SyntaxBomb - Indie Coders

Low-Resolution Mandelbrot Set { Sig[Z^2+c] < 2.0 } Fractal explorer
Limited to 255 iteration depth and the iteration steps are displayed in greyscale

This is quite basic and could benefit from greater controls, more intuitive feedback of the scale of current displayed complex plane ranges. I am thinking of a BMax NG version taking advantage of the MaxUI and multithreading to speed it up as well as 64-bit Double for greater depth and FP accuracy.


Initial Constants can be amended as parameters to adjust scale and speed


Const INFINITY_TEST_LIMIT#=2.0
Const ITERATION_LIMIT=256
Const GW=128
Const GH=128

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; COMPLEX Class
Type Complex
Field Real#
Field Imaginary#
End Type

Function Subtract.Complex(U.Complex,V.Complex)
Local Z.Complex=New Complex
Z\Real#=U\Real#-V\Real#
Z\Imaginary#=U\Imaginary#-V\Imaginary#
Return Z
End Function

Function Add.Complex(U.Complex,V.Complex)
Local Z.Complex=New Complex
Z\Real#=U\Real#+V\Real#
Z\Imaginary#=U\Imaginary#+V\Imaginary#
Return Z
End Function

Function Multiply.Complex(U.Complex,V.Complex)
Local Z.Complex=New Complex
Z\Real#=(U\Real#*V\Real#)-(U\Imaginary#*V\Imaginary#)
Z\Imaginary#=(U\Real#*V\Imaginary#)+(V\Real#*U\Imaginary#)
Return Z
End Function

Function Conjugate.Complex(Z.Complex)
Local W.Complex=New Complex
W\Real#=Z\Real#
W\Imaginary#=0.0-Z\Imaginary#
Return W
End Function

Function IsEqual(U.Complex,V.Complex)
Return (U\Real#=V\Real#) And (U\Imaginary#=V\Imaginary#)
End Function

Function CreateComplex.Complex(Real#,Imaginary#)
Local Z.Complex=New Complex
Z\Real#=Real#
Z\Imaginary#=Imaginary#
Return Z
End Function

Function PrintComplex(Z.Complex)
If (Z\Imaginary=0.0)Then Print Z\Real:Return
Local Operator$="+"
If (Z\Imaginary<0.0)Then Operator=""
Print Z\Real#+Operator+Z\Imaginary#+"i"
End Function

Function GraphPlot(a.Complex)
Plot a\Real#,a\Imaginary#
End Function
;____________________________________________________________________________________________________________________________________________________________

SeedRnd=MilliSecs()



Global FLOPS=0

Graphics GW,GH,32,2
SetBuffer BackBuffer()

Local X
Local Y

Local MX,MY

Local C.Complex
Local Max
Local Timestamp=MilliSecs()
While Not KeyHit(1)
FLOPS=0

C=New Complex
C\Real=Float((MX-(GW*0.5))/GW)
C\Imaginary=Float((MY-(GH*0.5))/GH)

Max=0

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;Text 0,GH-12,"WORKING..."
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;Flip

LockBuffer; BackBuffer()

Local w=GW-1
Local h=GH-1

Local fw#=Float(GW)
Local fh#=Float(GH)


For Y=0 To h
For X=0 To w
Local XX#=(1.0/fw)*X
Local YY#=(1.0/fh)*Y

FLOPS=FLOPS+4

Local Steps=Iterate(XX#,YY#,C) And 255

Local Col= Steps+(Steps Shl 8)+(Steps Shl 16)

If (Steps>Max) Then Max=Steps

WritePixelFast X,(GH-1)-Y,Col;,BackBuffer()

Next
Next

;Delay 1
UnlockBuffer; BackBuffer()
Timestamp=(MilliSecs()-Timestamp)*0.001

;;;;;;;;;;;;;;;;;;;;;;;;;;;;Text 0,GH-12,Str(FLOPS/Timestamp)+" Flops * Hertz"

Flip

; DebugLog Max

Delete C

FlushMouse
WaitMouse()
MX=MouseX()
MY=MouseY()
Cls
Flip

Wend

Function Iterate(ZReal#,Zimaginary#,C.Complex)
Local Count
Local Extern

Local Z.Complex=CreateComplex(ZReal#,Zimaginary#)

For Count=1 To ITERATION_LIMIT
Z.Complex=Algorithm(Z,C)

If ((Magnitude(Z))>INFINITY_TEST_LIMIT#)
Delete Z
Return Count
End If
Next
Delete Z
Return 0
End Function

Function Algorithm.Complex(Z.Complex,C.Complex)
Local U.Complex=Multiply(Z,Z)
Local V.Complex=Add(U,C)

FLOPS=FLOPS+2

Delete Z
Delete U

Return V
End Function

Function Magnitude#(Z.Complex)

FLOPS=FLOPS+3

Return Sqr((Z\Real#*Z\Real#)+(Z\Imaginary#*Z\Imaginary#))
End Function