# This text file describes bitmap :C:\Documents and Settings\adam\Pulpit\b2_error.bmp

it should be arg(phi) where phi = Boettcher coordinate but is not
added boundary of Mandelbrot set by DEM/M
#
#
# This bitmap shows Mandelbrot Set for  function F(z)=z*z+c   
#
#
# Bitmap details:
#------------------------------------------------------------
MainAlgorithmType:=maPhi  
#-----------------------------------------------------------
#  The image contains a rectangular region :   
#---------- corners of c-plane ---------------
C_Plane.eCxMin:=   -1,83333333333333
C_Plane.eCxMax:=   -0,5
C_Plane.eCyMin:=   -0,360902255639098
C_Plane.eCyMax:=   0,972431077694236
#--------- center and sides of c-plane -----------
C_Plane.Center.x:= -0,5
C_Plane.Center.y:= 0
C_Plane.width:=    1,33333333333333
C_Plane.height:=   1,33333333333333
#---------------------------------
#    Bitmap size in pixels:
Bitmap Width=      400
Bitmap Height=     400
Number of bitmap points  = 160000 points
Drawing Time := 391 miliseconds  
#
#        Bitmapa.PixelFormat = pf32bit
#------------------------------------
#    If Distorsion = 1 then image is not deformed
integer Width / Height Ratio =1
extended Width / Height Ratio =1
eWHR/iWHR = Distorsion=1
#----------------------------------------------------
# Maximal number of iterations 
IterationMax :integer:=  1000
Escape Radius :single:=  100
#-------------------------
#
#   Informations about program:
    program name: MandelbrotSetExplorer
#    It is made using:
#        programing language: object Pascal
#        compiler : VER 140-
#        IDE: Borland Delphi 6.0 - 7.0 personal edition - 10.0 Turbo Explorer
#    programing style : obiektowy
#    method : wizualna (RAD)
#    libaries : standard =  VCL
#    OS: windows 98 SE
#    hardware: PC: AMD Duron 600
#
# author:  Adam Majewski
#        adammaj1@o2.pl
#       republika.pl/fraktal
#        wa³brzych 27.06.20003- 2007





--------------------------------------
and here is delphi unit :
------------------------------------------------------------
unit BoettcherU;

interface

uses  ComplexU,
      Math, // RadToDeg
      graphics, // clBlack
      windows; // GetBValue


  Procedure GivePhi_M(c:TComplexNumber; iMax:integer; var b:TComplexNumber);  //----- color
  Procedure GiveBoettcherTerm_M(c,Zn:TComplexNumber; i:integer; var term:TComplexNumber);  //----- color
  Procedure DrawPhi_M;

//*********************************************************
implementation //******************************************
//*********************************************************



uses  BitmapU, MappingU, AlgorithmU, ColorU;


//--------------------------------
Procedure GiveBoettcherTerm_M
          (c,Zn:TComplexNumber; i:integer;var term:TComplexNumber);
  var iExponent:integer;
      temp,temp1:TComplexNumber;
      n:integer;
      eTemp:extended;
begin
  //  compute 2^i
  //iExponent:=2;
  //for n:=2 to i do iExponent:=2*iExponent;
  //
  CmplxSqr(Zn.x,Zn.y,temp.x,temp.y);
  CmplxDiv(c.x,c.y,temp.x,temp.y,temp1.x,temp1.y);
  //
  temp1.x:=1-temp1.x;
  temp1.y:=-temp1.y;
  //
  for n:=1 to i do
    begin
      CmplxSqr(temp1.x,temp1.y,temp.x,temp.y);
      temp1:=temp;
      if (temp.x>1000000000) or (temp.y>1000000000) then exit;
    end;
  //
  eTemp:=sqrt(sqrt(sqr(temp1.x)+sqr(temp1.y)));
  //
  term.x:= temp1.x *eTemp;
  term.y:=- temp1.y * eTemp;


end;
//-----------------------------------------------------------------------------
 Procedure GivePhi_M(c:TComplexNumber; iMax:integer; var b:TComplexNumber); // Bottcher function
 // phi(c) = Zn ^ (0.5 ^ n)
 // Z(n) = Fc( Z(n-1) )
 // Fc(z) = z*z + c

 var  temp,
      exponent:extended;
      i:integer;
      Zn,
      term:TComplexNumber;

 begin
   b:=c;
   Zn.x:=0;
   Zn.y:=0;
   for i:= 1 to iMax do
    begin
      temp:=sqr(Zn.x) - sqr(Zn.y)  + c.x;
      Zn.y:=2 * Zn.x *  Zn.y + c.y;
      Zn.x:=temp;
      //
      GiveBoettcherTerm_M(c,Zn,i,term);
      //

      
      CmplxMultiplication(b.x,b.y,term.x,term.y,b.x,b.y);
    end; //  for i:=

 end;

//------------------------
Procedure DrawPhi_M;


var iteration:integer;
     iY,iX:integer;
     eZx,eZy:extended; // eZ:=eZx + eZy*i
     eCy ,eCx:extended; // C:=eCx + eCy*i
     temp:extended;
     //Phi
     ePhiX,ePhiY:extended;
     c,b:TComplexNumber;
     //argument_Phi:extended;  //
     k:integer;
     //
     color:TColor;
     //
  begin
    For iY :=iYmin to iYMax do
      begin
        eCy:=Convert_iY_to_eY(iY);
        for iX:=iXmin to iXmax do
          begin
            eCx:=Convert_iX_to_eX(iX);
            //

            // Z0 = initial point
            eZx:=0;
            eZy:=0;
            For iteration:=0 to iterationMax-1 do
              begin
                // Z(n+1):= Sqr(Zn) + C
                temp:=Sqr(eZx)-Sqr(eZy) +eCx;
                eZy:=2*eZx*eZy+eCy;
                eZx:=temp;
                if (Sqr(eZx)+Sqr(eZy))> bailout2   then break;
              end;
              //

            // drawing procedure
            if iteration=IterationMax
              then
                // M-set
                with Bitmap1.FirstLine[iY*Bitmap1.LineLength+iX] do
                      begin
                        B := 0;
                        G := 0;
                        R := 0;
                        //A := 0;
                      end
              else // exterior of M-set
                begin
                   c.x:=eCx;
                   c.y:=eCy;
                  GivePhi_M(c,iteration,b);
                  k:= round(RadToDeg(CmplxArgumentInRad(b.x,b.y)));
                  color:=Rainbow(0,360,k );

                  with Bitmap1.FirstLine[iY*Bitmap1.LineLength+iX] do
                              begin
                                B := GetBValue(color); //
                                G := GetGValue(color);
                                R := GetRValue(color); //
                                //A := 0;
                              end ;
                 end ; //else
              //--------------
             //
           // end of drawing procedure ----------
      end; // for iX
    end; //For iY

end;
//---------------------------

end.