Spectrum two-liner
William McBrine
probably my favorite is this trivial little thing:
10 POKE 22528+RND*767,RND*63
20 GO TO 10
It was supposed to print squares of random color at random locations on
the screen. (Why? I dunno; that's just the sort of thing I did back then.)
But it didn't quite turn out that way. As more squares were plotted, a
distinct pattern emerged.
This program exposes the "pseudo" aspect of the psuedo-random number
generator. I also find it quite beautiful. The best part is that the
location of each plot does appear random, and there's some margin of
error, so that a particular cell may change colors a few times, while
remaining within the overall pattern. Replacing "63" with "127" also works
well.
If you reverse the order in which the two calls to RND are made, the
effect is lost.
--
William McBrine | http://www.clark.net/~wmcbrine/
wmcb...@clark.net | Disclaimer: I speak for God.
Richard Ward
As far as I know generating Random numbers on computers is impossible
as even the random number generator built in the spectrum is following
a formula. Most likely from the time and R register built in the
chip.
Rich
On Tue, 24 Aug 1999 16:05:58 GMT, William McBrine <wmcb...@clark.net>
wrote:
>Of all the programs I've written for my TS2068 (the American Spectrum),
>probably my favorite is this trivial little thing:
>
> 10 POKE 22528+RND*767,RND*63
> 20 GO TO 10
>
>It was supposed to print squares of random color at random locations on
>the screen. (Why? I dunno; that's just the sort of thing I did back then.)
>But it didn't quite turn out that way. As more squares were plotted, a
>distinct pattern emerged.
>
>This program exposes the "pseudo" aspect of the psuedo-random number
>generator. I also find it quite beautiful. The best part is that the
>location of each plot does appear random, and there's some margin of
>error, so that a particular cell may change colors a few times, while
>remaining within the overall pattern. Replacing "63" with "127" also works
>well.
>
>If you reverse the order in which the two calls to RND are made, the
>effect is lost.
====================
rich...@bigfoot.com
ICQ : 5267472
Philip Kendall
McBrine <wmcb...@clark.net> wrote
>Of all the programs I've written for my TS2068 (the American Spectrum),
>probably my favorite is this trivial little thing:
>
> 10 POKE 22528+RND*767,RND*63
> 20 GO TO 10
I have to say that's not particularly original. To quote from the
Spectrum manual (p.89):
10 POKE 22527+RND*704,RND*127
20 GOTO 10
:-)
Phil
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Marco Vacquier
In article <37c70bf6...@news.cableinet.co.uk>, rich...@bigfoot.com (Richard Ward) writes:
>
>As far as I know generating Random numbers on computers is impossible
>as even the random number generator built in the spectrum is following
>a formula. Most likely from the time and R register built in the
>chip.
>
>Rich
If the ramdom numbers are following a fixed formula, you'll always get the same
sequence of numbers, but the formula is not fixed. The Spectrum has a system
variable called a seed which is planted into the formula as a startingpoint.
Every time you do a RND instruction you move up 1 place in the sequence.
However, the Spectrum has the RANDOMIZE command to create a new seed,thus
making a new starting point for the formula. The new seed is derived from
another system variable, the frame counter. There the number of display frames
is being counted which have been generated since the Spectrum has been switched
on or since the counter overflowed.
If you use INKEY$ in a program to detect a key pressure on the keyboard, and
then issue a RANDOMIZE command, you'll get a proper random number with RND.
_____________________________________________________________________________
| Marco Vacquier | This article is based on my own opinion |
| | and is independent of the opinion of my |
| Alcatel Telecom Nederland B.V. | employer. |
| The Netherlands | QL stands for Quantum Leap |
-----------------------------------------------------------------------------
| Next Sin_QL_Air meeting in Eindhoven(NL): 4 September 1999, 10am-4pm |
-----------------------------------------------------------------------------
Robin Glover
:
: As far as I know generating Random numbers on computers is impossible
: as even the random number generator built in the spectrum is following
: a formula. Most likely from the time and R register built in the
: chip.
:
: Rich
I'd have thought it was probably a variant on the
not-very-random-'RANDU' routine that's fairly widely used. If I
remember rightly it involves addition of some large number modulo some
other large number. There's a discussion of Random number generation
in 'Numerical Recipies', which almost certainly refers back to some
stuff written by Donald Knuth...
The upshot is that it's not bad for a small number of random numbers,
but a pattern will begin to emerge (as the original poster
noted). Back when the National Lottery was new here in the UK, I wrote
a lottery simulator to confirm my suspicion those ideas of covering 7
numbers with 7 tickets to improve your chances being a load of
bull. My first version was hitting the jackpot about 1 time in 1
million due to the random number generator repeating itself. In the
end I set up an array of 49 numbers, initially filled with the numbers
1 to 49 in order. To draw a number, you pick a random element of the
array and take the value it contains, then swap the contents of two
random elements before continuing. In theory this could increase the
return period of the random numbers by a factor of 6*10^62 (49
factorial), but in practice it probably gets nowhere near this
factor. Anyhow, it was enough to deal with the lottery problem and
prove my point.
Oh yes, just for the record, Linux (and maybe other systems?) do
generate truly random numbers - Linux measures the timing of external
events (key presses, network packets, interrupts etc) to
micro(milli?)second accuracy to build up information to generate
truly random numbers.
Robin
Ian Collier
>I have to say that's not particularly original. To quote from the
>Spectrum manual (p.89):
D'oh. I was going to say that. (-:
>10 POKE 22527+RND*704,RND*127
>20 GOTO 10
Hmm, this could sometimes affect location 22527 (placing some random dots
in the bottom right hand corner of the screen). Using INT would be much
preferable. And, while the above shows the pattern pretty clearly, using
768 instead of 704 gives a more impressive result. (Also, using INT (RND*64)
for the colour value makes the stripes wider, thus accentuating the result).
--
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Ian Collier
>Richard Ward (rich...@bigfoot.com) wrote:
>: As far as I know generating Random numbers on computers is impossible
>: as even the random number generator built in the spectrum is following
>: a formula. Most likely from the time and R register built in the
>: chip.
>I'd have thought it was probably a variant on the
>not-very-random-'RANDU' routine that's fairly widely used. If I
>remember rightly it involves addition of some large number modulo some
>other large number. There's a discussion of Random number generation
>in 'Numerical Recipies', which almost certainly refers back to some
>stuff written by Donald Knuth...
Yes. As someone said, the time (in the sense of 'time since the Speccy was
switched on' since obviously most Spectrums don't have a real time clock) is
only used when you type RANDOMIZE with no (or zero) parameter, and the R
register is not used at all.
The formula used is: SEED <- ((1+SEED)*75 MOD 65537) - 1
This is a simple variant of a type of generator discussed by Knuth, in
which the modulus is a prime number and the formula will generate all
possible numbers except zero (so adding and subtracting 1 reduces the
range of numbers produced from 1-65536 to 0-65535). This form of random
number generator is reasonably good for simple applications and the fact
that the answer fits exactly in one word makes it ideal for the Speccy.
> Back when the National Lottery was new here in the UK, I wrote
>a lottery simulator to confirm my suspicion those ideas of covering 7
>numbers with 7 tickets to improve your chances being a load of
>bull. My first version was hitting the jackpot about 1 time in 1
>million due to the random number generator repeating itself. In the
>end I set up an array of 49 numbers, initially filled with the numbers
>1 to 49 in order. To draw a number, you pick a random element of the
>array and take the value it contains, then swap the contents of two
>random elements before continuing. In theory this could increase the
>return period of the random numbers by a factor of 6*10^62 (49
>factorial), but in practice it probably gets nowhere near this
>factor.
Knuth gives an algorithm for 'self shuffling' random numbers which seems
related to what you have there. It would go something like this.
10 REM initialisation
20 RANDOMIZE
30 LET N=32: DIM a(N): REM N can be anything, really
40 FOR i=1 TO N: LET a(i)=RND: NEXT i
50 LET Y=RND
100 REM for each random number do this
110 LET Y=INT(Y*N)+1
120 LET x=RND
130 LET tmp=a(Y): LET a(Y)=x: LET Y=tmp
140 PRINT Y: GO TO 100
>Oh yes, just for the record, Linux (and maybe other systems?) do
>generate truly random numbers - Linux measures the timing of external
>events (key presses, network packets, interrupts etc) to
>micro(milli?)second accuracy to build up information to generate
>truly random numbers.
Yep, and all these events are mixed up in a cryptographically secure
function so the resulting numbers are pretty unpredictable.
Also, ERNIE is a rather famous example of a computer with a true random
number generator.
William McBrine
: I have to say that's not particularly original. To quote from the
: Spectrum manual (p.89):
Ouch. :-) I don't think it was in the 2068 manual, but I'll have to check
now. I think I [re]discovered it independently, but it could just be that
my memory is failing me...
: 10 POKE 22527+RND*704,RND*127
^ a little early to start, no?
William McBrine
: 768 instead of 704 gives a more impressive result. (Also, using INT (RND*64)
: for the colour value makes the stripes wider, thus accentuating the result).
And in some ways, it looks best on a monochrome monitor -- you can see
that the stripes are arranged from dark to light.
Robert J. Baker
1999 21:18:57 GMT, rich...@bigfoot.com (Richard Ward) would say:
>As far as I know generating Random numbers on computers is impossible
>as even the random number generator built in the spectrum is following
>a formula. Most likely from the time and R register built in the
>chip.
I thought the formula RND uses was well-known. (In fact, I think it's
in the manual somewhere.) The new SEED, S', is calculated from the
old one (S) by:
S'=(((S+1)*75) | 65537)-1
and RND=S'/65536
You might like to do a Deja search for "Fast! RND Function", for a RND
replacement that's about five times faster...
--
--------------------------------------------------
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Philip Kendall
<rich...@bigfoot.com> wrote
>
>As far as I know generating Random numbers on computers is impossible
>as even the random number generator built in the spectrum is following
>a formula.
What about measuring the Johnson noise in a resistor, which is (a very
good approximation) to random? Machines to do this (and other things
along these lines) have been built.
>Most likely from the time and R register built in the chip.
That doesn't sound like a good way to produce random numbers to me --
the R register is far too predictable. The Speccy's method is documented
in the manual.
Phil
--
/ Philip Kendall (pa...@cam.ac.uk pa...@kendalls.demon.co.uk) \
| New? Read the FAQ: http://www.kendalls.demon.co.uk/cssfaq/ |
William McBrine
: Ouch. :-) I don't think it was in the 2068 manual, but I'll have to check
Nope, not there. So at least I didn't read it _there_. :-)
Heeeeeeeez back!
> On a modern PC with a soundcard - even without a Mic or line plug connected -
> there is background noise. As long as the noise is random, this sound levels
> could then be incorporated in the random generator. The Spectrum must have a
> signal coming from the tape player while conected even when not playing at
> tape...
The signal would be too small for the computer to read...
Look up quantisation in a signal processing book...
:)
And as for the speccy tape port, that only had a 1 bit quantisation...
1...or 0... Not very random...
--
| |What to do if you find yourself stuck in a crack|
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| |can't move, with no hope of rescue. |
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| in |good to you so far... |
| Computer Science | -The BOOK, Hitch-hiker's guide to the galaxy.|
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Ian Collier
the following story:
>10 plot int rnd*255, int rnd*192
>20 goto 10
>which just plots random dots
<pedantic> No, it just plots a single dot in the bottom left-hand corner.
Anyway, you want 176 not 192 because BASIC can't plot in the bottom two
lines.
</pedantic>
When I try this (or a suitably corrected version thereof) I get vertical
lines. Actually they are not vertical - they lean to the right by about
1 degree.
pall...@hotmail.com
rich...@bigfoot.com (Richard Ward) wrote:
>
> As far as I know generating Random numbers on computers is impossible
> as even the random number generator built in the spectrum is following
> chip.
How about getting a lava lamp, leaving it on for a bit to warm up while
you plug a webcam into your pc. digitize the lavalamp, ADD, XOR etc
the screenshots into a byte/word etc and voila - chaotic randomness.
possibly. i`m not exactly mr maths, but i cant see anything wrong with
this idea.
Alex. (Pallex a@t rocketmail dotty com)
Sent via Deja.com http://www.deja.com/
Share what you know. Learn what you don't.
Rupert Goodwins
Heeeeeeeez back! <spi...@news.freenet.co.uk> wrote in message
news:dje1q7...@bursar.freenet.co.uk...
> Matthew Holmes <m.ho...@clara.net> wrote:
> > On a modern PC with a soundcard - even without a Mic or line plug
connected -
> > there is background noise. As long as the noise is random, this sound
levels
> > could then be incorporated in the random generator. The Spectrum must
have a
> > signal coming from the tape player while conected even when not playing
at
> > tape...
>
> The signal would be too small for the computer to read...
> Look up quantisation in a signal processing book...
> :)
>
> And as for the speccy tape port, that only had a 1 bit quantisation...
> 1...or 0... Not very random...
>
> --
The Speccy tape port reads back zero if there's nothing coming into it --
you need quite a chunk of audio to get the Schmitt trigger (I *think* it was
a Schmitt trigger) to, er, trigger. Unlike a modern sound card, there's no
gain to speak of on the port: it's designed to be used with a few hundred
milliwatts of audio.
However, if you bung white noise in from, say, an untuned FM radio, you can
indeed use the port as a reasonable source of randomness. Read in a bit,
mask it into a register, rotate, wait for a few hundred T-states (so you'll
be sampling at a reasonable audio frequency) and repeat until you've filled
the register. It's fascinating (if you like this sort of thing) to then plot
the distribution of the data, and fiddle with the radio controls to see what
the quality of the output actually is.
You can also use this sort of thing to do other basic analysis on the audio
input: the 128 tape tester displayed a graph that effectively measured the
number of HF transitions on the port, with the idea that once you've managed
to maximise that you've got the best chance of getting data off the tape.
I'm not sure that was ever proved to work, but it seemed useful enough.
In reverse, I once wrote a little drum machine program that read out a chunk
of the ROM, bit by bit, through the tape port to simulate white noise.
Worked quite well if you picked the right starting point and used almost no
memory or CPU. If you multitracked the resulting noise on a Revox, you could
get some lovely phasing...
One thing to watch if you take the FM radio approach -- if you get signals
from within the Speccy feeding back into the FM receiver, you can quite
easily get non-random results. Cryptographers go to great lengths to avoid
this sort of thing, so if you're planning to set up an international data
encryption service using your Sinclair you may care to read further about
this. If you want to generate lots of random numbers, you might like to set
up a reverse-biassed zener diode circuit...
Rupert
Rupert Goodwins
<sam@greenaumARSE!ARSE!ARSE!.demon.co.uk> wrote in message
news:37c76384...@news.demon.co.uk...
> On Tue, 24 Aug 1999 21:18:57 GMT, rich...@bigfoot.com (Richard Ward)
> sprachen:
>
> >As far as I know generating Random numbers on computers is impossible
> >as even the random number generator built in the spectrum is following
> >a formula. Most likely from the time and R register built in the
> >chip.
>
> power of 75 and subtracts 1, or something. More consistent, because
> you can call it as often as you like and it'll still be random.
>
> ------------------------------------------------------------------------
>
> Why pamper life's complexity,
> when the leather runs smooth on the passenger seee-eee-aaat?
>
> http://www.greenaum.demon.co.uk/
Nah. There's *no* algorithmic way to generate truly random numbers, although
there are many that are easily good enough for many purposes -- shift
registers with feedback are popular. For true randomness, you need an input
from a physical system that demonstrates true random behaviour. Avalanche or
thermal noises from electronic components are the systems of choice: at a
pinch you can usually get away with timing keystrokes if you're careful.
Most users tend to be random beings if you look at them hard enough.
Rupert
Philip Kendall
>
>How about getting a lava lamp, leaving it on for a bit to warm up while
>you plug a webcam into your pc. digitize the lavalamp, ADD, XOR etc
>the screenshots into a byte/word etc and voila - chaotic randomness.
>possibly. i`m not exactly mr maths, but i cant see anything wrong with
>this idea.
I think Knuth is relevant here:
"Random number generators should not be determined randomly"
Phil
[Followup-To: set appropriately]
Spike!
> On Fri, 27 Aug 1999 23:30:52 +0100, Philip Kendall
> <pa...@kendalls.demon.co.uk> sprachen:
>>[Followup-To: set appropriately]
> Man that's so needlessly smug and smartassed. Why do it? I don't mean
> your justification for it, I mean, WHY?
I was wondering why as well...
It's not as if it's drifted that far off topic this time either....
--
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| |graphical shell for a 16 bit patch to an 8 bit |
| Andrew Halliwell BSc |operating system originally coded for a 4 bit |
| in |microprocessor, written by a 2 bit company,that|
| Computer Science | can't stand 1 bit of competition. |
-----------------------------------------------------------------------------
|GCv3.12 GCS>$ d-(dpu) s+/- a C++ US++ P L/L+ E-- W+ N++ o+ K PS+ w-- M+/++|
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-----------------------------------------------------------------------------
Philip Kendall
<spi...@news.freenet.co.uk> wrote
>sam@greenaumARSE!ARSE!ARSE!.demon.co.uk wrote:
>> On Fri, 27 Aug 1999 23:30:52 +0100, Philip Kendall
>> <pa...@kendalls.demon.co.uk> sprachen:
>
>>>[Followup-To: set appropriately]
>
>> Man that's so needlessly smug and smartassed. Why do it? I don't mean
>> your justification for it, I mean, WHY?
>
>I was wondering why as well...
>It's not as if it's drifted that far off topic this time either....
Because, at least IMHO, a discussion of how to program RNGs is not on-
topic in css. Specific implementations for the Speccy, yes. General
discussions how to write one, no.
If you think it is on-topic, you're perfectly welcome to override the
Followup-To: -- all Followup-To: means is where the author thinks that
follow ups would be most appropriate. There's no need to start flaming
because you don't agree with someone's opinion...
Phil
Dave Robinson
> On 26 Aug 1999 13:37:20 GMT, i...@comlab.ox.ac.uk (Ian Collier)
> sprachen:
>
> >Actually they are not vertical - they lean to the right by about
> >1 degree.
>
> So they are, in fact, diagonal?
[really pedantic]
They probably wouldn't have been vertical in the first place. A vertical
line segment is defined as being a straight line segment (technically, a
line is of infinite length) which passes through the centre of the
Earth. Horizontal is then defined as any straight direction
perpendicular to the horizontal. Finally, diagonal is any straight
direction which isn't horizontal or diagonal.
The use of the word "straight" is particularly important here. Since the
screen on which it was viewed was almost certainly curved, it would have
been damn near physically impossible to obtain a vertical, diagonal,
horizontal or any other form of straight line. Calling the line "curved"
is probably the safest way of going about it.
[/really pedantic]
If anybody wants to flame me and call me a picky, stupid, ignorant
wanker or some such, please feel free to do so.
Dave Robinson
ravyda...@hotmail.com
Dave Robinson
John Dow
>[really pedantic]
>They probably wouldn't have been vertical in the first place. A vertical
>line segment is defined as being a straight line segment (technically, a
>line is of infinite length) which passes through the centre of the
>Earth. Horizontal is then defined as any straight direction
>perpendicular to the horizontal. Finally, diagonal is any straight
>direction which isn't horizontal or diagonal.
[really really pedantic]
Is it just me or did that paragraph make absolutely no sense
whatsoever?
J
John Dow <j...@retrospec.co.uk>
Retro code monster
http://www.retrospec.co.uk
Let It Run
Niall Tracey
: Dave Robinson <ravyda...@hotmail.com> claims:
: >[really pedantic]
: >They probably wouldn't have been vertical in the first place. A vertical
: >line segment is defined as being a straight line segment (technically, a
: >line is of infinite length) which passes through the centre of the
: >Earth. Horizontal is then defined as any straight direction
: >perpendicular to the horizontal. Finally, diagonal is any straight
: >direction which isn't horizontal or diagonal.
: [really really pedantic]
: Is it just me or did that paragraph make absolutely no sense
: whatsoever?
Clearly Dave lives in a infinitely spacial dimensioned world. There is a
vertical, defined through the centre of the Earth, but he defines
horizontal as being "any straight direction perpendicular to the
horizontal". As this is in no way connected to the vertical, an
infinite axial recursion results providing limitless potential for
direction. Hence even the most (3 dimensionally) curved TV must look
damned flat to him, so I don't see what he's worried about...
--
NT As long as but a hundred of us remain alive, never will we on any
\ \/ /conditions be brought under English rule. It is in truth not for
\ / glory, nor riches, nor honours that we are fighting, but for
/ \ freedom -- for that alone, which no honest man gives up but with
/ /\ \life itself. -- Arbroath, 1320
Robert J. Baker
Sinclair Spectrums, they would eventually reproduce the
following</joke>, which was posted on Thu, 02 Sep 1999 16:43:12 +0100
by Dave Robinson <ravyda...@hotmail.com>:
>[really pedantic]
>They probably wouldn't have been vertical in the first place. A vertical
>line segment is defined as being a straight line segment (technically, a
>line is of infinite length) which passes through the centre of the
>Earth. Horizontal is then defined as any straight direction
>perpendicular to the horizontal. Finally, diagonal is any straight
>direction which isn't horizontal or diagonal.
<really, truly pedantic>
1) "Horizontal is that direction perpendicular to the horizontal"? To
the vertical, shurely?
Or are you not quite normal? ;<)
2) HTML / XML / fake-HTML tags use angle brackets, not square ones...
</really, truly pedantic>
[snip...]
>[/really pedantic]
>
>If anybody wants to flame me and call me a picky, stupid, ignorant
>wanker or some such, please feel free to do so.
OK -- you're a picky, stupid, ignorant wanker. Or some such... ;<)
(But aren't we all at times?...)
[dons asbestos vest and underpants, does runner...]
--
--------------------------------------------------
Regards, Robert the Eboreg
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