Why does this random pattern generator make an organized pattern over time?

[bplus]

I have to ponder on your suggestion, Steve.

In the meantime, here's demo, split screen, where the left side sees the looping Rnd variables to be non-power-of two, while the right side sees 8 Rnd variables in the loop.

But puzzle me this: Why does the right side appear to be a lighter color, overall? If you use _Height and _Width, to size the screen, the result looks darker, than if you use the actual pixel count. Rewrite the right side, using

z = (_Width / 2) + (420 * Rnd)

and you will see both sides equally dark. Weird.

Code: [Select]

Screen _NewImage(840, 480, 12)
Rem -------
Rem  Moral of the story: make sure *not* to define a power of 2, as total
Rem  number of random variables in the loop. Test this with 4 or 8 Rnd
Rem  variables, and you sill see diagonal patterns in the image.
Rem -------
Randomize Timer
Do
    x = Rnd * _Width
    y = Rnd * _Height
    z = 420 + Rnd * 420
    w = Rnd * _Height
    c = 1 + Int(Rnd * 15)
    q = Rnd
    r = Rnd
    s = Rnd
    Rem    t = Rnd
    Rem    u = Rnd
    PSet (x, y), c
    PSet (z, w), c
    If InKey$ = Chr$(27) Then End
    _Limit 10000
Loop
End


You have x over the whole width and z over 2nd half, so 2nd half gets more, about 1/2 of x was supposed to get.

Pete would tell you it's a half-width idea ;-))

fixed

Code: QB64: [Select]

1. Screen _NewImage(840, 480, 12)
2. Rem -------
3. Rem  Moral of the story: make sure *not* to define a power of 2, as total
4. Rem  number of random variables in the loop. Test this with 4 or 8 Rnd
5. Rem  variables, and you sill see diagonal patterns in the image.
6. Rem -------
7. Randomize Timer
8. Do
9.     x = Rnd * _Width / 2
10.     y = Rnd * _Height
11.     z = 420 + Rnd * 420
12.     w = Rnd * _Height
13.     c = 1 + Int(Rnd * 15)
14.     q = Rnd
15.     r = Rnd
16.     s = Rnd
17.     Rem    t = Rnd
18.     Rem    u = Rnd
19.     PSet (x, y), c
20.     PSet (z, w), c
21.     If InKey$ = Chr$(27) Then End
22.     _Limit 10000
23. Loop
24. End
25.  

[Bert22306]

You have x over the whole width and z over 2nd half, so 2nd half gets more, about 1/2 of x was supposed to get.

Pete would tell you it's a half-width idea ;-))

Damn, right again. Funny thing is, in my working copy, I had already fixed that. Looks like I made too many changes at the same time, and lost track of what fixed what. Thanks again, bplus!

P.S. You get a particularly beautiful color pattern, on the right side, if you define 16 random variables total. Seems brighter than with 8 variables. (Then again, not exactly what you want to see, in a PRNG test, eh?)

[luke]

I feel that perhaps the point I was trying to make was too subtle.

In particular, I was not saying anything about how to draw dots on a screen.

The point (pardon the pun) is that the random number generator has some very undesirable behaviours, namely a short period and non-uniform distribution.

The dots in screen was just a convenient way to show how damning the issue can be.

Making the on-screen pattern go away by changing which random numbers you choose is not fixing the problem, it's just hiding out from your eyes.

[SMcNeill]

Here's the perfect proof of repetition:

Code: QB64: [Select]

1. REDIM Array(100000000) AS SINGLE
2. DIM count AS _INTEGER64
3. Array(0) = RND
4. PRINT "START ", 0
5.  
6. DO
7.     count = count + 1
8.     Array(count) = RND
9.     IF Array(count) = Array(0) THEN
10.         PRINT "REPEAT ", count
11.         repeat = repeat + 1
12.     END IF
13. LOOP UNTIL repeat = 4
14.  
15. DO
16.     INPUT "Give me a number from 0 to 16777215 =>", x&
17.     PRINT Array(x&), Array(x& + 16777216), Array(x& + 16777216 * 2), Array(x& + 16777216 * 3)
18. LOOP UNTIL x& = 0
19.  
20.  

Every 16, 777, 216 numbers repeats.  That's 2^24, and it explains why it's so easy to replicate with "powers of 2", as you guys were looking at.  It'll repeat with other values as well, but it's just not as obvious plotting it, as I tried to show you with a minimal 4-number repeating data set.  ;)

[Dav]

I've been reading all the replies here.  Haven't responded much because I don't have anything worth adding - but I really appreciate everyones input so I'll reply with thanks.  My question has been answered.

Being cursed with curiosity I started trying to code getting a random number without using RND or external library functions.  Wow - I sure have been taking RND for granted.   I'm reading up on pseudo random number algorithms.  Way above my head right now.  Much respect to you who swim in those deep waters.  There is something in QB64's nature that always *seemed* random, the starting window position.  Maybe can use it as a random seed number.  RandomSeedNum& = _SCREENX * _SCREENY * TIMER.  That's about all this math-challenged guy can think of right now for getting one random number without RND.   

- Dav

   

[STxAxTIC]

This is gold!

There is something in QB64's nature that always *seemed* random, the starting window position.  Maybe can use it as a random seed number.

[Bert22306]

Every 16, 777, 216 numbers repeats.  That's 2^24, and it explains why it's so easy to replicate with "powers of 2", as you guys were looking at.  It'll repeat with other values as well, but it's just not as obvious plotting it, as I tried to show you with a minimal 4-number repeating data set.  ;)

This limitation, number of bits in the seed, applies to every PRNG. Yes, 24 bits is a small value.

When I started looking into the QB PRNG, not knowing how useful it was, I did increase the seed number, until it made no difference in the generated sequence of pseudo-random numbers. As I recall, it looked to me like it was only 22 bits wide, in effect. So, for sure, you have to take this into account, whenever PRNGs are used.

[bplus]

This 2 thing for random numbers might come from fact that 2 is most used lowest prime number factoring the most numbers.

Only one even prime and yet it factors 1/2 all numbers >= sum of all the numbers with odd prime as lowest factor.

[SpriggsySpriggs]

WinAPI has a function called CryptGenRandom, I think. It can be used to make some nice random numbers. I have code for it somewhere.

[SMcNeill]

This 2 thing for random numbers might come from fact that 2 is most used lowest prime number factoring the most numbers.

Only one even prime and yet it factors 1/2 all numbers >= sum of all the numbers with odd prime as lowest factor.

The “2 thing” is just because you have a repeating list in a value of a power of 2.

Here’s a question: With a list of 16 repeating values, how many do you have to draw to repeat the list perfectly, if you draw 1 at a time?  2 at a time?  3 at a time?  N at a time?

If you draw one at a time, after 16 numbers, you repeat perfectly. (0123456789ABCDEF.... 0123456789ABCDEF...)

If you draw 2 at a time, after 16 numbers, you repeat perfectly.  (01,23,45,67,89,AB,CD,EF...  01,23,45...)

If you draw 3 at a time, it takes 48 numbers to repeat your original pattern perfectly. (012,345,678,9AB,CDE,F01... 234,567,89A,BCD,EF0... 123,456,789,ABC, DEF... 012,345,678...)

Your repeat interval is the Lowest Common Denominator of the number you’re drawing and the number in your sequence.  It’s more obvious when dealing with this “2 thing” because you have the smallest possible repetition iteration, but it’s going to end up repeating perfectly no matter what, in the end.