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Does the seed for random numbers make any difference (apart from generating
a diff. sequence)? Are big numbers better than small numbers? Are fractional
numbers better than integers?
(by "better" I suppose I mean "a longer, more random, sequence")
Also, is the random number sequence a fixed sequence, with the seed just
controlling the point at which you join the sequence. If it is a fixed
sequence, how long is it?
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Tom Melly wrote:
>
> Does the seed for random numbers make any difference (apart from generating
> a diff. sequence)?
No.
> Are big numbers better than small numbers?
See above.
> Are fractional numbers better than integers?
>
> (by "better" I suppose I mean "a longer, more random, sequence")
See above.
> Also, is the random number sequence a fixed sequence, with the seed just
> controlling the point at which you join the sequence.
Yes.
> If it is a fixed sequence, how long is it?
I don't know.
--
Ken Tyler
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Tom Melly <tom### [at] tomandlu couk> wrote:
: Does the seed for random numbers make any difference (apart from generating
: a diff. sequence)? Are big numbers better than small numbers? Are fractional
: numbers better than integers?
I have never heard that it would make any difference.
--
char*i="b[7FK@`3NB6>B:b3O6>:B:b3O6><`3:;8:6f733:>::b?7B>:>^B>C73;S1";
main(_,c,m){for(m=32;c=*i++-49;c&m?puts(""):m)for(_=(
c/4)&7;putchar(m),_--?m:(_=(1<<(c&3))-1,(m^=3)&3););} /*- Warp -*/
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"Ken" <tyl### [at] pacbellnet> wrote in message
news:3A8182D3.B378D2C3@pacbell.net...
>
>
> Tom Melly wrote:
> >
>
> > Also, is the random number sequence a fixed sequence, with the seed just
> > controlling the point at which you join the sequence.
>
> Yes.
>
This resolves all the other questions.
> > If it is a fixed sequence, how long is it?
>
> I don't know.
>
Except this one.
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Tom Melly wrote:
>
> This resolves all the other questions.
>
> > > If it is a fixed sequence, how long is it?
> >
> > I don't know.
> >
>
> Except this one.
I don't know about this particular random number generator, but a good one
should have a period of at least several millions.
According to the comments in the HF-Lab/gforge source code, the best
existing random number generator has a period of 10^600 while the one used
there has 2^144.
Christoph
--
Christoph Hormann <chr### [at] gmxde>
IsoWood include, radiosity tutorial, TransSkin and other
things on: http://www.schunter.etc.tu-bs.de/~chris/
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On Wed, 7 Feb 2001 15:47:27 -0000, Tom Melly wrote:
>If it is a fixed sequence, how long is it?
The generator function is
next_rand[stream] = next_rand[stream] * 1812433253L + 12345L;
which doesn't look particularly well-chosen to me. But if it's done right,
I'd guess that the period is pretty large (i.e. at least 1812433253).
Perhaps someone who's read volume 3 of Knuth more recently than I can
confirm or deny. Or perhaps I can dig out my copy of volume 3 and try to
find a better PRNG for 3.5, since we've all seen some of the bad results
you can get from the current one.
--
Ron Parker http://www2.fwi.com/~parkerr/traces.html
My opinions. Mine. Not anyone else's.
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On 2001-02-07 15:47, Tom Melly <tom### [at] tomandlucouk> wrote:
>If it is a fixed sequence, how long is it?
2^32.
hp
--
_ | Peter J. Holzer | All Linux applications run on Solaris,
|_|_) | Sysadmin WSR | which is our implementation of Linux.
| | | hjp### [at] wsracat |
__/ | http://www.hjp.at/ | -- Scott McNealy, Dec. 2000
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If you look around you will find lots of generators better than the one used
in POV. By the way (and this is an official request to POVTeam) even without
switching to the best currently known even the Park-Miller minimal standard
is better ...and YES, they are not significantly slower.
Some URLs:
*) A place to start: http://csrc.nist.gov/rng/
*) Park Miller Minimal Standard
http://htm4.ee.queensu.ca:8000/ling/minrng.html
*) Mersenne Twister, currently the best known
http://www.math.keio.ac.jp/~matumoto/emt.html, period is 2**19937-1 it's
not a typo... about 10**6000!!!
Alessandro Coppo
a.c### [at] iolit
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Ron Parker wrote:
> better PRNG for 3.5, since we've all seen some of the bad results
> you can get from the current one.
..bad results ??
i use the function a whole lot - what do i need to look out for?
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If you use it to randomly locate objects on a square, they look somewhat
"gridded". I noticed this creating scenes with lots (1000's) of "simple
trees" viewed from above. Anyway, this generator is known from a long time
not to pass several simple tests (well, apart from the infamous RANDU, it is
actually one of the worst).
Alessandro Coppo
a.c### [at] iolit
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Peter J. Holzer wrote in message ...
>On 2001-02-07 15:47, Tom Melly <tom### [at] tomandlucouk> wrote:
>>If it is a fixed sequence, how long is it?
>
>2^32.
I think it is actually (2^32)-2
--
Mark
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Ron Parker <ron### [at] povrayorg> wrote:
: next_rand[stream] = next_rand[stream] * 1812433253L + 12345L;
: which doesn't look particularly well-chosen to me.
It depends on what you want to do, but basically you are right, it's not
excellent.
There are better methods which give more randomness and much large periods.
For example the C library function (not standard but found in most unix
compilers and perhaps others as well) for random() is described in the
following way:
The random() function uses a nonlinear additive feedback
random-number generator employing a default state array size
of 31 long integers to return successive pseudo-random
numbers in the range from 0 to 2**31-1. The period of this
random-number generator is approximately 16 x (2**31-1). The
size of the state array determines the period of the
random-number generator. Increasing the state array size
increases the period.
If I understand this correctly, it uses a whole array as seed value instead
of one integer. I suppose that this way more randomness is achieved and
a much larger period (16*(2^31-1) is pretty large).
--
char*i="b[7FK@`3NB6>B:b3O6>:B:b3O6><`3:;8:6f733:>::b?7B>:>^B>C73;S1";
main(_,c,m){for(m=32;c=*i++-49;c&m?puts(""):m)for(_=(
c/4)&7;putchar(m),_--?m:(_=(1<<(c&3))-1,(m^=3)&3););} /*- Warp -*/
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Tom Melly <tom### [at] tomandlucouk> wrote:
> "Ken" <tyl### [at] pacbellnet> wrote in message
> news:3A8182D3.B378D2C3@pacbell.net...
>>
>>
>> Tom Melly wrote:
>> >
>>
>> > Also, is the random number sequence a fixed sequence, with the seed just
>> > controlling the point at which you join the sequence.
>>
>> Yes.
>>
> This resolves all the other questions.
>> > If it is a fixed sequence, how long is it?
>>
>> I don't know.
>>
> Except this one.
Well, most random number sequences these days use the 1/sec > heat death
system. Ie, if you got one number a second, then the sequence would take
longer than the heat death of the universe to repeat. If Pov's isn't this
good, I can get them the code for the Mersenne Twister, which is some
obscene multiple of the heat death criteria, and is also really good
randomly. And it's *fast*, which is also a big plus. We use it for high
end simulation where I work, where time is critical.
Geoff
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On Thu, 8 Feb 2001 00:36:36 +0100, Alessandro Coppo wrote:
>*) Park Miller Minimal Standard
>http://htm4.ee.queensu.ca:8000/ling/minrng.html
This one looks good, but it doesn't have any sort of writeup. Is there
another page that goes with this that might include copyright details?
>*) Mersenne Twister, currently the best known
>http://www.math.keio.ac.jp/~matumoto/emt.html, period is 2**19937-1 it's
>not a typo... about 10**6000!!!
We can't use this one at this time as its license is GPL.
--
Ron Parker http://www2.fwi.com/~parkerr/traces.html
My opinions. Mine. Not anyone else's.
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In article <slr### [at] fwicom>, ron### [at] povrayorg
wrote:
>On Thu, 8 Feb 2001 00:36:36 +0100, Alessandro Coppo wrote:
>>*) Mersenne Twister, currently the best known
>>http://www.math.keio.ac.jp/~matumoto/emt.html, period is 2**19937-1 it's
>>not a typo... about 10**6000!!!
>
>We can't use this one at this time as its license is GPL.
I saw the Mersenne Twister described in the latest WebTechniques. It
looked pretty simple. GPL is a copyright, not a patent, as far as I
know. Though I am not a lawyer, I'm pretty sure that recoding from an
English description would not infringe on a copyright.
Jerry
--
http://www.hoboes.com/jerry/
"Give a man a fish and you feed him for a day. Teach him to fish, and you've
depleted the lake."--It Isn't Murder If They're Yankees
(http://www.hoboes.com/jerry/Murder/)
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On Thu, 08 Feb 2001 08:17:05 -0800, Jerry wrote:
>In article <slr### [at] fwicom>, ron### [at] povrayorg
>wrote:
>
>>On Thu, 8 Feb 2001 00:36:36 +0100, Alessandro Coppo wrote:
>>>*) Mersenne Twister, currently the best known
>>>http://www.math.keio.ac.jp/~matumoto/emt.html, period is 2**19937-1 it's
>>>not a typo... about 10**6000!!!
>>
>>We can't use this one at this time as its license is GPL.
>
>I saw the Mersenne Twister described in the latest WebTechniques. It
>looked pretty simple. GPL is a copyright, not a patent, as far as I
>know. Though I am not a lawyer, I'm pretty sure that recoding from an
>English description would not infringe on a copyright.
True. It would only be infringement to use the posted code.
--
Ron Parker http://www2.fwi.com/~parkerr/traces.html
My opinions. Mine. Not anyone else's.
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Ron Parker wrote:
<snippage>
>find a better PRNG for 3.5, since we've all seen some of the bad results
>you can get from the current one.
I am curious: "bad results?" Is the povray generator *that*
bad? I mean, I have not done a rigorous statistical analysis of the
random output but it seems as good (as bad?) as any other random
number generator that I've used. Whenever I get bad results, I use
a different seed.
On thing I *have* noticed about the the random numbers that
pov kicks out is that they *seem* to be more like a stream of pink
"1/f" noise rather than the expected "white" noise: consecutive
values do not differ as much as one would expect (it's as if a "real"
random stream had been run through a mild low pass filter). I have
read that for more "artistic" uses, this "1/f" noise yeilds more
"pleasing" or "natural" results.
Or I could just be full of it. :-)
I suppose one could write a random number generator in the
pov langauge (Arc 4 would work nicely), or another way would be
to just use four random streams, one stream picks which of the other
three streams' output to use. You would be randomly switching
between 3 random streams. Have not tried this.
Pete
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On 7 Feb 2001 21:49:22 -0500, Pete wrote:
>Ron Parker wrote:
>
> <snippage>
>>find a better PRNG for 3.5, since we've all seen some of the bad results
>>you can get from the current one.
>
> I am curious: "bad results?" Is the povray generator *that*
>bad? I mean, I have not done a rigorous statistical analysis of the
>random output but it seems as good (as bad?) as any other random
>number generator that I've used. Whenever I get bad results, I use
>a different seed.
There's a high correlation between results, and it can lead to very
recognizable patterns. I can find a reference to the original
discussion here, if you're interested.
> On thing I *have* noticed about the the random numbers that
>pov kicks out is that they *seem* to be more like a stream of pink
>"1/f" noise rather than the expected "white" noise: consecutive
>values do not differ as much as one would expect (it's as if a "real"
>random stream had been run through a mild low pass filter). I have
>read that for more "artistic" uses, this "1/f" noise yeilds more
>"pleasing" or "natural" results.
Nope, the generator is the one I posted. Nothing fractal about it. It's
just not a very good generator. The numbers (or at least the 12345) look
just a little arbitrary.
--
Ron Parker http://www2.fwi.com/~parkerr/traces.html
My opinions. Mine. Not anyone else's.
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Jerry <jer### [at] acusdedu> wrote:
: I saw the Mersenne Twister described in the latest WebTechniques. It
: looked pretty simple. GPL is a copyright, not a patent, as far as I
: know. Though I am not a lawyer, I'm pretty sure that recoding from an
: English description would not infringe on a copyright.
It think that the problem with GPL is not that you can't use the source
code (all the contrary, GPL requires that the source code is available
and usable). The problem is that if you use the source code, the new code
you make must be GPL as well.
LGPL would be different.
--
char*i="b[7FK@`3NB6>B:b3O6>:B:b3O6><`3:;8:6f733:>::b?7B>:>^B>C73;S1";
main(_,c,m){for(m=32;c=*i++-49;c&m?puts(""):m)for(_=(
c/4)&7;putchar(m),_--?m:(_=(1<<(c&3))-1,(m^=3)&3););} /*- Warp -*/
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On 2001-02-09 04:09, Ron Parker <ron### [at] povrayorg> wrote:
>On 7 Feb 2001 21:49:22 -0500, Pete wrote:
>Nope, the generator is the one I posted. Nothing fractal about it. It's
>just not a very good generator. The numbers (or at least the 12345)
>look just a little arbitrary.
The example in the C standard also uses 12345 as the offset, but a
different multiplicator. Basically, for this kind of RNG, the three
numbers (the multiplicator, the offset and the modulus), must have a
GCD of 1[1], which is true for 1812433253 = 1289 * 1406077, 12345 = 3 *
5 * 823 and 4294967296 = 2 ^ 32). Then the sequence will produce all
non-negative numbers less than the modulus. Of course, some sequences
look more random than others ...
One problem with this type of RNG is than it produces "subsequences"
for each divisor of the modulus. For a modulus which is a power of two
this is particularly annoying since the lowest bit will run through a
sequence of two, the lowest two bits through a sequence of four etc.
Thus, to get random results, you should always take the highest bits,
not the lowest. Unlike C, Povray makes this "natural", by converting the
value to a double of range [0...1).
hp
[1] My memory is a bit fuzzy here - correct me, if I'm wrong.
--
_ | Peter J. Holzer | All Linux applications run on Solaris,
|_|_) | Sysadmin WSR | which is our implementation of Linux.
| | | hjp### [at] wsracat |
__/ | http://www.hjp.at/ | -- Scott McNealy, Dec. 2000
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