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class Tut_1_4_Standard_Mandelbrot(common.ulb:DivergentFormula) {
;
; Object version of Mandelbrot in Standard.ufm.
; Generic Mandelbrot set.
;
public:
  complex func Init(complex pz)
    fPixelx = real(pz)
    fPixely = imag(pz)
    fPixelz = @zslice

    x=real(@start)
    y=imag(@start)
    z=@start2
    ;just return something
    return @start
  endfunc

  complex func Iterate(complex pz)
  float newreal=       exponentiateWithRealX(x,y,z,real(@p_power))
  float newimag=       exponentiateWithRealY(x,y,z,real(@p_power))
  float newz=       exponentiateWithRealZ(x,y,z,real(@p_power))

    x=newreal+fPixelx
    y=newimag+fPixely
     z=newz+fPixelz
    ; just return something
    return pz;


  endfunc

  bool func IsBailedOut(complex pz)
  ; perform bailout test using our local variables...
		return sqrt(x*x+y*y+z*z) > @p_bailout
	endfunc
	
  float func exponentiateWithRealX(float x,float y,float z ,float exponent)
          ; Convert Complex Number z to polar form via:
          float length=sqrt(x*x+y*y+z*z) ; modulus, or simply the length of the number: hello phytagoras!
         if(length==0)
                      length=0.000001
                      endif
                      

          float angle=atan2(x+flip(y)) ; nasty atan2 function that returns the angle of the point from coordinate origin...

          float angle2=asin( z/length)

          ; exponentiate length, just like a normal real number ... when exponentiating it is stretched on x-axis,
          ; in polar coordinates it is stretched along its direction
          float newlength= length^exponent
          ; hence complex multiplication is a rotation, e.g. (0,1i)*(0,1i)=(-1,0) where a 90 degree rotation is performed
          ; we multiply the angle with the exponent ...
          float newangle= angle*exponent
          
          float newangle2= angle2*exponent

          ; now create the complex number from newlength and newangle
          ; using standard sin/cos multiplied by length
          float newreal= (cos(newangle2)*cos(newangle))*newlength
          ;float newimag= sin(newangle)*newlength

          ; create complex number and return, the flip serves as helper to convert the real number to imaginary....
          ; seems to be some compiler problem in uf ... return (newreal,newimag) does an "operator needed" compiler error, dunno why....
          return newreal



  endfunc
  float func exponentiateWithRealY(float x,float y,float z ,float exponent)
          ; Convert Complex Number z to polar form via:
          float length=sqrt(x*x+y*y+z*z) ; modulus, or simply the length of the number: hello phytagoras!
       if(length==0)
                      length=0.000001
                      endif

                         float angle=atan2(x+flip(y)) ; nasty atan2 function that returns the angle of the point from coordinate origin...

              float angle2=asin( z/length)


          ; exponentiate length, just like a normal real number ... when exponentiating it is stretched on x-axis,
          ; in polar coordinates it is stretched along its direction
          float newlength= length^exponent
          ; hence complex multiplication is a rotation, e.g. (0,1i)*(0,1i)=(-1,0) where a 90 degree rotation is performed
          ; we multiply the angle with the exponent ...
          float newangle= angle*exponent
            float newangle2= angle2*exponent

          ; now create the complex number from newlength and newangle
          ; using standard sin/cos multiplied by length
          ;float newreal= cos(newangle)*newlength
          float newimag= (cos(newangle2)*sin(newangle))*newlength

          ; create complex number and return, the flip serves as helper to convert the real number to imaginary....
          ; seems to be some compiler problem in uf ... return (newreal,newimag) does an "operator needed" compiler error, dunno why....
          return newimag

  endfunc

  float func exponentiateWithRealZ(float x,float y,float z ,float exponent)
          ; Convert Complex Number z to polar form via:
          float length=sqrt(x*x+y*y+z*z) ; modulus, or simply the length of the number: hello phytagoras!
      if(length==0)
                      length=0.000001
                      endif

                          float angle=atan2(x+flip(y)) ; nasty atan2 function that returns the angle of the point from coordinate origin...

              float angle2=asin( z/length)


          ; exponentiate length, just like a normal real number ... when exponentiating it is stretched on x-axis,
          ; in polar coordinates it is stretched along its direction
          float newlength= length^exponent
          ; hence complex multiplication is a rotation, e.g. (0,1i)*(0,1i)=(-1,0) where a 90 degree rotation is performed
          ; we multiply the angle with the exponent ...
          ;float newangle= angle*exponent
            float newangle2= angle2*exponent

          ; now create the complex number from newlength and newangle
          ; using standard sin/cos multiplied by length
          ;float newreal= cos(newangle)*newlength
          float newz= sin(newangle2)*newlength

          ; create complex number and return, the flip serves as helper to convert the real number to imaginary....
          ; seems to be some compiler problem in uf ... return (newreal,newimag) does an "operator needed" compiler error, dunno why....
          return newz

  endfunc




private:
  float fPixelx
  float fPixely
  float fPixelz

  float x;
  float y;
  float z;



default:
  title = "Mandelbulb Tut 1_4 - Triplex Exponentiation"
  rating = recommended
  helpfile = "Uf*.chm"
  helptopic = "Html/formulas/standard/mandelbrot.html"
  param start
    caption = "Starting point X/Y"
    default = (0,0)
    hint = "The starting point parameter can be used to distort the Mandelbrot \
            set. Use (0, 0) for the standard Mandelbrot set."
  endparam
  param start2
    caption = "Starting point Z"
    default = 0.0
    hint = "Z-Value Starting Point"
  endparam
 param zslice
    caption = "Z Slice"
    default = 0.0
    hint = "Z-Value Starting Point"
  endparam
  param p_power ; Overrides p_power from Formula
    caption = "Power"
    default = (2.0,0)
    hint = ""
  endparam
  float param p_bailout ; Overrides p_bailout from DivergentFormula
    caption = "Bailout value"
    default = 4.0
    min = 1.0
    exponential = true
    hint = "This parameter defines how soon an orbit bails out while \
            iterating. Larger values give smoother outlines; values around 4 \
            give more interesting shapes around the set. Values less than 4 \
            will distort the fractal."
  endparam
}