desired number of iterations."
So even if I put in say 2 or 3 iterations to the sponge, it would still be
"fractal," although perhaps a better description is "the 3rd order approximation
of the Sierpinski gadget (/sponge??)". If I wanted to do a zoom encompassing 12
orders of magnitude on the Sierpinski gadget with interesting details all the
way down, I would have to put in a lot of iterations in the structure--let's say
12 as a first guess. And the parse time and memory usage for the object at the
1E12 zoom would likely exceed the capacity of my PC and/or C and/or the Intel
chip. Mandel, however, is quite cool. See an image I posted in p.b.i.
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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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