Prime numbers spiral exploration
Posted: Thu May 26, 2011 1:52 pm
Some guys played a bit with prime numbers on french forum. I've imagined a way to find some special patterns if numbers were distributed on 2D ; I've thought of spiral and discovered someone did that before (isn't it strange 
) : http://www.numberspiral.com/index.html. Anyway, I tried to alter dynamically the spiral parameters to push further the exploration. Here's the code, if you find the magical pattern, don't forget me
Edit: optimised IsPrime() function
) : http://www.numberspiral.com/index.html. Anyway, I tried to alter dynamically the spiral parameters to push further the exploration. Here's the code, if you find the magical pattern, don't forget me Code: Select all
;**********************************
;
; Primes numbers spiral exploration
; 26/05/2011
; by djes (djes@free.fr)
; Thx to Sirius-2337, Demivec, Gnasen for IsPrime optim
; Thx to DjPoke, Fig, zaphod, graph100, LSI & Nat the Great for LookForPrimes() optim
;
;**********************************
Global PrimesNb, ww, wh, GadgetAngle, GadgetDeviation, TextFlag
Global Dim Primes(80000)
Procedure IsPrime(number.l)
If number = 2
ProcedureReturn 1
ElseIf number % 2 = 0
ProcedureReturn 0
Else
x = Sqr(number)
For t = 3 To x Step 2
If number % t = 0
ProcedureReturn 0
EndIf
Next t
EndIf
ProcedureReturn 1
EndProcedure
Procedure SpiralDraw()
cx = ww / 2 - 20 : cy = wh / 2
Angle.d = #PI / (GetGadgetState(0) / 100)
Deviation.d = #PI / (GetGadgetState(1) / 10 )
i.d = 0
e.d = 0
;PreviousPrime = 0
StartDrawing(ImageOutput(0))
Box(0, 0, ww - 40, wh, $FFFFFF)
If TextFlag
DrawingMode(#PB_2DDrawing_Transparent|#PB_2DDrawing_XOr)
For u = 0 To PrimesNb - 1
x = cx + e * Sin(i)
y = cy + e * Cos(i)
DrawText(x, y, Str(Primes(u)), RGB($FF, $FF, 0))
i = Angle * Primes(u)
;e = Deviation * Primes(u) ;deviation from the center is based on the prime value
e + Deviation ;deviation is linear
Next u
EndIf
i.d = 0
e.d = 0
DrawingMode(#PB_2DDrawing_Default)
For u = 0 To PrimesNb - 1
x = cx + e * Sin(i)
y = cy + e * Cos(i)
If x >= 0 And x < ww - 40 And y >= 0 And y < wh
Plot(x, y, 0)
EndIf
i = Angle * Primes(u)
;e = Deviation * Primes(u) ;deviation from the center is based on the prime value
e + Deviation ;deviation is linear
;PreviousPrime = Primes(u)
Next u
StopDrawing()
StartDrawing(WindowOutput(0))
DrawImage(ImageID(0), 0, 0)
DrawText(0, 0, "Angle : PI/" + StrD(GetGadgetState(0) / 100, 2), 0, $FFFFFF)
DrawText(0, 20, "Deviation : PI/" + Str(GetGadgetState(1)), 0, $FFFFFF)
StopDrawing()
EndProcedure
Procedure GUIInit()
ww = WindowWidth(0) : wh = WindowHeight(0)
CreateImage(0, ww - 40, wh)
TrackBarGadget(0, WindowWidth(0) - 40, 16, 20, WindowHeight(0) - 16, 1, 31410, #PB_TrackBar_Vertical)
TrackBarGadget(1, WindowWidth(0) - 20, 16, 20, WindowHeight(0) - 16, 1, 4000, #PB_TrackBar_Vertical)
CheckBoxGadget(2, WindowWidth(0) - 40, 1, 40, 16, "Text")
SetGadgetState(0, GadgetAngle)
SetGadgetState(1, GadgetDeviation)
EndProcedure
Procedure LookForPrimes(RangeSearch)
;
; TextGadget(4, 5, wh / 2 - 20, ww - 40 - 5, 20, "Looking for primes numbers - Please wait", #PB_Text_Right)
; ProgressBarGadget(3, 5, wh / 2, ww - 40 - 5, 20, 0, RangeSearch, #PB_ProgressBar_Smooth)
;
; PrimesNb = 0
; For u = 2 To RangeSearch
; If IsPrime(u)
; Primes(PrimesNb) = u
; PrimesNb + 1
; EndIf
; SetGadgetState(3, u)
; Next u
; SetGadgetText(4, Str(PrimesNb) + " found")
; Delay(1000)
; FreeGadget(3)
; FreeGadget(4)
; algo nat the great pour blitzmax
; port en pb by zaphod - 23/05/2011
Define num.i = RangeSearch
Define sqrnum.i = Sqr(RangeSearch)+1
Dim PrimeFlags.i(RangeSearch)
ReDim Primes.i(RangeSearch)
Define tim.i
PrimesNb = 1
For x = 3 To sqrnum Step 2
If PrimeFlags(x) = #False
Primes(PrimesNb) = x
PrimesNb+1
tim = x + x
Repeat
PrimeFlags(tim) = #True
tim + x
Until tim >= num
EndIf
Next
Primes(0) = 2
For y = x To num Step 2
If PrimeFlags(y) = #False
Primes(PrimesNb) = y
PrimesNb+1
EndIf
Next
EndProcedure
;-MAIN
If OpenWindow(0, 0, 0, 600, 600, "Prime nb spiral explorer by djes@free.fr - Use top/down keys on gadgets", #PB_Window_SystemMenu | #PB_Window_MinimizeGadget | #PB_Window_MaximizeGadget | #PB_Window_SizeGadget)
WindowBounds(0, 500, 500, 4000, 4000)
TextFlag = #False
GadgetAngle = 247
GadgetDeviation = 600
GUIInit()
LookForPrimes(500000)
SpiralDraw()
Repeat
Event = WaitWindowEvent()
Select Event
Case #PB_Event_SizeWindow
GUIInit()
SpiralDraw()
Case #PB_Event_Gadget
Select EventGadget()
Case 0, 1
GadgetAngle = GetGadgetState(0)
GadgetDeviation = GetGadgetState(1)
SpiralDraw()
Case 2
TextFlag = ~TextFlag
SpiralDraw()
EndSelect
Case #PB_Event_CloseWindow
Quit = 1
EndSelect
Until Quit = 1
EndIf
End
)