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Active Forums => Programs => Topic started by: Phlashlite on February 06, 2022, 12:33:37 pm

Title: Little break to visualize prime numbers in a million real numbers.
Post by: Phlashlite on February 06, 2022, 12:33:37 pm
Thought I'd take a little break from "storm chasing" to wonder in the visualization of prime numbers. :)

WORKING CODE uploaded below.

Code: QB64: [Select]
  1. _TITLE "The Patterns in Primes"
  2.  
  3. CONST WDTH = 999
  4. CONST HGHT = 999
  5.  
  6. SCREEN _NEWIMAGE(WDTH, HGHT, 32)
  7.  
  8. DEFLNG A-Z
  9.  
  10. Limit = WDTH * HGHT
  11.  
  12. DIM Flags(Limit) AS LONG
  13.  
  14. Flags(0) = 0
  15. Flags(1) = 0
  16. FOR N = 2 TO SQR(Limit)
  17.     IF Flags(N) = 0 THEN
  18.         FOR K = N * N TO Limit STEP N
  19.             Flags(K) = 1
  20.         NEXT K
  21.     END IF
  23.  
  24. ' Display the primes
  25.  
  26. 'Spiral________________________________________________________________________
  27. 'N = 2
  28. 'E = UBOUND(Flags)
  29. 'Radius! = 0
  30. 'HalfWdth = WDTH / 2
  31. 'HalfHght = HGHT / 2
  32.  
  33. 'FOR i# = 0 TO Limit STEP .007
  34. '    IF Flags(N) = 0 THEN
  35. '        PSET (HalfWdth + Radius# * COS(i#), HalfHght - Radius# * SIN(i#)), _RGB(0, 160, 0)
  36. '    ELSE
  37. '        PSET (HalfWdth + Radius# * COS(i#), HalfHght - Radius# * SIN(i#)), _RGB(0, 0, 0)
  38. '    END IF
  39. '    IF N = E THEN EXIT FOR
  40. '    N = N + 1
  41. '    'PSET (HalfWdth + Radius# * COS(i#), HalfHght - Radius# * SIN(i#))
  42. '    Radius# = Radius# + .0007
  43. 'NEXT i#
  44.  
  45. 'L to R, T to B________________________________________________________________
  46. E = UBOUND(Flags)
  47. FOR X = 0 TO HGHT
  48.     FOR Y = 0 TO WDTH
  49.         IF Flags(N) = 0 THEN
  50.             PSET (Y, X), _RGB(0, 160, 0)
  51.         ELSE
  52.             PSET (Y, X), _RGB(0, 0, 0)
  53.         END IF
  54.         IF N = E THEN EXIT FOR
  55.         N = N + 1
  56.     NEXT
  58.  
  59.  
  60.  
Title: Re: Little break to visualize prime numbers in a million real numbers.
Post by: Phlashlite on February 06, 2022, 12:50:46 pm
Hmmm.... now that I start looking closely I'm not certain this is actually working correctly...
Title: Re: Little break to visualize prime numbers in a million real numbers.
Post by: dbox on February 06, 2022, 01:10:42 pm
I think I can see Agent Smith.
Title: Re: Little break to visualize prime numbers in a million real numbers.
Post by: Phlashlite on February 06, 2022, 01:18:51 pm
OK... this one works :)

It's interesting.  with WDTH and HGHT of 999... all the "4,5,6" line up and put clear vertical stripes  of non primes in the image.

Code: QB64: [Select]
  1. '$DEBUG
  2. _TITLE "The Patterns in Primes"
  3.  
  4. CONST WDTH = 1000
  5. CONST HGHT = 1000
  6.  
  7. SCREEN _NEWIMAGE(WDTH, HGHT, 32)
  8.  
  9. DEFLNG A-Z
  10.  
  11. Limit = WDTH * HGHT
  12.  
  13. DIM Flags(Limit) AS LONG
  14.  
  15.  
  16. Flags(0) = 1
  17. Flags(1) = 1
  18. Flags(2) = 0
  19. Flags(3) = 0
  20. FOR N = 2 TO SQR(Limit)
  21.     IF Flags(N) = 0 THEN
  22.         FOR K = N * N TO Limit STEP N
  23.             Flags(K) = 1
  24.         NEXT K
  25.     END IF
  27.  
  28. ' Display the primes
  29.  
  30. 'Spiral________________________________________________________________________
  31. 'N = 2
  32. 'E = UBOUND(Flags)
  33. 'Radius! = 0
  34. 'HalfWdth = WDTH / 2
  35. 'HalfHght = HGHT / 2
  36.  
  37. 'FOR i# = 0 TO Limit STEP .007
  38. '    IF Flags(N) = 0 THEN
  39. '        PSET (HalfWdth + Radius# * COS(i#), HalfHght - Radius# * SIN(i#)), _RGB(0, 160, 0)
  40. '    ELSE
  41. '        PSET (HalfWdth + Radius# * COS(i#), HalfHght - Radius# * SIN(i#)), _RGB(0, 0, 0)
  42. '    END IF
  43. '    IF N = E THEN EXIT FOR
  44. '    N = N + 1
  45. '    'PSET (HalfWdth + Radius# * COS(i#), HalfHght - Radius# * SIN(i#))
  46. '    Radius# = Radius# + .0007
  47. 'NEXT i#
  48.  
  49. 'L to R, T to B________________________________________________________________
  50. N = 0
  51. E = UBOUND(Flags)
  52. FOR X = 0 TO HGHT
  53.     FOR Y = 0 TO WDTH
  54.         IF Flags(N) = 0 THEN
  55.             PSET (Y, X), _RGB(0, 160, 0)
  56.         ELSE
  57.             PSET (Y, X), _RGB(0, 0, 0)
  58.         END IF
  59.         IF N = E THEN EXIT FOR
  60.         N = N + 1
  61.     NEXT
  63.  
  64.  
  65.  
Title: Re: Little break to visualize prime numbers in a million real numbers.
Post by: Phlashlite on February 06, 2022, 01:23:32 pm
Quote from: dbox on February 06, 2022, 01:10:42 pm
I think I can see Agent Smith.

That's a different program :)
Title: Re: Little break to visualize prime numbers in a million real numbers.
Post by: bplus on February 06, 2022, 09:42:23 pm
Prime spiral with zoom in / out and number ID at mouse point:
Code: QB64: [Select]
  1. _Title "Primes Blue, Composites Red:    i to focus in,    o to focus out"
  2. 'ashish copy 2018-01-08
  3.  
  4. 'bplus mods:
  5. '2018-01-08  mod of isPrime%% speeds up graphic
  6. '2018-01-09  now with focus in and out!
  7.  
  8.  
  9. w = 600
  10. Screen _NewImage(w, w, 32)
  11. Dim numData(w, w) As _Unsigned Integer
  12.  
  13. ox = w / 2
  14. oy = w / 2
  15. limit = w / 3
  16. xx = ox
  17. yy = oy
  18. path = 1
  19. direction = 1
  20. numData(ox, oy) = 0
  22.     Select Case direction
  23.         Case 1 'down
  24.             For i = 1 To path
  25.                 yy = yy + 1
  26.                 n = n + 1
  27.                 numData(xx, yy) = n
  28.             Next
  29.         Case 2 'right
  30.             For i = 1 To path
  31.                 xx = xx + 1
  32.                 n = n + 1
  33.                 numData(xx, yy) = n
  34.             Next
  35.             path = path + 1
  36.         Case 3 'up
  37.             For i = 1 To path
  38.                 yy = yy - 1
  39.                 n = n + 1
  40.                 numData(xx, yy) = n
  41.             Next
  42.         Case 4 'left
  43.             For i = 1 To path
  44.                 xx = xx - 1
  45.                 n = n + 1
  46.                 numData(xx, yy) = n
  47.             Next
  48.             path = path + 1
  49.     End Select
  50.     direction = direction + 1
  51.     If direction > 4 Then direction = 1
  52. Loop Until path > w
  53.  
  54.  
  55. sq = 3
  56. Dim vs(path, path) As _Unsigned Integer
  57. Color _RGB(255, 255, 255)
  59.     yy = 0
  60.     For y = Int(oy - path / (2 * sq) + 1) To Int(oy + path / (2 * sq) - 1)
  61.         yy = yy + 1: xx = 0
  62.         For x = Int(ox - path / (2 * sq) + 1) To Int(ox + path / (2 * sq) - 1)
  63.             xx = xx + 1
  64.             For vy = 0 To sq
  65.                 If yy * sq - sq + vy >= 0 And yy * sq - sq + vy < path Then
  66.                     For vx = 0 To sq
  67.                         If xx * sq - sq + vx >= 0 And xx * sq - sq + vx < path Then
  68.                             vs(xx * sq - sq + vx, yy * sq - sq + vy) = numData(x, y)
  69.                         End If
  70.                     Next
  71.                 End If
  72.             Next
  73.             'LINE (xx * sq - 1, yy * sq - 1)-STEP(sq - 1, sq - 1), C&, BF
  74.         Next
  75.     Next
  76.     Cls
  77.     Do
  78.         K$ = InKey$
  79.         If K$ = Chr$(27) Then
  80.             End 'escape clause
  81.         ElseIf K$ = "i" Then
  82.             If sq + 1 < 50 Then
  83.                 sq = sq + 1
  84.                 Exit Do
  85.             End If
  86.         ElseIf K$ = "o" Then
  87.             If sq - 1 >= 3 Then
  88.                 sq = sq - 3
  89.                 Exit Do
  90.             End If
  91.         End If
  92.         Cls
  93.         yy = 0
  94.         For y = Int(oy - path / (2 * sq) + 1) To Int(oy + path / (2 * sq) - 1)
  95.             yy = yy + 1: xx = 0
  96.             For x = Int(ox - path / (2 * sq) + 1) To Int(ox + path / (2 * sq) - 1)
  97.                 xx = xx + 1
  98.                 If isPrime(numData(x, y)) Then C& = _RGB(0, 0, 255) Else C& = _RGB(255, 0, 0)
  99.                 Line (xx * sq - sq, yy * sq - sq)-Step(sq - 2, sq - 2), C&, BF
  100.                 If x = ox And y = oy Then
  101.                     Line (xx * sq - sq, yy * sq - sq)-Step(sq - 2, sq - 2), _RGB(255, 255, 0), BF
  102.                 End If
  103.             Next
  104.         Next
  105.  
  106.         While _MouseInput: Wend
  107.         mouseX = _MouseX
  108.         mouseY = _MouseY
  109.  
  110.         If mouseX >= 0 And mouseY >= 0 And mouseX <= path And mouseY <= path Then
  111.             t$ = LTrim$(Str$(vs(mouseX, mouseY)))
  112.             If mouseX < 100 Then
  113.                 xAdj = 10
  114.             ElseIf mouseX > w - 100 Then
  115.                 xAdj = -Len(t$) * 8 - 10
  116.             Else
  117.                 xAdj = -Len(t$) * 4
  118.             End If
  119.             If mouseY <= w / 2 Then yAdj = 20 Else yAdj = -20
  120.  
  121.             _PrintString (mouseX + xAdj, mouseY + yAdj), t$
  122.             _Display
  123.         End If
  124.         _Display
  125.         _Limit 60
  126.     Loop
  128.  
  129. Function isPrime%% (num)
  130.     If num Mod 2 = 0 Then
  131.         If num = 2 Then isPrime%% = -1
  132.         Exit Function
  133.     Else
  134.         If num = 1 Then
  135.             Exit Function
  136.         Else
  137.             For i = 3 To Sqr(num) Step 2
  138.                 If num Mod i = 0 Then Exit Function
  139.             Next
  140.             isPrime%% = -1
  141.         End If
  142.     End If
  144.  
  145.  
Title: Re: Little break to visualize prime numbers in a million real numbers.
Post by: _vince on February 06, 2022, 09:45:16 pm
Quote from: bplus on February 06, 2022, 09:42:23 pm
Prime spiral with zoom in / out and number ID at mouse point:

is this a Golden Spiral?
Title: Re: Little break to visualize prime numbers in a million real numbers.
Post by: bplus on February 06, 2022, 09:46:34 pm
Heck no, it a simple little square spiral by a deranged spider :-))
Title: Re: Little break to visualize prime numbers in a million real numbers.
Post by: johnno56 on February 07, 2022, 03:03:22 am
"I'm seeing spots before my eyes!"
"Have you seen a Doctor?"
"No. Just spots..."
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