January 20, 2001
  
  This module deals with 1)variations of the cubic standard formula 
  and 2) other methods of producing 2D-images of the four dimensional 
  hyper space of cubic polynomials expressed by the standard-formula. 
  Please read the rtf-dokument "GetStarted" attached to the zip-file 
  together with a set parameter-files. Many thanks to Stig Pettersson 
  for helping me with this module, and to Stephen C Ferguson and 
  Professor Holger Jaenisch for sharing some interesting formulas.
    
  Regards,
  Ingvar Kullberg
  
  www.come.to/kullberg
  

MilnorAB {


init:
  float c=0
  float d=0
  float t=0
  float aa=0
  a=0+0i
  b=0+0i
  c=real(#pixel)
  d=imag(#pixel)
  float IX=@InterX
  float IY=@InterY
  float yrot=0
  float xrot=0
  float xrotu=0
  float yrotu=0
  float zrot=0
  float uzrot=0
  float projxz=0
  float projyz=0
  float projxu=0
  float projyu=0

    IF @yrot!=0
      yrot=(@yrot%360)*pi/180
      t=cabs(c+IX*1i)      
      aa=atan2(c+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        c=-t
        IX=0
      ELSEIF aa==pi/2
        c=0
        IX=t
      ELSEIF aa==-pi/2
        c=0
        IX=-t
      ELSE
        c=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+d*1i)     
      aa=atan2(IX+d*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        d=0
      ELSEIF aa==pi/2
        IX=0
        d=t
      ELSEIF aa==-pi/2
        IX=0
        d=-t
      ELSE
        IX=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
    
    IF @yrotu!=0
      yrotu=(@yrotu%360)*pi/180
      t=cabs(c+IY*1i)      
      aa=atan2(c+IY*1i) 
      aa=yrotu+aa
      IF abs(aa)==pi
        c=-t
        IY=0
      ELSEIF aa==pi/2
        c=0
        IY=t
      ELSEIF aa==-pi/2
        c=0
        IY=-t
      ELSE
        c=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrotu!=0
      xrotu=(@xrotu%360)*pi/180
      t=cabs(IY+d*1i)      
      aa=atan2(IY+d*1i) 
      aa=xrotu+aa
      IF abs(aa)==pi
        IY=-t
        d=0
      ELSEIF aa==pi/2
        IY=0
        d=t
      ELSEIF aa==-pi/2
        IY=0
        d=-t
      ELSE
        IY=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0
      zrot=(@zrot%360)*pi/180
      t=cabs(c+d*1i)
      aa=atan2(c+d*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        c=-t
        d=0
      ELSEIF aa==pi/2
        c=0
        d=t
      ELSEIF aa==-pi/2
        c=0
        d=-t
      ELSE
        c=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
    
     
    IF @uzrot!=0
      uzrot=(@uzrot%360)*pi/180
      t=cabs(IX+IY*1i)    
      aa=atan2(IX+IY*1i)
      aa=uzrot+aa
      IF abs(aa)==pi
        IX=-t
        IY=0
      ELSEIF aa==pi/2
        IX=0
        IY=t
      ELSEIF aa==-pi/2
        IX=0
        IY=-t
      ELSE
        IX=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF


    IF @projxz!=0
      projxz=(@projxz%360)*pi/180
      IF @projxz==90      
        IX=c+IX
        c=0
      ELSE
        IX=c*sin(projxz)+IX
        c=c*cos(projxz)
      ENDIF
    ENDIF
  
    IF @projyz!=0
      projyz=(@projyz%360)*pi/180
      IF @projyz==90      
        IX=d+IX
        d=0
      ELSE
        IX=d*sin(projyz)+IX
        d=d*cos(projyz)
      ENDIF
    ENDIF
    
    IF @projxu!=0
      projxu=(@projxu%360)*pi/180
      IF @projxu==90      
        IY=c+IY
        c=0
      ELSE
        IY=c*sin(projxu)+IY
        c=c*cos(projxu)
      ENDIF
    ENDIF
    
    IF @projyu!=0
      projyu=(@projyu%360)*pi/180
      IF @projyu==90      
        IY=d+IY
        d=0
      ELSE
        IY=d*sin(projyu)+IY
        d=d*cos(projyu)
      ENDIF
    ENDIF
    
  IF @FLIP==1
    IX=d
    d=@FlipValue
  ELSEIF @FLIP==2
    IY=d
    d=@FlipValue
  ELSEIF @FLIP==3
    IX=c
    c=@FlipValue
  ELSEIF @FLIP==4
    IY=c
    c=@FlipValue
  ENDIF
  
  If @MovePlane == true
    IX = real(#center)
    IY = imag(#center)
  ENDIF
    
  IF @IterPlane==0
    a=c+d*1i
    b=IX+IY*1i 
  ELSEIF @IterPlane==1
    a=c+IX*1i
    b=d+IY*1i
  ELSEIF @IterPlane==2
    a=c+IX*1i
    b=IY+d*1i
  ELSEIF @IterPlane==3
    a=IX+c*1i
    b=d+IY*1i
  ELSEIF @IterPlane==4
    a=IX+c*1i
    b=Iy+d*1i
  ELSE 
    a=IX+IY*1i
    b=c+d*1i
  ENDIF
  
  IF @M==false
    z=sqrt(A)
  ELSE 
    z=-sqrt(A)
  ENDIF
    
  loop:
    z=z*z*z-3*A*z+sqrt(B)
    
bailout:
  |z|<@bailout
  
  
switch:
  type="ToMilnorJulia"
  seed=#pixel
  IterPlane=IterPlane
  InterX=InterX
  InterY=InterY
  yrot=yrot
  xrot=xrot
  yrotu=yrotu
  xrotu=xrotu
  zrot=zrot
  uzrot=uzrot
  projxz=projxz
  projxu=projxu
  projyz=projyz
  projyu=projyu
  FlipValue=FlipValue
  FLIP=FLIP
  M=M
  MovePlane=MovePlane
  bailout=bailout
  
default:
  title = "MilnorAB"
  
  param IterPlane
    enum = "(A-real,A-imag)" "(A-real,B-real)" "(A-real,B-imag)" "(A-imag,B-real)" \
    "(A-imag,B-imag)" "(B-real,B-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param InterX
    caption=" z-axis"
    hint="Complement to Iterative Plane.For ex. iter: a-imag,b-real this should be a-real"
    default=0.0
  endparam
  
 param InterY
    caption=" u-axis"
    hint="Complement to Iterative Plane.For iter: a-real,b-imag this should be b-real"
    default=0.0
  endparam
  
 param yrot
    caption="Rotates xz-plane."
    hint= "Rotates xyz-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrot
    caption="Rotates yz-plane."
    hint= "Rotates xyz-plane in degrees around the x-axes."
    default=0.0
  endparam
  
 param yrotu
    caption="Rotates xu-plane."
    hint= "Rotates the xyu-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrotu
    caption="Rotates yu-plane."
    hint= "Rotating xyu-plane in degrees around the x-axis."
    default=0.0
  endparam
  
  param zrot
    caption="Rotates xy-plane."
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
  param uzrot
    caption="Rotates uz-plane"
    hint="Rotates the uz-plane in degrees."
    default=0.0
  endparam
  
  param projxz
    caption="Project x on z."
    hint="Projecting x on z in degrees."
    default=0.0
  endparam
  
 param projxu
    caption="Project x on u."
    hint="Projecting x on u in degrees."
    default=0.0
  endparam
  
  param projyz
    caption="Project y on z."
    hint="Projecting y on z in degrees."
    default=0.0
  endparam
  
  param projyu
    caption="Project y on u."
    hint="Projecting y on u in degrees."
    default=0.0
  endparam
  
   
  param FlipValue
    caption="flip value"
    hint="Value for flip. Should be be taken from properties/location/center. \
    y for y-flip x for x-flip. \
    Donīt forget to zero the coordinate at location after flip or simply cut the coordinate."
    default=0.0
  endparam
  
  param FLIP
    enum = "No Flip" "Flip y -> z" "Flip y -> u" "Flip x -> z" "Flip x -> u"
    hint="Turns coordinateplane 90 deg. Paste the coordinate you want to flip from location. \
    Donīt forget to zero the coordinate at location after the flip or simly cut the coordinate."
    default=0
  endparam
  
  param M
    caption="-sqrt(A)"
    hint="Sets the sign of the initial parameter a. If set it will be negative."
    default=false
  endparam 
  
  param MovePlane
    caption = "Move On"
    default=false
    hint = "Is to play with. Be sure interceptcoords. are zero (default location).\
            Put MovePlane on. Push control as you move the area in the window \
            (hold left mousebutton down). If you move the mouse in x-direction \
            the set will move along the z-axis. In y-direction along u-axis. Enjoy." 
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
    min=1
  endparam
     
  }

ToMilnorJulia {
init:
  
  complex c=@seed
  complex z=#pixel
  g=@IterPlane
  d=@InterX+flip(@interY)
  IF g==0
     a=c
     b=d
  ELSEIF g==1
    a=real(c)+real(d)*1i
    b=imag(c)+imag(d)*1i
  ELSEIF g==2
    a=real(c)+real(d)*1i
    b=imag(d)+imag(c)*1i
  ELSEIF g==3
    a=real(d)+real(c)*1i
    b=imag(c)+imag(d)*1i
  ELSEIF g==4
    a=real(d)+real(c)*1i
    b=imag(d)+imag(c)*1i
  ELSE
    a=d
    b=c
  ENDIF
   
   
loop:
  z=z*z*z-3*A*z+sqrt(B)
  
bailout:
  |z|<@bailout
  
switch:
  type="MilnorAB"
  IterPlane=IterPlane
  InterX=InterX
  InterY=InterY
  yrot=yrot
  xrot=xrot
  yrotu=yrotu
  xrotu=xrotu
  zrot=zrot
  uzrot=uzrot
  projxz=projxz
  projxu=projxu
  projyz=projyz
  projyu=projyu
  FlipValue=FlipValue
  FLIP=FLIP
  M=M
  MovePlane=MovePlane
  bailout=bailout

default:
  title = "ToMilnorJulia"
  
  param IterPlane
    enum = "(a-real,a-imag)" "(a-real,b-real)" "(a-real,b-imag)" "(a-imag,breal)" \
    "(a-imag,b-imag)" "(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param InterX
    caption=" z-axis"
    hint="Complement to Iterative Plane.For ex. iter: a-imag,b-real this should be a-real"
    default=0.0
  endparam
  
 param InterY
    caption=" u-axis"
    hint="Complement to Iterative Plane.For iter: a-real,b-imag this should be b-real"
    default=0.0
  endparam
  
 param yrot
    caption="Rotates xz-plane."
    hint= "Rotates xyz-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrot
    caption="Rotates yz-plane."
    hint= "Rotates xyz-plane in degrees around the x-axes."
    default=0.0
  endparam
  
 param yrotu
    caption="Rotates xu-plane."
    hint= "Rotates the xyu-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrotu
    caption="Rotates yu-plane."
    hint= "Rotating xyu-plane in degrees around the x-axis."
    default=0.0
  endparam
  
  param zrot
    caption="Rotates xy-plane."
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
  param uzrot
    caption="Rotates uz-plane"
    hint="Rotates the uz-plane in degrees."
    default=0.0
  endparam
  
  param projxz
    caption="Project x on z."
    hint="Projecting x on z in degrees."
    default=0.0
  endparam
  
 param projxu
    caption="Project x on u."
    hint="Projecting x on u in degrees."
    default=0.0
  endparam
  
  param projyz
    caption="Project y on z."
    hint="Projecting y on z in degrees."
    default=0.0
  endparam
  
  param projyu
    caption="Project y on u."
    hint="Projecting y on u in degrees."
    default=0.0
  endparam
  
   
  param FlipValue
    caption="flip value"
    hint="Value for flip. Should be be taken from properties/location/center. \
    y for y-flip x for x-flip. \
    Donīt forget to zero the coordinate at location after flip or simply cut the coordinate."
    default=0.0
  endparam
  
  param FLIP
    enum = "No Flip" "Flip y -> z" "Flip y -> u" "Flip x -> z" "Flip x -> u"
    hint="Turns coordinateplane 90 deg. Paste the coordinate you want to flip from location. \
    Donīt forget to zero the coordinate at location after the flip or simly cut the coordinate."
    default=0
  endparam
  
  param M
    caption="-sqrt(A)"
    hint="Sets the sign of the initial parameter sqrt(A). If set it will be negative."
    default=false
  endparam 
  
  param MovePlane
    caption = "Move On"
    default=false
    hint = "Is to play with. Be sure interceptcoords. are zero (default location).\
            Put MovePlane on. Push control as you move the area in the window \
            (hold left mousebutton down). If you move the mouse in x-direction \
            the set will move along the z-axis. In y-direction along u-axis. Enjoy." 
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
    min=1
  endparam

}

MilnorJulia {
init:
  a=@areal+@aimag*1i
  b=@breal+@bimag*1i
  z=#pixel
loop:
  z=z*z*z-3*A*z+sqrt(B)  
bailout:
  |z|<@bailout
default:
  title = "MilnorJulia"
  
  param areal
    caption="a-real"
    hint="Real part of a-parameter"
    default=0.0
  endparam
  
   param aimag
    caption="a-imag"
    hint="Imaginary part of a-parameter"
    default=0.0
  endparam
  
   param breal
    caption="b-real"
    hint="Real part of b-parameter"
    default=0.0
  endparam
  
    
   param bimag
    caption="b-imag"
    hint="Imaginary part of b-parameter"
    default=0.0
  endparam
  
    
   param bailout
    caption="bailout"
    hint="Value of bailout"
    default=100.0  
  endparam
  

  param bailout
    caption="bailout"
    default=0.00001
    hint="Bailout value."
   endparam

}

SorensenCubic {


init:
  float c=0
  float d=0
  float t=0
  float aa=0
  a=0+0i
  b=0+0i
  c=real(#pixel)
  d=imag(#pixel)
  float IX=@InterX
  float IY=@InterY
  float yrot=0
  float xrot=0
  float xrotu=0
  float yrotu=0
  float zrot=0
  float uzrot=0
  float projxz=0
  float projyz=0
  float projxu=0
  float projyu=0

    IF @yrot!=0
      yrot=(@yrot%360)*pi/180
      t=cabs(c+IX*1i)      
      aa=atan2(c+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        c=-t
        IX=0
      ELSEIF aa==pi/2
        c=0
        IX=t
      ELSEIF aa==-pi/2
        c=0
        IX=-t
      ELSE
        c=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+d*1i)     
      aa=atan2(IX+d*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        d=0
      ELSEIF aa==pi/2
        IX=0
        d=t
      ELSEIF aa==-pi/2
        IX=0
        d=-t
      ELSE
        IX=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
    
    IF @yrotu!=0
      yrotu=(@yrotu%360)*pi/180
      t=cabs(c+IY*1i)      
      aa=atan2(c+IY*1i) 
      aa=yrotu+aa
      IF abs(aa)==pi
        c=-t
        IY=0
      ELSEIF aa==pi/2
        c=0
        IY=t
      ELSEIF aa==-pi/2
        c=0
        IY=-t
      ELSE
        c=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrotu!=0
      xrotu=(@xrotu%360)*pi/180
      t=cabs(IY+d*1i)      
      aa=atan2(IY+d*1i) 
      aa=xrotu+aa
      IF abs(aa)==pi
        IY=-t
        d=0
      ELSEIF aa==pi/2
        IY=0
        d=t
      ELSEIF aa==-pi/2
        IY=0
        d=-t
      ELSE
        IY=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0
      zrot=(@zrot%360)*pi/180
      t=cabs(c+d*1i)
      aa=atan2(c+d*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        c=-t
        d=0
      ELSEIF aa==pi/2
        c=0
        d=t
      ELSEIF aa==-pi/2
        c=0
        d=-t
      ELSE
        c=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
    
     
    IF @uzrot!=0
      uzrot=(@uzrot%360)*pi/180
      t=cabs(IX+IY*1i)    
      aa=atan2(IX+IY*1i)
      aa=uzrot+aa
      IF abs(aa)==pi
        IX=-t
        IY=0
      ELSEIF aa==pi/2
        IX=0
        IY=t
      ELSEIF aa==-pi/2
        IX=0
        IY=-t
      ELSE
        IX=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF


    IF @projxz!=0
      projxz=(@projxz%360)*pi/180
      IF @projxz==90      
        IX=c+IX
        c=0
      ELSE
        IX=c*sin(projxz)+IX
        c=c*cos(projxz)
      ENDIF
    ENDIF
  
    IF @projyz!=0
      projyz=(@projyz%360)*pi/180
      IF @projyz==90      
        IX=d+IX
        d=0
      ELSE
        IX=d*sin(projyz)+IX
        d=d*cos(projyz)
      ENDIF
    ENDIF
    
    IF @projxu!=0
      projxu=(@projxu%360)*pi/180
      IF @projxu==90      
        IY=c+IY
        c=0
      ELSE
        IY=c*sin(projxu)+IY
        c=c*cos(projxu)
      ENDIF
    ENDIF
    
    IF @projyu!=0
      projyu=(@projyu%360)*pi/180
      IF @projyu==90      
        IY=d+IY
        d=0
      ELSE
        IY=d*sin(projyu)+IY
        d=d*cos(projyu)
      ENDIF
    ENDIF
    
  IF @FLIP==1
    IX=d
    d=@FlipValue
  ELSEIF @FLIP==2
    IY=d
    d=@FlipValue
  ELSEIF @FLIP==3
    IX=c
    c=@FlipValue
  ELSEIF @FLIP==4
    IY=c
    c=@FlipValue
  ENDIF
  
  If @MovePlane == true
    IX = real(#center)
    IY = imag(#center)
  ENDIF
    
  IF @IterPlane==0
    a=c+d*1i
    b=IX+IY*1i 
  ELSEIF @IterPlane==1
    a=c+IX*1i
    b=d+IY*1i
  ELSEIF @IterPlane==2
    a=c+IX*1i
    b=IY+d*1i
  ELSEIF @IterPlane==3
    a=IX+c*1i
    b=d+IY*1i
  ELSEIF @IterPlane==4
    a=IX+c*1i
    b=Iy+d*1i
  ELSE 
    a=IX+IY*1i
    b=c+d*1i
  ENDIF
  
  IF @M==false
    z=-a/3+sqrt(a*a/9-b/3)
  ELSE 
    z=-a/3-sqrt(a*a/9-b/3)
  ENDIF
    
  loop:
    z=z*z*z+a*z*z+b*z
    
bailout:
  |z|<@bailout
  
  
switch:
  type="ToSorensenCubicJulia"
  seed=#pixel
  IterPlane=IterPlane
  InterX=InterX
  InterY=InterY
  yrot=yrot
  xrot=xrot
  yrotu=yrotu
  xrotu=xrotu
  zrot=zrot
  uzrot=uzrot
  projxz=projxz
  projxu=projxu
  projyz=projyz
  projyu=projyu
  FlipValue=FlipValue
  FLIP=FLIP
  M=M
  MovePlane=MovePlane
  bailout=bailout
  
default:
  title = "SorensenCubic"
  
  param IterPlane
    enum = "(a-real,a-imag)" "(a-real,b-real)" "(a-real,b-imag)" "(a-imag,b-real)" \
    "(a-imag,b-imag)" "(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param InterX
    caption=" z-axis"
    hint="Complement to Iterative Plane.For ex. iter: a-imag,b-real this should be a-real"
    default=0.0
  endparam
  
 param InterY
    caption=" u-axis"
    hint="Complement to Iterative Plane.For iter: a-real,b-imag this should be b-real"
    default=0.0
  endparam
  
 param yrot
    caption="Rotates xz-plane."
    hint= "Rotates xyz-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrot
    caption="Rotates yz-plane."
    hint= "Rotates xyz-plane in degrees around the x-axes."
    default=0.0
  endparam
  
 param yrotu
    caption="Rotates xu-plane."
    hint= "Rotates the xyu-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrotu
    caption="Rotates yu-plane."
    hint= "Rotating xyu-plane in degrees around the x-axis."
    default=0.0
  endparam
  
  param zrot
    caption="Rotates xy-plane."
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
  param uzrot
    caption="Rotates uz-plane"
    hint="Rotates the uz-plane in degrees."
    default=0.0
  endparam
  
  param projxz
    caption="Project x on z."
    hint="Projecting x on z in degrees."
    default=0.0
  endparam
  
 param projxu
    caption="Project x on u."
    hint="Projecting x on u in degrees."
    default=0.0
  endparam
  
  param projyz
    caption="Project y on z."
    hint="Projecting y on z in degrees."
    default=0.0
  endparam
  
  param projyu
    caption="Project y on u."
    hint="Projecting y on u in degrees."
    default=0.0
  endparam
  
   
  param FlipValue
    caption="flip value"
    hint="Value for flip. Should be be taken from properties/location/center. \
    y for y-flip x for x-flip. \
    Donīt forget to zero the coordinate at location after flip or simply cut the coordinate."
    default=0.0
  endparam
  
  param FLIP
    enum = "No Flip" "Flip y -> z" "Flip y -> u" "Flip x -> z" "Flip x -> u"
    hint="Turns coordinateplane 90 deg. Paste the coordinate you want to flip from location. \
    Donīt forget to zero the coordinate at location after the flip or simly cut the coordinate."
    default=0
  endparam
  
  param M
    caption="-a/3-sqrt(a*a/9-b/3)"
    hint="Change to the other critical point. If set it will be negative."
    default=false
  endparam 
  
  param MovePlane
    caption = "Move On"
    default=false
    hint = "Is to play with. Be sure interceptcoords. are zero (default location).\
            Put MovePlane on. Push control as you move the area in the window \
            (hold left mousebutton down). If you move the mouse in x-direction \
            the set will move along the z-axis. In y-direction along u-axis. Enjoy." 
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
    min=1
  endparam
     
  }

ToSorensenCubicJulia {
init:
  
  complex c=@seed
  complex z=#pixel
  g=@IterPlane
  d=@InterX+flip(@interY)
  IF g==0
     a=c
     b=d
  ELSEIF g==1
    a=real(c)+real(d)*1i
    b=imag(c)+imag(d)*1i
  ELSEIF g==2
    a=real(c)+real(d)*1i
    b=imag(d)+imag(c)*1i
  ELSEIF g==3
    a=real(d)+real(c)*1i
    b=imag(c)+imag(d)*1i
  ELSEIF g==4
    a=real(d)+real(c)*1i
    b=imag(d)+imag(c)*1i
  ELSE
    a=d
    b=c
  ENDIF
   
   
loop:
  z=z*z*z+a*z*z+b*z
  
bailout:
  |z|<@bailout
  
switch:
  type="SorensenCubic"
  IterPlane=IterPlane
  InterX=InterX
  InterY=InterY
  yrot=yrot
  xrot=xrot
  yrotu=yrotu
  xrotu=xrotu
  zrot=zrot
  uzrot=uzrot
  projxz=projxz
  projxu=projxu
  projyz=projyz
  projyu=projyu
  FlipValue=FlipValue
  FLIP=FLIP
  M=M
  MovePlane=MovePlane
  bailout=bailout

default:
  title = "ToSorensenCubicJulia"
  
  param IterPlane
    enum = "(a-real,a-imag)" "(a-real,b-real)" "(a-real,b-imag)" "(a-imag,breal)" \
    "(a-imag,b-imag)" "(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param InterX
    caption=" z-axis"
    hint="Complement to Iterative Plane.For ex. iter: a-imag,b-real this should be a-real"
    default=0.0
  endparam
  
 param InterY
    caption=" u-axis"
    hint="Complement to Iterative Plane.For iter: a-real,b-imag this should be b-real"
    default=0.0
  endparam
  
 param yrot
    caption="Rotates xz-plane."
    hint= "Rotates xyz-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrot
    caption="Rotates yz-plane."
    hint= "Rotates xyz-plane in degrees around the x-axes."
    default=0.0
  endparam
  
 param yrotu
    caption="Rotates xu-plane."
    hint= "Rotates the xyu-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrotu
    caption="Rotates yu-plane."
    hint= "Rotating xyu-plane in degrees around the x-axis."
    default=0.0
  endparam
  
  param zrot
    caption="Rotates xy-plane."
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
  param uzrot
    caption="Rotates uz-plane"
    hint="Rotates the uz-plane in degrees."
    default=0.0
  endparam
  
  param projxz
    caption="Project x on z."
    hint="Projecting x on z in degrees."
    default=0.0
  endparam
  
 param projxu
    caption="Project x on u."
    hint="Projecting x on u in degrees."
    default=0.0
  endparam
  
  param projyz
    caption="Project y on z."
    hint="Projecting y on z in degrees."
    default=0.0
  endparam
  
  param projyu
    caption="Project y on u."
    hint="Projecting y on u in degrees."
    default=0.0
  endparam
  
   
  param FlipValue
    caption="flip value"
    hint="Value for flip. Should be be taken from properties/location/center. \
    y for y-flip x for x-flip. \
    Donīt forget to zero the coordinate at location after flip or simply cut the coordinate."
    default=0.0
  endparam
  
  param FLIP
    enum = "No Flip" "Flip y -> z" "Flip y -> u" "Flip x -> z" "Flip x -> u"
    hint="Turns coordinateplane 90 deg. Paste the coordinate you want to flip from location. \
    Donīt forget to zero the coordinate at location after the flip or simly cut the coordinate."
    default=0
  endparam
  
  param M
    caption="-a/3-sqrt(a*a/9-b/3)"
    hint="Sets the sign of the initial parameter sqrt(A). If set it will be negative."
    default=false
  endparam 
  
  param MovePlane
    caption = "Move On"
    default=false
    hint = "Is to play with. Be sure interceptcoords. are zero (default location).\
            Put MovePlane on. Push control as you move the area in the window \
            (hold left mousebutton down). If you move the mouse in x-direction \
            the set will move along the z-axis. In y-direction along u-axis. Enjoy." 
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
    min=1
  endparam

}

SorensenCubicJulia {
init:
  a=@areal+@aimag*1i
  b=@breal+@bimag*1i
  z=#pixel
loop:
  z=z*z*z+a*z*z+b*z  
bailout:
  |z|<@bailout
default:
  title = "SorensenCubicJulia"
  
  param areal
    caption="a-real"
    hint="Real part of a-parameter"
    default=0.0
  endparam
  
   param aimag
    caption="a-imag"
    hint="Imaginary part of a-parameter"
    default=0.0
  endparam
  
   param breal
    caption="b-real"
    hint="Real part of b-parameter"
    default=0.0
  endparam
  
    
   param bimag
    caption="b-imag"
    hint="Imaginary part of b-parameter"
    default=0.0
  endparam
  
    
   param bailout
    caption="bailout"
    hint="Value of bailout"
    default=100.0  
  endparam
  

  param bailout
    caption="bailout"
    default=0.00001
    hint="Bailout value."
   endparam

}

KullbergCubic {


init:
  float c=0
  float d=0
  float t=0
  float aa=0
  a=0+0i
  b=0+0i
  c=real(#pixel)
  d=imag(#pixel)
  float IX=@InterX
  float IY=@InterY
  float yrot=0
  float xrot=0
  float xrotu=0
  float yrotu=0
  float zrot=0
  float uzrot=0
  float projxz=0
  float projyz=0
  float projxu=0
  float projyu=0

    IF @yrot!=0
      yrot=(@yrot%360)*pi/180
      t=cabs(c+IX*1i)      
      aa=atan2(c+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        c=-t
        IX=0
      ELSEIF aa==pi/2
        c=0
        IX=t
      ELSEIF aa==-pi/2
        c=0
        IX=-t
      ELSE
        c=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+d*1i)     
      aa=atan2(IX+d*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        d=0
      ELSEIF aa==pi/2
        IX=0
        d=t
      ELSEIF aa==-pi/2
        IX=0
        d=-t
      ELSE
        IX=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
    
    IF @yrotu!=0
      yrotu=(@yrotu%360)*pi/180
      t=cabs(c+IY*1i)      
      aa=atan2(c+IY*1i) 
      aa=yrotu+aa
      IF abs(aa)==pi
        c=-t
        IY=0
      ELSEIF aa==pi/2
        c=0
        IY=t
      ELSEIF aa==-pi/2
        c=0
        IY=-t
      ELSE
        c=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrotu!=0
      xrotu=(@xrotu%360)*pi/180
      t=cabs(IY+d*1i)      
      aa=atan2(IY+d*1i) 
      aa=xrotu+aa
      IF abs(aa)==pi
        IY=-t
        d=0
      ELSEIF aa==pi/2
        IY=0
        d=t
      ELSEIF aa==-pi/2
        IY=0
        d=-t
      ELSE
        IY=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0
      zrot=(@zrot%360)*pi/180
      t=cabs(c+d*1i)
      aa=atan2(c+d*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        c=-t
        d=0
      ELSEIF aa==pi/2
        c=0
        d=t
      ELSEIF aa==-pi/2
        c=0
        d=-t
      ELSE
        c=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
    
     
    IF @uzrot!=0
      uzrot=(@uzrot%360)*pi/180
      t=cabs(IX+IY*1i)    
      aa=atan2(IX+IY*1i)
      aa=uzrot+aa
      IF abs(aa)==pi
        IX=-t
        IY=0
      ELSEIF aa==pi/2
        IX=0
        IY=t
      ELSEIF aa==-pi/2
        IX=0
        IY=-t
      ELSE
        IX=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF


    IF @projxz!=0
      projxz=(@projxz%360)*pi/180
      IF @projxz==90      
        IX=c+IX
        c=0
      ELSE
        IX=c*sin(projxz)+IX
        c=c*cos(projxz)
      ENDIF
    ENDIF
  
    IF @projyz!=0
      projyz=(@projyz%360)*pi/180
      IF @projyz==90      
        IX=d+IX
        d=0
      ELSE
        IX=d*sin(projyz)+IX
        d=d*cos(projyz)
      ENDIF
    ENDIF
    
    IF @projxu!=0
      projxu=(@projxu%360)*pi/180
      IF @projxu==90      
        IY=c+IY
        c=0
      ELSE
        IY=c*sin(projxu)+IY
        c=c*cos(projxu)
      ENDIF
    ENDIF
    
    IF @projyu!=0
      projyu=(@projyu%360)*pi/180
      IF @projyu==90      
        IY=d+IY
        d=0
      ELSE
        IY=d*sin(projyu)+IY
        d=d*cos(projyu)
      ENDIF
    ENDIF
    
  IF @FLIP==1
    IX=d
    d=@FlipValue
  ELSEIF @FLIP==2
    IY=d
    d=@FlipValue
  ELSEIF @FLIP==3
    IX=c
    c=@FlipValue
  ELSEIF @FLIP==4
    IY=c
    c=@FlipValue
  ENDIF
  
  If @MovePlane == true
    IX = real(#center)
    IY = imag(#center)
  ENDIF
    
  IF @IterPlane==0
    a=c+d*1i
    b=IX+IY*1i 
  ELSEIF @IterPlane==1
    a=c+IX*1i
    b=d+IY*1i
  ELSEIF @IterPlane==2
    a=c+IX*1i
    b=IY+d*1i
  ELSEIF @IterPlane==3
    a=IX+c*1i
    b=d+IY*1i
  ELSEIF @IterPlane==4
    a=IX+c*1i
    b=Iy+d*1i
  ELSE 
    a=IX+IY*1i
    b=c+d*1i
  ENDIF
  
  IF @M==false
    z=0
  ELSE 
    z=-2*a/3
  ENDIF
    
  loop:
    z=z*z*z+a*z*z+b
    
bailout:
  |z|<@bailout
  
  
switch:
  type="ToKullbergCubicJulia"
  seed=#pixel
  IterPlane=IterPlane
  InterX=InterX
  InterY=InterY
  yrot=yrot
  xrot=xrot
  yrotu=yrotu
  xrotu=xrotu
  zrot=zrot
  uzrot=uzrot
  projxz=projxz
  projxu=projxu
  projyz=projyz
  projyu=projyu
  FlipValue=FlipValue
  FLIP=FLIP
  M=M
  MovePlane=MovePlane
  bailout=bailout
  
default:
  title = "KullbergCubic"
  
  param IterPlane
    enum = "(a-real,a-imag)" "(a-real,b-real)" "(a-real,b-imag)" "(a-imag,b-real)" \
    "(a-imag,b-imag)" "(b-real,b-imag)"
    default=5
    hint="The axis that will be plotted."
  endparam
  
  param InterX
    caption=" z-axis"
    hint="Complement to Iterative Plane.For ex. iter: a-imag,b-real this should be a-real"
    default=0.0
  endparam
  
 param InterY
    caption=" u-axis"
    hint="Complement to Iterative Plane.For iter: a-real,b-imag this should be b-real"
    default=0.0
  endparam
  
 param yrot
    caption="Rotates xz-plane."
    hint= "Rotates xyz-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrot
    caption="Rotates yz-plane."
    hint= "Rotates xyz-plane in degrees around the x-axes."
    default=0.0
  endparam
  
 param yrotu
    caption="Rotates xu-plane."
    hint= "Rotates the xyu-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrotu
    caption="Rotates yu-plane."
    hint= "Rotating xyu-plane in degrees around the x-axis."
    default=0.0
  endparam
  
  param zrot
    caption="Rotates xy-plane."
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
  param uzrot
    caption="Rotates uz-plane"
    hint="Rotates the uz-plane in degrees."
    default=0.0
  endparam
  
  param projxz
    caption="Project x on z."
    hint="Projecting x on z in degrees."
    default=0.0
  endparam
  
 param projxu
    caption="Project x on u."
    hint="Projecting x on u in degrees."
    default=0.0
  endparam
  
  param projyz
    caption="Project y on z."
    hint="Projecting y on z in degrees."
    default=0.0
  endparam
  
  param projyu
    caption="Project y on u."
    hint="Projecting y on u in degrees."
    default=0.0
  endparam
  
   
  param FlipValue
    caption="flip value"
    hint="Value for flip. Should be be taken from properties/location/center. \
    y for y-flip x for x-flip. \
    Donīt forget to zero the coordinate at location after flip or simply cut the coordinate."
    default=0.0
  endparam
  
  param FLIP
    enum = "No Flip" "Flip y -> z" "Flip y -> u" "Flip x -> z" "Flip x -> u"
    hint="Turns coordinateplane 90 deg. Paste the coordinate you want to flip from location. \
    Donīt forget to zero the coordinate at location after the flip or simly cut the coordinate."
    default=0
  endparam
  
  param M
    caption="-2a/3"
    hint="Change to the other critical point-2a/3. If set it will be negative."
    default=false
  endparam 
  
  param MovePlane
    caption = "Move On"
    default=false
    hint = "Is to play with. Be sure interceptcoords. are zero (default location).\
            Put MovePlane on. Push control as you move the area in the window \
            (hold left mousebutton down). If you move the mouse in x-direction \
            the set will move along the z-axis. In y-direction along u-axis. Enjoy." 
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
    min=1
  endparam
     
  }

ToKullbergCubicJulia {
init:
  
  complex c=@seed
  complex z=#pixel
  g=@IterPlane
  d=@InterX+flip(@interY)
  IF g==0
     a=c
     b=d
  ELSEIF g==1
    a=real(c)+real(d)*1i
    b=imag(c)+imag(d)*1i
  ELSEIF g==2
    a=real(c)+real(d)*1i
    b=imag(d)+imag(c)*1i
  ELSEIF g==3
    a=real(d)+real(c)*1i
    b=imag(c)+imag(d)*1i
  ELSEIF g==4
    a=real(d)+real(c)*1i
    b=imag(d)+imag(c)*1i
  ELSE
    a=d
    b=c
  ENDIF
   
   
loop:
  z=z*z*z+a*z*z+b
  
bailout:
  |z|<@bailout
  
switch:
  type="SorensenCubic"
  IterPlane=IterPlane
  InterX=InterX
  InterY=InterY
  yrot=yrot
  xrot=xrot
  yrotu=yrotu
  xrotu=xrotu
  zrot=zrot
  uzrot=uzrot
  projxz=projxz
  projxu=projxu
  projyz=projyz
  projyu=projyu
  FlipValue=FlipValue
  FLIP=FLIP
  M=M
  MovePlane=MovePlane
  bailout=bailout

default:
  title = "ToKullbergCubicJulia"
  
  param IterPlane
    enum = "(a-real,a-imag)" "(a-real,b-real)" "(a-real,b-imag)" "(a-imag,breal)" \
    "(a-imag,b-imag)" "(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param InterX
    caption=" z-axis"
    hint="Complement to Iterative Plane.For ex. iter: a-imag,b-real this should be a-real"
    default=0.0
  endparam
  
 param InterY
    caption=" u-axis"
    hint="Complement to Iterative Plane.For iter: a-real,b-imag this should be b-real"
    default=0.0
  endparam
  
 param yrot
    caption="Rotates xz-plane."
    hint= "Rotates xyz-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrot
    caption="Rotates yz-plane."
    hint= "Rotates xyz-plane in degrees around the x-axes."
    default=0.0
  endparam
  
 param yrotu
    caption="Rotates xu-plane."
    hint= "Rotates the xyu-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrotu
    caption="Rotates yu-plane."
    hint= "Rotating xyu-plane in degrees around the x-axis."
    default=0.0
  endparam
  
  param zrot
    caption="Rotates xy-plane."
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
  param uzrot
    caption="Rotates uz-plane"
    hint="Rotates the uz-plane in degrees."
    default=0.0
  endparam
  
  param projxz
    caption="Project x on z."
    hint="Projecting x on z in degrees."
    default=0.0
  endparam
  
 param projxu
    caption="Project x on u."
    hint="Projecting x on u in degrees."
    default=0.0
  endparam
  
  param projyz
    caption="Project y on z."
    hint="Projecting y on z in degrees."
    default=0.0
  endparam
  
  param projyu
    caption="Project y on u."
    hint="Projecting y on u in degrees."
    default=0.0
  endparam
  
   
  param FlipValue
    caption="flip value"
    hint="Value for flip. Should be be taken from properties/location/center. \
    y for y-flip x for x-flip. \
    Donīt forget to zero the coordinate at location after flip or simply cut the coordinate."
    default=0.0
  endparam
  
  param FLIP
    enum = "No Flip" "Flip y -> z" "Flip y -> u" "Flip x -> z" "Flip x -> u"
    hint="Turns coordinateplane 90 deg. Paste the coordinate you want to flip from location. \
    Donīt forget to zero the coordinate at location after the flip or simly cut the coordinate."
    default=0
  endparam
  
  param M
    caption="-a/3-sqrt(a*a/9-b/3)"
    hint="Sets the sign of the initial parameter sqrt(A). If set it will be negative."
    default=false
  endparam 
  
  param MovePlane
    caption = "Move On"
    default=false
    hint = "Is to play with. Be sure interceptcoords. are zero (default location).\
            Put MovePlane on. Push control as you move the area in the window \
            (hold left mousebutton down). If you move the mouse in x-direction \
            the set will move along the z-axis. In y-direction along u-axis. Enjoy." 
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
    min=1
  endparam

}

KullbergCubicJulia {
init:
  a=@areal+@aimag*1i
  b=@breal+@bimag*1i
  z=#pixel
loop:
  z=z*z*z+a*z*z+b  
bailout:
  |z|<@bailout
default:
  title = "KullbergCubicJulia"
  
  param areal
    caption="a-real"
    hint="Real part of a-parameter"
    default=0.0
  endparam
  
   param aimag
    caption="a-imag"
    hint="Imaginary part of a-parameter"
    default=0.0
  endparam
  
   param breal
    caption="b-real"
    hint="Real part of b-parameter"
    default=0.0
  endparam
  
    
   param bimag
    caption="b-imag"
    hint="Imaginary part of b-parameter"
    default=0.0
  endparam
  
    
   param bailout
    caption="bailout"
    hint="Value of bailout"
    default=100.0  
  endparam
  

  param bailout
    caption="bailout"
    default=0.00001
    hint="Bailout value."
   endparam

}

DevaneyCubic {


init:
  float c=0
  float d=0
  float t=0
  float aa=0
  a=0+0i
  b=0+0i
  c=real(#pixel)
  d=imag(#pixel)
  float IX=@InterX
  float IY=@InterY
  float yrot=0
  float xrot=0
  float xrotu=0
  float yrotu=0
  float zrot=0
  float uzrot=0
  float projxz=0
  float projyz=0
  float projxu=0
  float projyu=0

    IF @yrot!=0
      yrot=(@yrot%360)*pi/180
      t=cabs(c+IX*1i)      
      aa=atan2(c+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        c=-t
        IX=0
      ELSEIF aa==pi/2
        c=0
        IX=t
      ELSEIF aa==-pi/2
        c=0
        IX=-t
      ELSE
        c=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+d*1i)     
      aa=atan2(IX+d*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        d=0
      ELSEIF aa==pi/2
        IX=0
        d=t
      ELSEIF aa==-pi/2
        IX=0
        d=-t
      ELSE
        IX=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
    
    IF @yrotu!=0
      yrotu=(@yrotu%360)*pi/180
      t=cabs(c+IY*1i)      
      aa=atan2(c+IY*1i) 
      aa=yrotu+aa
      IF abs(aa)==pi
        c=-t
        IY=0
      ELSEIF aa==pi/2
        c=0
        IY=t
      ELSEIF aa==-pi/2
        c=0
        IY=-t
      ELSE
        c=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrotu!=0
      xrotu=(@xrotu%360)*pi/180
      t=cabs(IY+d*1i)      
      aa=atan2(IY+d*1i) 
      aa=xrotu+aa
      IF abs(aa)==pi
        IY=-t
        d=0
      ELSEIF aa==pi/2
        IY=0
        d=t
      ELSEIF aa==-pi/2
        IY=0
        d=-t
      ELSE
        IY=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0
      zrot=(@zrot%360)*pi/180
      t=cabs(c+d*1i)
      aa=atan2(c+d*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        c=-t
        d=0
      ELSEIF aa==pi/2
        c=0
        d=t
      ELSEIF aa==-pi/2
        c=0
        d=-t
      ELSE
        c=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
    
     
    IF @uzrot!=0
      uzrot=(@uzrot%360)*pi/180
      t=cabs(IX+IY*1i)    
      aa=atan2(IX+IY*1i)
      aa=uzrot+aa
      IF abs(aa)==pi
        IX=-t
        IY=0
      ELSEIF aa==pi/2
        IX=0
        IY=t
      ELSEIF aa==-pi/2
        IX=0
        IY=-t
      ELSE
        IX=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF


    IF @projxz!=0
      projxz=(@projxz%360)*pi/180
      IF @projxz==90      
        IX=c+IX
        c=0
      ELSE
        IX=c*sin(projxz)+IX
        c=c*cos(projxz)
      ENDIF
    ENDIF
  
    IF @projyz!=0
      projyz=(@projyz%360)*pi/180
      IF @projyz==90      
        IX=d+IX
        d=0
      ELSE
        IX=d*sin(projyz)+IX
        d=d*cos(projyz)
      ENDIF
    ENDIF
    
    IF @projxu!=0
      projxu=(@projxu%360)*pi/180
      IF @projxu==90      
        IY=c+IY
        c=0
      ELSE
        IY=c*sin(projxu)+IY
        c=c*cos(projxu)
      ENDIF
    ENDIF
    
    IF @projyu!=0
      projyu=(@projyu%360)*pi/180
      IF @projyu==90      
        IY=d+IY
        d=0
      ELSE
        IY=d*sin(projyu)+IY
        d=d*cos(projyu)
      ENDIF
    ENDIF
    
  IF @FLIP==1
    IX=d
    d=@FlipValue
  ELSEIF @FLIP==2
    IY=d
    d=@FlipValue
  ELSEIF @FLIP==3
    IX=c
    c=@FlipValue
  ELSEIF @FLIP==4
    IY=c
    c=@FlipValue
  ENDIF
  
  If @MovePlane == true
    IX = real(#center)
    IY = imag(#center)
  ENDIF
    
  IF @IterPlane==0
    a=c+d*1i
    b=IX+IY*1i 
  ELSEIF @IterPlane==1
    a=c+IX*1i
    b=d+IY*1i
  ELSEIF @IterPlane==2
    a=c+IX*1i
    b=IY+d*1i
  ELSEIF @IterPlane==3
    a=IX+c*1i
    b=d+IY*1i
  ELSEIF @IterPlane==4
    a=IX+c*1i
    b=Iy+d*1i
  ELSE 
    a=IX+IY*1i
    b=c+d*1i
  ENDIF
  
  IF @M==false
    z=1i*sqrt(a/3)
  ELSE 
    z=-1i*sqrt(a/3)
  ENDIF
    
  loop:
    z=z*z*z+a*z+b
    
bailout:
  |z|<@bailout
  
  
switch:
  type="ToDevaneyCubicJulia"
  seed=#pixel
  IterPlane=IterPlane
  InterX=InterX
  InterY=InterY
  yrot=yrot
  xrot=xrot
  yrotu=yrotu
  xrotu=xrotu
  zrot=zrot
  uzrot=uzrot
  projxz=projxz
  projxu=projxu
  projyz=projyz
  projyu=projyu
  FlipValue=FlipValue
  FLIP=FLIP
  M=M
  MovePlane=MovePlane
  bailout=bailout
  
default:
  title = "DevaneyCubic"
  
  param IterPlane
    enum = "(a-real,a-imag)" "(a-real,b-real)" "(a-real,b-imag)" "(a-imag,b-real)" \
    "(a-imag,b-imag)" "(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param InterX
    caption=" z-axis"
    hint="Complement to Iterative Plane.For ex. iter: a-imag,b-real this should be a-real"
    default=0.0
  endparam
  
 param InterY
    caption=" u-axis"
    hint="Complement to Iterative Plane.For iter: a-real,b-imag this should be b-real"
    default=0.0
  endparam
  
 param yrot
    caption="Rotates xz-plane."
    hint= "Rotates xyz-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrot
    caption="Rotates yz-plane."
    hint= "Rotates xyz-plane in degrees around the x-axes."
    default=0.0
  endparam
  
 param yrotu
    caption="Rotates xu-plane."
    hint= "Rotates the xyu-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrotu
    caption="Rotates yu-plane."
    hint= "Rotating xyu-plane in degrees around the x-axis."
    default=0.0
  endparam
  
  param zrot
    caption="Rotates xy-plane."
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
  param uzrot
    caption="Rotates uz-plane"
    hint="Rotates the uz-plane in degrees."
    default=0.0
  endparam
  
  param projxz
    caption="Project x on z."
    hint="Projecting x on z in degrees."
    default=0.0
  endparam
  
 param projxu
    caption="Project x on u."
    hint="Projecting x on u in degrees."
    default=0.0
  endparam
  
  param projyz
    caption="Project y on z."
    hint="Projecting y on z in degrees."
    default=0.0
  endparam
  
  param projyu
    caption="Project y on u."
    hint="Projecting y on u in degrees."
    default=0.0
  endparam
  
   
  param FlipValue
    caption="flip value"
    hint="Value for flip. Should be be taken from properties/location/center. \
    y for y-flip x for x-flip. \
    Donīt forget to zero the coordinate at location after flip or simply cut the coordinate."
    default=0.0
  endparam
  
  param FLIP
    enum = "No Flip" "Flip y -> z" "Flip y -> u" "Flip x -> z" "Flip x -> u"
    hint="Turns coordinateplane 90 deg. Paste the coordinate you want to flip from location. \
    Donīt forget to zero the coordinate at location after the flip or simly cut the coordinate."
    default=0
  endparam
  
  param M
    caption="-1i*sqrt(a/3)"
    hint="Change to the other critical point. If set it will be negative."
    default=false
  endparam 
  
  param MovePlane
    caption = "Move On"
    default=false
    hint = "Is to play with. Be sure interceptcoords. are zero (default location).\
            Put MovePlane on. Push control as you move the area in the window \
            (hold left mousebutton down). If you move the mouse in x-direction \
            the set will move along the z-axis. In y-direction along u-axis. Enjoy." 
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
    min=1
  endparam
     
  }

ToDevaneyCubicJulia {
init:
  
  complex c=@seed
  complex z=#pixel
  g=@IterPlane
  d=@InterX+flip(@interY)
  IF g==0
     a=c
     b=d
  ELSEIF g==1
    a=real(c)+real(d)*1i
    b=imag(c)+imag(d)*1i
  ELSEIF g==2
    a=real(c)+real(d)*1i
    b=imag(d)+imag(c)*1i
  ELSEIF g==3
    a=real(d)+real(c)*1i
    b=imag(c)+imag(d)*1i
  ELSEIF g==4
    a=real(d)+real(c)*1i
    b=imag(d)+imag(c)*1i
  ELSE
    a=d
    b=c
  ENDIF
   
   
loop:
  z=z*z*z+a*z+b
  
bailout:
  |z|<@bailout
  
switch:
  type="DevaneyCubic"
  IterPlane=IterPlane
  InterX=InterX
  InterY=InterY
  yrot=yrot
  xrot=xrot
  yrotu=yrotu
  xrotu=xrotu
  zrot=zrot
  uzrot=uzrot
  projxz=projxz
  projxu=projxu
  projyz=projyz
  projyu=projyu
  FlipValue=FlipValue
  FLIP=FLIP
  M=M
  MovePlane=MovePlane
  bailout=bailout

default:
  title = "ToDevaneyCubicJulia"
  
  param IterPlane
    enum = "(a-real,a-imag)" "(a-real,b-real)" "(a-real,b-imag)" "(a-imag,breal)" \
    "(a-imag,b-imag)" "(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param InterX
    caption=" z-axis"
    hint="Complement to Iterative Plane.For ex. iter: a-imag,b-real this should be a-real"
    default=0.0
  endparam
  
 param InterY
    caption=" u-axis"
    hint="Complement to Iterative Plane.For iter: a-real,b-imag this should be b-real"
    default=0.0
  endparam
  
 param yrot
    caption="Rotates xz-plane."
    hint= "Rotates xyz-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrot
    caption="Rotates yz-plane."
    hint= "Rotates xyz-plane in degrees around the x-axes."
    default=0.0
  endparam
  
 param yrotu
    caption="Rotates xu-plane."
    hint= "Rotates the xyu-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrotu
    caption="Rotates yu-plane."
    hint= "Rotating xyu-plane in degrees around the x-axis."
    default=0.0
  endparam
  
  param zrot
    caption="Rotates xy-plane."
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
  param uzrot
    caption="Rotates uz-plane"
    hint="Rotates the uz-plane in degrees."
    default=0.0
  endparam
  
  param projxz
    caption="Project x on z."
    hint="Projecting x on z in degrees."
    default=0.0
  endparam
  
 param projxu
    caption="Project x on u."
    hint="Projecting x on u in degrees."
    default=0.0
  endparam
  
  param projyz
    caption="Project y on z."
    hint="Projecting y on z in degrees."
    default=0.0
  endparam
  
  param projyu
    caption="Project y on u."
    hint="Projecting y on u in degrees."
    default=0.0
  endparam
  
   
  param FlipValue
    caption="flip value"
    hint="Value for flip. Should be be taken from properties/location/center. \
    y for y-flip x for x-flip. \
    Donīt forget to zero the coordinate at location after flip or simply cut the coordinate."
    default=0.0
  endparam
  
  param FLIP
    enum = "No Flip" "Flip y -> z" "Flip y -> u" "Flip x -> z" "Flip x -> u"
    hint="Turns coordinateplane 90 deg. Paste the coordinate you want to flip from location. \
    Donīt forget to zero the coordinate at location after the flip or simly cut the coordinate."
    default=0
  endparam
  
  param M
    caption="-1i*sqrt(a/3)"
    hint="Sets the sign of the initial parameter 1i*sqrt(a/3). If set it will be negative."
    default=false
  endparam 
  
  param MovePlane
    caption = "Move On"
    default=false
    hint = "Is to play with. Be sure interceptcoords. are zero (default location).\
            Put MovePlane on. Push control as you move the area in the window \
            (hold left mousebutton down). If you move the mouse in x-direction \
            the set will move along the z-axis. In y-direction along u-axis. Enjoy." 
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
    min=1
  endparam

}

DevaneyCubicJulia {
init:
  a=@areal+@aimag*1i
  b=@breal+@bimag*1i
  z=#pixel
loop:
  z=z*z*z+a*z+b  
bailout:
  |z|<@bailout
default:
  title = "DevaneyCubicJulia"
  
  param areal
    caption="a-real"
    hint="Real part of a-parameter"
    default=0.0
  endparam
  
   param aimag
    caption="a-imag"
    hint="Imaginary part of a-parameter"
    default=0.0
  endparam
  
   param breal
    caption="b-real"
    hint="Real part of b-parameter"
    default=0.0
  endparam
  
    
   param bimag
    caption="b-imag"
    hint="Imaginary part of b-parameter"
    default=0.0
  endparam
  
    
   param bailout
    caption="bailout"
    hint="Value of bailout"
    default=100.0  
  endparam
  

  param bailout
    caption="bailout"
    default=0.00001
    hint="Bailout value."
   endparam

}

BrannerSpecialCubic {


init:
  float c=0
  float d=0
  float t=0
  float aa=0
  a=0+0i
  b=0+0i
  c=real(#pixel)
  d=imag(#pixel)
  float IX=@InterX
  float IY=@InterY
  float yrot=0
  float xrot=0
  float xrotu=0
  float yrotu=0
  float zrot=0
  float uzrot=0
  float projxz=0
  float projyz=0
  float projxu=0
  float projyu=0

    IF @yrot!=0
      yrot=(@yrot%360)*pi/180
      t=cabs(c+IX*1i)      
      aa=atan2(c+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        c=-t
        IX=0
      ELSEIF aa==pi/2
        c=0
        IX=t
      ELSEIF aa==-pi/2
        c=0
        IX=-t
      ELSE
        c=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+d*1i)     
      aa=atan2(IX+d*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        d=0
      ELSEIF aa==pi/2
        IX=0
        d=t
      ELSEIF aa==-pi/2
        IX=0
        d=-t
      ELSE
        IX=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
    
    IF @yrotu!=0
      yrotu=(@yrotu%360)*pi/180
      t=cabs(c+IY*1i)      
      aa=atan2(c+IY*1i) 
      aa=yrotu+aa
      IF abs(aa)==pi
        c=-t
        IY=0
      ELSEIF aa==pi/2
        c=0
        IY=t
      ELSEIF aa==-pi/2
        c=0
        IY=-t
      ELSE
        c=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrotu!=0
      xrotu=(@xrotu%360)*pi/180
      t=cabs(IY+d*1i)      
      aa=atan2(IY+d*1i) 
      aa=xrotu+aa
      IF abs(aa)==pi
        IY=-t
        d=0
      ELSEIF aa==pi/2
        IY=0
        d=t
      ELSEIF aa==-pi/2
        IY=0
        d=-t
      ELSE
        IY=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0
      zrot=(@zrot%360)*pi/180
      t=cabs(c+d*1i)
      aa=atan2(c+d*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        c=-t
        d=0
      ELSEIF aa==pi/2
        c=0
        d=t
      ELSEIF aa==-pi/2
        c=0
        d=-t
      ELSE
        c=t*cos(aa)
        d=t*sin(aa)
      ENDIF
    ENDIF
    
     
    IF @uzrot!=0
      uzrot=(@uzrot%360)*pi/180
      t=cabs(IX+IY*1i)    
      aa=atan2(IX+IY*1i)
      aa=uzrot+aa
      IF abs(aa)==pi
        IX=-t
        IY=0
      ELSEIF aa==pi/2
        IX=0
        IY=t
      ELSEIF aa==-pi/2
        IX=0
        IY=-t
      ELSE
        IX=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF


    IF @projxz!=0
      projxz=(@projxz%360)*pi/180
      IF @projxz==90      
        IX=c+IX
        c=0
      ELSE
        IX=c*sin(projxz)+IX
        c=c*cos(projxz)
      ENDIF
    ENDIF
  
    IF @projyz!=0
      projyz=(@projyz%360)*pi/180
      IF @projyz==90      
        IX=d+IX
        d=0
      ELSE
        IX=d*sin(projyz)+IX
        d=d*cos(projyz)
      ENDIF
    ENDIF
    
    IF @projxu!=0
      projxu=(@projxu%360)*pi/180
      IF @projxu==90      
        IY=c+IY
        c=0
      ELSE
        IY=c*sin(projxu)+IY
        c=c*cos(projxu)
      ENDIF
    ENDIF
    
    IF @projyu!=0
      projyu=(@projyu%360)*pi/180
      IF @projyu==90      
        IY=d+IY
        d=0
      ELSE
        IY=d*sin(projyu)+IY
        d=d*cos(projyu)
      ENDIF
    ENDIF
    
  IF @FLIP==1
    IX=d
    d=@FlipValue
  ELSEIF @FLIP==2
    IY=d
    d=@FlipValue
  ELSEIF @FLIP==3
    IX=c
    c=@FlipValue
  ELSEIF @FLIP==4
    IY=c
    c=@FlipValue
  ENDIF
  
  If @MovePlane == true
    IX = real(#center)
    IY = imag(#center)
  ENDIF
    
  IF @IterPlane==0
    a=c+d*1i
    b=IX+IY*1i 
  ELSEIF @IterPlane==1
    a=c+IX*1i
    b=d+IY*1i
  ELSEIF @IterPlane==2
    a=c+IX*1i
    b=IY+d*1i
  ELSEIF @IterPlane==3
    a=IX+c*1i
    b=d+IY*1i
  ELSEIF @IterPlane==4
    a=IX+c*1i
    b=Iy+d*1i
  ELSE 
    a=IX+IY*1i
    b=c+d*1i
  ENDIF
  
  IF @M==false
    z=+1
  ELSE 
    z=-1
  ENDIF
    
  loop:
    z=(b/4-a/4)*(z*z*z-3*z)+a/2+b/2
    
bailout:
  |z|<@bailout
  
  
switch:
  type="ToBrannerSpecialCubicJulia"
  seed=#pixel
  IterPlane=IterPlane
  InterX=InterX
  InterY=InterY
  yrot=yrot
  xrot=xrot
  yrotu=yrotu
  xrotu=xrotu
  zrot=zrot
  uzrot=uzrot
  projxz=projxz
  projxu=projxu
  projyz=projyz
  projyu=projyu
  FlipValue=FlipValue
  FLIP=FLIP
  M=M
  MovePlane=MovePlane
  bailout=bailout
  
default:
  title = "BrannerSpecialCubic"
  
  param IterPlane
    enum = "(a-real,a-imag)" "(a-real,b-real)" "(a-real,b-imag)" "(a-imag,b-real)" \
    "(a-imag,b-imag)" "(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param InterX
    caption=" z-axis"
    hint="Complement to Iterative Plane.For ex. iter: a-imag,b-real this should be a-real"
    default=0.0
  endparam
  
 param InterY
    caption=" u-axis"
    hint="Complement to Iterative Plane.For iter: a-real,b-imag this should be b-real"
    default=0.0
  endparam
  
 param yrot
    caption="Rotates xz-plane."
    hint= "Rotates xyz-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrot
    caption="Rotates yz-plane."
    hint= "Rotates xyz-plane in degrees around the x-axes."
    default=0.0
  endparam
  
 param yrotu
    caption="Rotates xu-plane."
    hint= "Rotates the xyu-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrotu
    caption="Rotates yu-plane."
    hint= "Rotating xyu-plane in degrees around the x-axis."
    default=0.0
  endparam
  
  param zrot
    caption="Rotates xy-plane."
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
  param uzrot
    caption="Rotates uz-plane"
    hint="Rotates the uz-plane in degrees."
    default=0.0
  endparam
  
  param projxz
    caption="Project x on z."
    hint="Projecting x on z in degrees."
    default=0.0
  endparam
  
 param projxu
    caption="Project x on u."
    hint="Projecting x on u in degrees."
    default=0.0
  endparam
  
  param projyz
    caption="Project y on z."
    hint="Projecting y on z in degrees."
    default=0.0
  endparam
  
  param projyu
    caption="Project y on u."
    hint="Projecting y on u in degrees."
    default=0.0
  endparam
  
   
  param FlipValue
    caption="flip value"
    hint="Value for flip. Should be be taken from properties/location/center. \
    y for y-flip x for x-flip. \
    Donīt forget to zero the coordinate at location after flip or simply cut the coordinate."
    default=0.0
  endparam
  
  param FLIP
    enum = "No Flip" "Flip y -> z" "Flip y -> u" "Flip x -> z" "Flip x -> u"
    hint="Turns coordinateplane 90 deg. Paste the coordinate you want to flip from location. \
    Donīt forget to zero the coordinate at location after the flip or simly cut the coordinate."
    default=0
  endparam
  
  param M
    caption="-1"
    hint="Change to the other critical point. If set it will be negative."
    default=false
  endparam 
  
  param MovePlane
    caption = "Move On"
    default=false
    hint = "Is to play with. Be sure interceptcoords. are zero (default location).\
            Put MovePlane on. Push control as you move the area in the window \
            (hold left mousebutton down). If you move the mouse in x-direction \
            the set will move along the z-axis. In y-direction along u-axis. Enjoy." 
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
    min=1
  endparam
     
  }

ToBrannerSpecialCubicJulia {
init:
  
  complex c=@seed
  complex z=#pixel
  g=@IterPlane
  d=@InterX+flip(@interY)
  IF g==0
     a=c
     b=d
  ELSEIF g==1
    a=real(c)+real(d)*1i
    b=imag(c)+imag(d)*1i
  ELSEIF g==2
    a=real(c)+real(d)*1i
    b=imag(d)+imag(c)*1i
  ELSEIF g==3
    a=real(d)+real(c)*1i
    b=imag(c)+imag(d)*1i
  ELSEIF g==4
    a=real(d)+real(c)*1i
    b=imag(d)+imag(c)*1i
  ELSE
    a=d
    b=c
  ENDIF
   
   
loop:
  z=(b/4-a/4)*(z*z*z-3*z)+a/2+b/2
  
bailout:
  |z|<@bailout
  
switch:
  type="BrannerSpecialCubic"
  IterPlane=IterPlane
  InterX=InterX
  InterY=InterY
  yrot=yrot
  xrot=xrot
  yrotu=yrotu
  xrotu=xrotu
  zrot=zrot
  uzrot=uzrot
  projxz=projxz
  projxu=projxu
  projyz=projyz
  projyu=projyu
  FlipValue=FlipValue
  FLIP=FLIP
  M=M
  MovePlane=MovePlane
  bailout=bailout

default:
  title = "ToBrannerSpecialCubicJulia"
  
  param IterPlane
    enum = "(a-real,a-imag)" "(a-real,b-real)" "(a-real,b-imag)" "(a-imag,breal)" \
    "(a-imag,b-imag)" "(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param InterX
    caption=" z-axis"
    hint="Complement to Iterative Plane.For ex. iter: a-imag,b-real this should be a-real"
    default=0.0
  endparam
  
 param InterY
    caption=" u-axis"
    hint="Complement to Iterative Plane.For iter: a-real,b-imag this should be b-real"
    default=0.0
  endparam
  
 param yrot
    caption="Rotates xz-plane."
    hint= "Rotates xyz-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrot
    caption="Rotates yz-plane."
    hint= "Rotates xyz-plane in degrees around the x-axes."
    default=0.0
  endparam
  
 param yrotu
    caption="Rotates xu-plane."
    hint= "Rotates the xyu-plane in degrees around the y-axis."
    default=0.0
 endparam
  
  param xrotu
    caption="Rotates yu-plane."
    hint= "Rotating xyu-plane in degrees around the x-axis."
    default=0.0
  endparam
  
  param zrot
    caption="Rotates xy-plane."
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
  param uzrot
    caption="Rotates uz-plane"
    hint="Rotates the uz-plane in degrees."
    default=0.0
  endparam
  
  param projxz
    caption="Project x on z."
    hint="Projecting x on z in degrees."
    default=0.0
  endparam
  
 param projxu
    caption="Project x on u."
    hint="Projecting x on u in degrees."
    default=0.0
  endparam
  
  param projyz
    caption="Project y on z."
    hint="Projecting y on z in degrees."
    default=0.0
  endparam
  
  param projyu
    caption="Project y on u."
    hint="Projecting y on u in degrees."
    default=0.0
  endparam
  
   
  param FlipValue
    caption="flip value"
    hint="Value for flip. Should be be taken from properties/location/center. \
    y for y-flip x for x-flip. \
    Donīt forget to zero the coordinate at location after flip or simply cut the coordinate."
    default=0.0
  endparam
  
  param FLIP
    enum = "No Flip" "Flip y -> z" "Flip y -> u" "Flip x -> z" "Flip x -> u"
    hint="Turns coordinateplane 90 deg. Paste the coordinate you want to flip from location. \
    Donīt forget to zero the coordinate at location after the flip or simly cut the coordinate."
    default=0
  endparam
  
  param M
    caption="-1"
    hint="Sets the sign of the initial parameter sqrt(A). If set it will be negative."
    default=false
  endparam 
  
  param MovePlane
    caption = "Move On"
    default=false
    hint = "Is to play with. Be sure interceptcoords. are zero (default location).\
            Put MovePlane on. Push control as you move the area in the window \
            (hold left mousebutton down). If you move the mouse in x-direction \
            the set will move along the z-axis. In y-direction along u-axis. Enjoy." 
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
    min=1
  endparam

}

BrannerSpecialCubicJulia {
init:
  a=@areal+@aimag*1i
  b=@breal+@bimag*1i
  z=#pixel
loop:
  z=(b/4-a/4)*(z*z*z-3*z)+a/2+b/2  
bailout:
  |z|<@bailout
default:
  title = "BrannerSpecialCubicJulia"
  
  param areal
    caption="a-real"
    hint="Real part of a-parameter"
    default=0.0
  endparam
  
   param aimag
    caption="a-imag"
    hint="Imaginary part of a-parameter"
    default=0.0
  endparam
  
   param breal
    caption="b-real"
    hint="Real part of b-parameter"
    default=0.0
  endparam
  
    
   param bimag
    caption="b-imag"
    hint="Imaginary part of b-parameter"
    default=0.0
  endparam
  
    
  param bailout
    caption="bailout"
    default=100
    hint="Bailout value."
   endparam

}

MilnorAB2 {

init:
  int n=0
  int m1save=0
  int m2save=0
  float abs1=0
  float abs2=0
  complex z=0
  complex oldz=0
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(#pixel)
  float dd=imag(#pixel)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;A-real, A-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;A-real, B-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;A-real, B-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;A-imag, B-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;A-imag, B-imag
    IX=@areal
    IY=@breal
  ELSE                    ;B-real, B-imag
    IX=@areal
    IY=@aimag
  ENDIF
    
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t

      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
  
  IF @PlottedPlane==0      ;A-real, A-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;A-real, B-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;A-real, B-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;A-imag, B-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;A-imag, B-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;B-real, B-imag
    b=cc+dd*1i
  ENDIF


  if (@M==0)&&(@mode==0)
    z=sqrt(A)
  elseif (@M==1)&&(@mode==0)
    z=-sqrt(A)
  else
    z=sqrt(A)
    while (|z|<@bailout)&&(n<#maxiter)
      n=n+1
      z=z*z*z-3*A*z+sqrt(B)
    endwhile
    m1save=n
    abs1=|z|
    n=0
    z=-sqrt(A)
    while (|z|<@bailout)&&(n<#maxiter)
      n=n+1
      z=z*z*z-3*A*z+sqrt(B)
    endwhile
    m2save=n
    abs2=|z|

    if @mode==1
      if @M==0  ;M1
        if m1save==#maxiter
          z=sqrt(A)
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=sqrt(A)
          else
            z=-sqrt(A)
          endif
        else
          z=sqrt(A)
        endif
        
      elseif @M==1  ;M2
        if m2save==#maxiter
          z=-sqrt(A)
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=sqrt(A)
          else
            z=-sqrt(A)
          endif
        else 
          z=-sqrt(A)
        endif
        
      elseif (@M==2)
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=sqrt(A)
          else
            z=-sqrt(A)
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=sqrt(A)
          else
            z=-sqrt(A)
          endif
        elseif m1save==#maxiter
          z=-sqrt(A)
        elseif m2save==#maxiter
          z=sqrt(A)
        else
          if m1save>m2save
            z=sqrt(A)
          else
            z=-sqrt(A)
          endif
        endif       
      elseif @M==3
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=sqrt(A)
          else
            z=-sqrt(A)
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=sqrt(A)
          else
            z=-sqrt(A)
          endif
        elseif (m1save==#maxiter)
          z=sqrt(A)
        else
          z=-sqrt(A)
        endif
      endif     
    else
      if (@M==2)
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1<abs2
            z=sqrt(A)
          else
            z=-sqrt(A)
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save<m2save
            z=sqrt(A)
          else
            z=-sqrt(A)
          endif
        elseif m1save==#maxiter
          z=-sqrt(A)
        elseif m2save==#maxiter
          z=sqrt(A)
        else
          if m1save<m2save
            z=sqrt(A)
          else
            z=-sqrt(A)
          endif
        endif
      elseif @M==3
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=sqrt(A)
          else
            z=-sqrt(A)
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=sqrt(A)
          else

            z=-sqrt(A)
          endif
        elseif (m1save==#maxiter)
          z=sqrt(A)
        else
          z=-sqrt(A)
        endif
      endif
    endif                 
  endif
   
loop:
  oldz=z
  z=z*z*z-3*A*z+sqrt(B)

    
bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="MilnorJulia2"
  seed=#pixel
  PlottedPlane=PlottedPlane
  M=M
  mode=mode
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff
  bailout=bailout
  

  
default:
  title = "MilnorAB2"
  periodicity=0
  method=multipass
  
  
  param PlottedPlane
    enum = "1.(A-real,A-imag)" "2.(A-real,B-real)" "3.(A-real,B-imag)" "4.(A-imag,B-real)"   \
           "5.(A-imag,B-imag)" "6.(B-real,B-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param M
    enum="M+" "M-" "CCL" "M+ and/or M-"
    hint="The choosen critical point to initialize z"
    default=0
  endparam 
  
  param mode
    enum="Normal" "High"
    default=0
  endparam
  
  param areal
    caption=" A-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" A-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" B-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" B-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"
    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam

  
  param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
     
  }
  
  
MilnorJulia2 {

init:
  complex z=#pixel
  complex oldz=0+0i
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(@seed)
  float dd=imag(@seed)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;A-real, A-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;A-real, B-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;A-real, B-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;A-imag, B-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;A-imag, B-imag
    IX=@areal
    IY=@breal
  ELSE                    ;B-real, B-imag
    IX=@areal
    IY=@aimag
  ENDIF
  
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t
      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
    
  
  IF @PlottedPlane==0      ;A-real, A-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;A-real, B-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;A-real, B-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;A-imag, B-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;Aa-imag, B-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;B-real, B-imag
    b=cc+dd*1i
  ENDIF

    
  
loop:
  oldz=z
  z=z*z*z-3*A*z+sqrt(B)

    
bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:

  type="MilnorAB2"
  PlottedPlane=PlottedPlane
  M=M
  mode=mode
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff

  bailout=bailout
  

  
default:
  title = "MilnorJulia2"
  periodicity=0
  method=multipass
  
  

  
  param PlottedPlane
    enum = "1.(A-real,A-imag)" "2.(A-real,B-real)" "3.(A-real,B-imag)" "4.(A-imag,B-real)"   \
           "5.(A-imag,B-imag)" "6.(B-real,B-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param M
    enum="M+" "M-" "CCL" "M+ and/or M-"
    hint="The choosen critical point to initialize z"
    default=0
  endparam 
  
  param mode

    enum="Normal" "High"
    default=0
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"

    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
 

   param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
  
  
  param seed
    caption="Seed"
    default=(0,0)
    hint="Seed for Julia"
  endparam
     
  }


SorensenCubic2 {

init:
  int n=0
  int m1save=0
  int m2save=0
  float abs1=0
  float abs2=0
  complex z=0
  complex oldz=0
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(#pixel)
  float dd=imag(#pixel)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;a-real, a-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;a-real, b-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;a-real, b-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;a-imag, b-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;a-imag, b-imag
    IX=@areal
    IY=@breal
  ELSE                    ;b-real, b-imag
    IX=@areal
    IY=@aimag
  ENDIF
    
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t

      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
  
  IF @PlottedPlane==0      ;a-real, a-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;a-real, b-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;a-real, b-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;a-imag, b-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;a-imag, b-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;b-real, b-imag
    b=cc+dd*1i
  ENDIF


  if (@M==0)&&(@mode==0)
    z=-a/3+sqrt(a*a/9-b/3)
  elseif (@M==1)&&(@mode==0)
    z=-a/3-sqrt(a*a/9-b/3)
  else
    z=-a/3+sqrt(a*a/9-b/3)
    while (|z|<@bailout)&&(n<#maxiter)
      n=n+1
      z=z*z*z+a*z*z+b*z
    endwhile
    m1save=n
    abs1=|z|
    n=0
    z=-a/3-sqrt(a*a/9-b/3)
    while (|z|<@bailout)&&(n<#maxiter)
      n=n+1
      z=z*z*z+a*z*z+b*z
    endwhile
    m2save=n
    abs2=|z|

    if @mode==1
      if @M==0  ;M1
        if m1save==#maxiter
          z=-a/3+sqrt(a*a/9-b/3)
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=-a/3+sqrt(a*a/9-b/3)
          else
            z=-a/3-sqrt(a*a/9-b/3)
          endif
        else
          z=-a/3+sqrt(a*a/9-b/3)
        endif
        
      elseif @M==1  ;M2
        if m2save==#maxiter
          z=-a/3-sqrt(a*a/9-b/3)
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=-a/3+sqrt(a*a/9-b/3)
          else
            z=-a/3-sqrt(a*a/9-b/3)
          endif
        else 
          z=-a/3-sqrt(a*a/9-b/3)
        endif
        
      elseif (@M==2)
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=-a/3+sqrt(a*a/9-b/3)
          else
            z=-a/3-sqrt(a*a/9-b/3)
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=-a/3+sqrt(a*a/9-b/3)
          else
            z=-a/3-sqrt(a*a/9-b/3)
          endif
        elseif m1save==#maxiter
          z=-a/3-sqrt(a*a/9-b/3)
        elseif m2save==#maxiter
          z=-a/3+sqrt(a*a/9-b/3)
        else
          if m1save>m2save
            z=-a/3+sqrt(a*a/9-b/3)
          else
            z=-a/3-sqrt(a*a/9-b/3)
          endif
        endif       
      elseif @M==3
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=-a/3+sqrt(a*a/9-b/3)
          else
            z=-a/3-sqrt(a*a/9-b/3)
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=-a/3+sqrt(a*a/9-b/3)
          else
            z=-a/3-sqrt(a*a/9-b/3)
          endif
        elseif (m1save==#maxiter)
          z=-a/3+sqrt(a*a/9-b/3)
        else
          z=-a/3-sqrt(a*a/9-b/3)
        endif
      endif     
    else
      if (@M==2)
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1<abs2
            z=-a/3+sqrt(a*a/9-b/3)
          else
            z=-a/3-sqrt(a*a/9-b/3)
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save<m2save
            z=-a/3+sqrt(a*a/9-b/3)
          else
            z=-a/3-sqrt(a*a/9-b/3)
          endif
        elseif m1save==#maxiter
          z=-a/3-sqrt(a*a/9-b/3)
        elseif m2save==#maxiter
          z=-a/3+sqrt(a*a/9-b/3)
        else
          if m1save<m2save
            z=-a/3+sqrt(a*a/9-b/3)
          else
            z=-a/3-sqrt(a*a/9-b/3)
          endif
        endif
      elseif @M==3
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=-a/3+sqrt(a*a/9-b/3)
          else
            z=-a/3-sqrt(a*a/9-b/3)
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=-a/3+sqrt(a*a/9-b/3)
          else

            z=-a/3-sqrt(a*a/9-b/3)
          endif
        elseif (m1save==#maxiter)
          z=-a/3+sqrt(a*a/9-b/3)
        else
          z=-a/3-sqrt(a*a/9-b/3)
        endif
      endif
    endif                 
  endif
   
loop:
  oldz=z
  z=z*z*z+a*z*z+b*z

    
bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="SorensenCubicJulia2"
  seed=#pixel
  PlottedPlane=PlottedPlane
  M=M
  mode=mode
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff
  bailout=bailout
  

  
default:
  title = "SorensenCubic2"
  periodicity=0
  method=multipass
  
  
  param PlottedPlane
    enum = "1.(a-real,a-imag)" "2.(a-real,b-real)" "3.(a-real,b-imag)" "4.(a-imag,b-real)"   \
           "5.(a-imag,b-imag)" "6.(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param M
    enum="M+" "M-" "CCL" "M+ and/or M-"
    hint="The choosen critical point to initialize z"
    default=0
  endparam 
  
  param mode
    enum="Normal" "High"
    default=0
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"
    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam

  
  param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
     
  }
  
  
SorensenCubicJulia2 {

init:
  complex z=#pixel
  complex oldz=0+0i
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(@seed)
  float dd=imag(@seed)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;a-real, a-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;a-real, b-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;a-real, b-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;a-imag, b-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;a-imag, b-imag
    IX=@areal
    IY=@breal
  ELSE                    ;b-real, b-imag
    IX=@areal
    IY=@aimag
  ENDIF
  
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t
      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
    
  
  IF @PlottedPlane==0      ;a-real, a-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;a-real, b-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;a-real, b-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;a-imag, b-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;a-imag, b-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;b-real, b-imag
    b=cc+dd*1i
  ENDIF

    
loop:
  oldz=z
  z=z*z*z+a*z*z+b*z

    
bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:

  type="SorensenCubic2"
  PlottedPlane=PlottedPlane
  M=M
  mode=mode
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff
  bailout=bailout
  

  
default:
  title = "SorensenCubicJulia2"
  periodicity=0
  method=multipass
  
  

  
  param PlottedPlane
    enum = "1.(a-real,a-imag)" "2.(a-real,b-real)" "3.(a-real,b-imag)" "4.(a-imag,b-real)"   \
           "5.(a-imag,b-imag)" "6.(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param M
    enum="M+" "M-" "CCL" "M+ and/or M-"
    hint="The choosen critical point to initialize z"
    default=0
  endparam 
  
  param mode

    enum="Normal" "High"
    default=0
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"

    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
 

   param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
  
  
  param seed
    caption="Seed"
    default=(0,0)
    hint="Seed for Julia"
  endparam
     
  }


KullbergCubic2 {

init:
  int n=0
  int m1save=0
  int m2save=0
  float abs1=0
  float abs2=0
  complex z=0
  complex oldz=0
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(#pixel)
  float dd=imag(#pixel)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;a-real, a-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;a-real, b-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;a-real, b-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;a-imag, b-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;a-imag, b-imag
    IX=@areal
    IY=@breal
  ELSE                    ;b-real, b-imag
    IX=@areal
    IY=@aimag
  ENDIF
    
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t

      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
  
  IF @PlottedPlane==0      ;a-real, a-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;a-real, b-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;a-real, b-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;a-imag, b-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;a-imag, b-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;b-real, b-imag
    b=cc+dd*1i
  ENDIF


  if (@M==0)&&(@mode==0)
    z=0
  elseif (@M==1)&&(@mode==0)
    z=-2*a/3
  else
    z=0
    while (|z|<@bailout)&&(n<#maxiter)
      n=n+1
      z=z*z*z+a*z*z+b
    endwhile
    m1save=n
    abs1=|z|
    n=0
    z=-2*a/3
    while (|z|<@bailout)&&(n<#maxiter)
      n=n+1
      z=z*z*z+a*z*z+b
    endwhile
    m2save=n
    abs2=|z|

    if @mode==1
      if @M==0  ;M1
        if m1save==#maxiter
          z=0
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=0
          else
            z=-2*a/3
          endif
        else
          z=0
        endif
        
      elseif @M==1  ;M2
        if m2save==#maxiter
          z=-2*a/3
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=0
          else
            z=-2*a/3
          endif
        else 
          z=-2*a/3
        endif
        
      elseif (@M==2)
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=0
          else
            z=-2*a/3
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=0
          else
            z=-2*a/3
          endif
        elseif m1save==#maxiter
          z=-2*a/3
        elseif m2save==#maxiter
          z=0
        else
          if m1save>m2save
            z=0
          else
            z=-2*a/3
          endif
        endif       
      elseif @M==3
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=0
          else
            z=-2*a/3
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=0
          else
            z=-2*a/3
          endif
        elseif (m1save==#maxiter)
          z=0
        else
          z=-2*a/3
        endif
      endif     
    else
      if (@M==2)
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1<abs2
            z=0
          else
            z=-2*a/3
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save<m2save
            z=0
          else
            z=-2*a/3
          endif
        elseif m1save==#maxiter
          z=-2*a/3
        elseif m2save==#maxiter
          z=0
        else
          if m1save<m2save
            z=0
          else
            z=-2*a/3
          endif
        endif
      elseif @M==3
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=0
          else
            z=-2*a/3
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=0
          else

            z=-2*a/3
          endif
        elseif (m1save==#maxiter)
          z=0
        else
          z=-2*a/3
        endif
      endif
    endif                 
  endif
   
loop:
  oldz=z
  z=z*z*z+a*z*z+b

    
bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="KullbergCubicJulia2"
  seed=#pixel
  PlottedPlane=PlottedPlane
  M=M
  mode=mode
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff
  bailout=bailout
  

  
default:
  title = "KullbergCubic2"
  periodicity=0
  method=multipass
  
  
  param PlottedPlane
    enum = "1.(a-real,a-imag)" "2.(a-real,b-real)" "3.(a-real,b-imag)" "4.(a-imag,b-real)"   \
           "5.(a-imag,b-imag)" "6.(b-real,b-imag)"
    default=5
    hint="The axis that will be plotted."
  endparam
  
  param M
    enum="M+" "M-" "CCL" "M+ and/or M-"
    hint="The choosen critical point to initialize z"
    default=0
  endparam 
  
  param mode
    enum="Normal" "High"
    default=0
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"
    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam

  
  param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
     
  }
  
  
KullbergCubicJulia2 {

init:
  complex z=#pixel
  complex oldz=0+0i
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(@seed)
  float dd=imag(@seed)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;a-real, a-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;a-real, b-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;a-real, b-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;a-imag, b-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;a-imag, b-imag
    IX=@areal
    IY=@breal
  ELSE                    ;b-real, b-imag
    IX=@areal
    IY=@aimag
  ENDIF
  
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t
      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
    
  
  IF @PlottedPlane==0      ;a-real, a-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;a-real, b-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;a-real, b-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;a-imag, b-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;a-imag, b-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;b-real, b-imag
    b=cc+dd*1i
  ENDIF

    
  
loop:
  oldz=z
  z=z*z*z+a*z*z+b

    
bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:

  type="KullbergCubic2"
  PlottedPlane=PlottedPlane
  M=M
  mode=mode
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff

  bailout=bailout
  

  
default:
  title = "KullbergCubicJulia2"
  periodicity=0
  method=multipass
  
  

  
  param PlottedPlane
    enum = "1.(a-real,a-imag)" "2.(a-real,b-real)" "3.(a-real,b-imag)" "4.(a-imag,b-real)"   \
           "5.(a-imag,b-imag)" "6.(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param M
    enum="M+" "M-" "CCL" "M+ and/or M-"
    hint="The choosen critical point to initialize z"
    default=0
  endparam 
  
  param mode

    enum="Normal" "High"
    default=0
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"

    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
 

   param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
  
  
  param seed
    caption="Seed"
    default=(0,0)
    hint="Seed for Julia"
  endparam
     
  }

DevaneyCubic2 {

init:
  int n=0
  int m1save=0
  int m2save=0
  float abs1=0
  float abs2=0
  complex z=0
  complex oldz=0
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(#pixel)
  float dd=imag(#pixel)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;a-real, a-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;a-real, b-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;a-real, b-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;a-imag, b-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;a-imag, b-imag
    IX=@areal
    IY=@breal
  ELSE                    ;b-real, b-imag
    IX=@areal
    IY=@aimag
  ENDIF
    
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t

      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
  
  IF @PlottedPlane==0      ;a-real, a-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;a-real, b-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;a-real, b-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;a-imag, b-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;a-imag, b-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;b-real, b-imag
    b=cc+dd*1i
  ENDIF


  if (@M==0)&&(@mode==0)
    z=1i*sqrt(a/3)
  elseif (@M==1)&&(@mode==0)
    z=-1i*sqrt(a/3)
  else
    z=1i*sqrt(a/3)
    while (|z|<@bailout)&&(n<#maxiter)
      n=n+1
      z=z*z*z+a*z+b
    endwhile
    m1save=n
    abs1=|z|
    n=0
    z=-1i*sqrt(a/3)
    while (|z|<@bailout)&&(n<#maxiter)
      n=n+1
      z=z*z*z+a*z+b
    endwhile
    m2save=n
    abs2=|z|

    if @mode==1
      if @M==0  ;M1
        if m1save==#maxiter
          z=1i*sqrt(a/3)
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1i*sqrt(a/3)
          else
            z=-1i*sqrt(a/3)
          endif
        else
          z=1i*sqrt(a/3)
        endif
        
      elseif @M==1  ;M2
        if m2save==#maxiter
          z=-1i*sqrt(a/3)
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1i*sqrt(a/3)
          else
            z=-1i*sqrt(a/3)
          endif
        else 
          z=-1i*sqrt(a/3)
        endif
        
      elseif (@M==2)
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=1i*sqrt(a/3)
          else
            z=-1i*sqrt(a/3)
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1i*sqrt(a/3)
          else
            z=-1i*sqrt(a/3)
          endif
        elseif m1save==#maxiter
          z=-1i*sqrt(a/3)
        elseif m2save==#maxiter
          z=1i*sqrt(a/3)
        else
          if m1save>m2save
            z=1i*sqrt(a/3)
          else
            z=-1i*sqrt(a/3)
          endif
        endif       
      elseif @M==3
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=1i*sqrt(a/3)
          else
            z=-1i*sqrt(a/3)
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1i*sqrt(a/3)
          else
            z=-1i*sqrt(a/3)
          endif
        elseif (m1save==#maxiter)
          z=1i*sqrt(a/3)
        else
          z=-1i*sqrt(a/3)
        endif
      endif     
    else
      if (@M==2)
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1<abs2
            z=1i*sqrt(a/3)
          else
            z=-1i*sqrt(a/3)
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save<m2save
            z=1i*sqrt(a/3)
          else
            z=-1i*sqrt(a/3)
          endif
        elseif m1save==#maxiter
          z=-1i*sqrt(a/3)
        elseif m2save==#maxiter
          z=1i*sqrt(a/3)
        else
          if m1save<m2save
            z=1i*sqrt(a/3)
          else
            z=-1i*sqrt(a/3)
          endif
        endif
      elseif @M==3
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=1i*sqrt(a/3)
          else
            z=-1i*sqrt(a/3)
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1i*sqrt(a/3)
          else

            z=-1i*sqrt(a/3)
          endif
        elseif (m1save==#maxiter)
          z=1i*sqrt(a/3)
        else
          z=-1i*sqrt(a/3)
        endif
      endif
    endif                 
  endif
   
loop:
  oldz=z
  z=z*z*z+a*z+b

    
bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="DevaneyCubicJulia2"
  seed=#pixel
  PlottedPlane=PlottedPlane
  M=M
  mode=mode
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff
  bailout=bailout
  

  
default:
  title = "DevaneyCubic2"
  periodicity=0
  method=multipass
  
  
  param PlottedPlane
    enum = "1.(a-real,a-imag)" "2.(a-real,b-real)" "3.(a-real,b-imag)" "4.(a-imag,b-real)"   \
           "5.(a-imag,b-imag)" "6.(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param M
    enum="M+" "M-" "CCL" "M+ and/or M-"
    hint="The choosen critical point to initialize z"
    default=0
  endparam 
  
  param mode
    enum="Normal" "High"
    default=0
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"
    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam

  
  param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
     
  }
  
  
DevaneyCubicJulia2 {

init:
  complex z=#pixel
  complex oldz=0+0i
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(@seed)
  float dd=imag(@seed)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;a-real, a-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;a-real, b-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;a-real, b-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;a-imag, b-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;a-imag, b-imag
    IX=@areal
    IY=@breal
  ELSE                    ;b-real, b-imag
    IX=@areal
    IY=@aimag
  ENDIF
  
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t
      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
    
  
  IF @PlottedPlane==0      ;a-real, a-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;a-real, b-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;a-real, b-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;a-imag, b-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;a-imag, b-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;b-real, b-imag
    b=cc+dd*1i
  ENDIF

    
  
loop:
  oldz=z
  z=z*z*z+a*z+b

    
bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:

  type="DevaneyCubic2"
  PlottedPlane=PlottedPlane
  M=M
  mode=mode
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff
  bailout=bailout
  

  
default:
  title = "DevaneyCubicJulia2"
  periodicity=0
  method=multipass
  
  

  
  param PlottedPlane
    enum = "1.(a-real,a-imag)" "2.(a-real,b-real)" "3.(a-real,b-imag)" "4.(a-imag,b-real)"   \
           "5.(a-imag,b-imag)" "6.(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param M
    enum="M+" "M-" "CCL" "M+ and/or M-"
    hint="The choosen critical point to initialize z"
    default=0
  endparam 
  
  param mode

    enum="Normal" "High"
    default=0
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"

    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
 
   param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
  
  
  param seed
    caption="Seed"
    default=(0,0)
    hint="Seed for Julia"
  endparam
     
  }


BrannerSpecialCubic2 {

init:
  int n=0
  int m1save=0
  int m2save=0
  float abs1=0
  float abs2=0
  complex z=0
  complex oldz=0
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(#pixel)
  float dd=imag(#pixel)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;a-real, a-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;a-real, b-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;a-real, b-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;a-imag, b-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;a-imag, b-imag
    IX=@areal
    IY=@breal
  ELSE                    ;b-real, b-imag
    IX=@areal
    IY=@aimag
  ENDIF
    
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t

      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
  
  IF @PlottedPlane==0      ;a-real, a-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;a-real, b-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;a-real, b-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;a-imag, b-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;a-imag, b-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;b-real, b-imag
    b=cc+dd*1i
  ENDIF


  if (@M==0)&&(@mode==0)
    z=1
  elseif (@M==1)&&(@mode==0)
    z=-1
  else
    z=1
    while (|z|<@bailout)&&(n<#maxiter)
      n=n+1
      z=a*(z*z*z-3*z)+b
    endwhile
    m1save=n
    abs1=|z|
    n=0
    z=-1
    while (|z|<@bailout)&&(n<#maxiter)
      n=n+1
      z=(b/4-a/4)*(z*z*z-3*z)+a/2+b/2
    endwhile
    m2save=n
    abs2=|z|

    if @mode==1
      if @M==0  ;M1
        if m1save==#maxiter
          z=1
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1
          else
            z=-1
          endif
        else
          z=1
        endif
        
      elseif @M==1  ;M2
        if m2save==#maxiter
          z=-1
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1
          else
            z=-1
          endif
        else 
          z=-1
        endif
        
      elseif (@M==2)
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=1
          else
            z=-1
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1
          else
            z=-1
          endif
        elseif m1save==#maxiter
          z=-1
        elseif m2save==#maxiter
          z=1
        else
          if m1save>m2save
            z=1
          else
            z=-1
          endif
        endif       
      elseif @M==3
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=1
          else
            z=-1
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1
          else
            z=-1
          endif
        elseif (m1save==#maxiter)
          z=1
        else
          z=-1
        endif
      endif     
    else
      if (@M==2)
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1<abs2
            z=1
          else
            z=-1
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save<m2save
            z=1
          else
            z=-1
          endif
        elseif m1save==#maxiter
          z=-1
        elseif m2save==#maxiter
          z=1
        else
          if m1save<m2save
            z=1
          else
            z=-1
          endif
        endif
      elseif @M==3
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=1
          else
            z=-1
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1
          else

            z=-1
          endif
        elseif (m1save==#maxiter)
          z=1
        else
          z=-1
        endif
      endif
    endif                 
  endif
   
loop:
  oldz=z
  z=(b/4-a/4)*(z*z*z-3*z)+a/2+b/2

    
bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="BrannerSpecialCubicJulia2"
  seed=#pixel
  PlottedPlane=PlottedPlane
  M=M
  mode=mode
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff
  bailout=bailout
  

  
default:
  title = "BrannerSpecialCubic2"
  periodicity=0
  method=multipass
  
  
  param PlottedPlane
    enum = "1.(a-real,a-imag)" "2.(a-real,b-real)" "3.(a-real,b-imag)" "4.(a-imag,b-real)"   \
           "5.(a-imag,b-imag)" "6.(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param M
    enum="M+" "M-" "CCL" "M+ and/or M-"
    hint="The choosen critical point to initialize z"
    default=0
  endparam 
  
  param mode
    enum="Normal" "High"
    default=0
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"
    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam

  
  param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
     
  }
  
  
BrannerSpecialCubicJulia2 {

init:
  complex z=#pixel
  complex oldz=0+0i
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(@seed)
  float dd=imag(@seed)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;a-real, a-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;a-real, b-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;a-real, b-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;a-imag, b-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;a-imag, b-imag
    IX=@areal
    IY=@breal
  ELSE                    ;b-real, b-imag
    IX=@areal
    IY=@aimag
  ENDIF
  
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t
      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
    
  
  IF @PlottedPlane==0      ;a-real, a-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;a-real, b-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;a-real, b-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;a-imag, b-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;a-imag, b-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;b-real, b-imag
    b=cc+dd*1i
  ENDIF

    
  
loop:
  oldz=z
  z=(b/4-a/4)*(z*z*z-3*z)+a/2+b/2

    
bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:

  type="BrannerSpecialCubic2"
  PlottedPlane=PlottedPlane
  M=M
  mode=mode
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff

  bailout=bailout
  

  
default:
  title = "BrannerSpecialCubicJulia2"
  periodicity=0
  method=multipass
  
  

  
  param PlottedPlane
    enum = "1.(a-real,a-imag)" "2.(a-real,b-real)" "3.(a-real,b-imag)" "4.(a-imag,b-real)"   \
           "5.(a-imag,b-imag)" "6.(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param M
    enum="M+" "M-" "CCL" "M+ and/or M-"
    hint="The choosen critical point to initialize z"
    default=0
  endparam 
  
  param mode

    enum="Normal" "High"
    default=0
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"

    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
 

   param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
  
  
  param seed
    caption="Seed"
    default=(2,0)
    hint="Seed for Julia"
  endparam
     
  }


EpsteinCubic2 {

init:
  int n=0
  int m1save=0
  int m2save=0
  float abs1=0
  float abs2=0
  complex z=0
  complex oldz=0
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(#pixel)
  float dd=imag(#pixel)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;a-real, a-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;a-real, b-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;a-real, b-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;a-imag, b-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;a-imag, b-imag
    IX=@areal
    IY=@breal
  ELSE                    ;b-real, b-imag
    IX=@areal
    IY=@aimag
  ENDIF
    
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t

      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
  
  IF @PlottedPlane==0      ;a-real, a-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;a-real, b-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;a-real, b-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;a-imag, b-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;a-imag, b-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;b-real, b-imag
    b=cc+dd*1i
  ENDIF


  if (@M==0)&&(@mode==0)
    z=1
  elseif (@M==1)&&(@mode==0)
    z=-1
  else
    z=1
    while (|z|<@bailout)&&(n<#maxiter)
      n=n+1
      z=a*(z*z*z-3*z)+b
    endwhile
    m1save=n
    abs1=|z|
    n=0
    z=-1
    while (|z|<@bailout)&&(n<#maxiter)
      n=n+1
      z=a*(z*z*z-3*z)+b
    endwhile
    m2save=n
    abs2=|z|

    if @mode==1
      if @M==0  ;M1
        if m1save==#maxiter
          z=1
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1
          else
            z=-1
          endif
        else
          z=1
        endif
        
      elseif @M==1  ;M2
        if m2save==#maxiter
          z=-1
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1
          else
            z=-1
          endif
        else 
          z=-1
        endif
        
      elseif (@M==2)
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=1
          else
            z=-1
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1
          else
            z=-1
          endif
        elseif m1save==#maxiter
          z=-1
        elseif m2save==#maxiter
          z=1
        else
          if m1save>m2save
            z=1
          else
            z=-1
          endif
        endif       
      elseif @M==3
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=1
          else
            z=-1
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1
          else
            z=-1
          endif
        elseif (m1save==#maxiter)
          z=1
        else
          z=-1
        endif
      endif     
    else
      if (@M==2)
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1<abs2
            z=1
          else
            z=-1
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save<m2save
            z=1
          else
            z=-1
          endif
        elseif m1save==#maxiter
          z=-1
        elseif m2save==#maxiter
          z=1
        else
          if m1save<m2save
            z=1
          else
            z=-1
          endif
        endif
      elseif @M==3
        if (m1save==#maxiter)&&(m2save==#maxiter)
          if abs1>abs2
            z=1
          else
            z=-1
          endif
        elseif (m1save<#maxiter)&&(m2save<#maxiter)
          if m1save>m2save
            z=1
          else

            z=-1
          endif
        elseif (m1save==#maxiter)
          z=1
        else
          z=-1
        endif
      endif
    endif                 
  endif
   
loop:
  oldz=z
  z=a*(z*z*z-3*z)+b

bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="EpsteinCubicJulia2"
  seed=#pixel
  PlottedPlane=PlottedPlane
  M=M
  mode=mode
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff
  bailout=bailout
  

  
default:
  title = "EpsteinCubic2"
  periodicity=0
  method=multipass
  
  
  param PlottedPlane
    enum = "1.(a-real,a-imag)" "2.(a-real,b-real)" "3.(a-real,b-imag)" "4.(a-imag,b-real)"   \
           "5.(a-imag,b-imag)" "6.(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param M
    enum="M+" "M-" "CCL" "M+ and/or M-"
    hint="The choosen critical point to initialize z"
    default=0
  endparam 
  
  param mode
    enum="Normal" "High"
    default=0
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"
    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam

  
  param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
     
  }
  
  
EpsteinCubicJulia2 {

init:
  complex z=#pixel
  complex oldz=0+0i
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(@seed)
  float dd=imag(@seed)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;a-real, a-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;a-real, b-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;a-real, b-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;a-imag, b-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;a-imag, b-imag
    IX=@areal
    IY=@breal
  ELSE                    ;b-real, b-imag
    IX=@areal
    IY=@aimag
  ENDIF
  
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t
      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
    
  
  IF @PlottedPlane==0      ;a-real, a-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;a-real, b-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;a-real, b-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;a-imag, b-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;a-imag, b-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;b-real, b-imag
    b=cc+dd*1i
  ENDIF

    
  
loop:
  oldz=z
  z=a*(z*z*z-3*z)+b

    
bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:

  type="EpsteinCubic2"
  PlottedPlane=PlottedPlane
  M=M
  mode=mode
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff
  bailout=bailout
  

default:
  title = "EpsteinCubicJulia2"
  periodicity=0
  method=multipass
  
  
  param PlottedPlane
    enum = "1.(a-real,a-imag)" "2.(a-real,b-real)" "3.(a-real,b-imag)" "4.(a-imag,b-real)"   \
           "5.(a-imag,b-imag)" "6.(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param M
    enum="M+" "M-" "CCL" "M+ and/or M-"
    hint="The choosen critical point to initialize z"
    default=0
  endparam 
  
  param mode

    enum="Normal" "High"
    default=0
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"

    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
 

   param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
  
  
  param seed
    caption="Seed"
    default=(0,0.4)
    hint="Seed for Julia"
  endparam
     
  }



CBAP {
init:
  t=#pixel
  t3=3*t
  t2=t*t
  a=(t2+1)/t3
  b=2*a*a*a+(t2-2)/t3
  aa3=a*a*3
  z=-a

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="CBAPjulia"
  seed=#pixel
  diff=diff
  bailout=bailout
  
default:
  title = "CBAP"
  periodicity=0
  method=multipass
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam

  param bailout
    caption="bailout"
    default=100.0
  endparam

}

CCAP {
init:
  a=#pixel
  b=2*a*a*a+a
  aa3=a*a*3
  z=-a

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))

switch:
  type="CCAPjulia"
  seed=#pixel
  diff=diff
  bailout=bailout
  
default:
  title = "CCAP"
  periodicity=0
  method=multipass
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    default=100.0
  endparam

}

CFAP {
init:
  a=#pixel
  b=2*a*a*a-2*a
  aa3=a*a*3
  z=-a

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="CFAPjulia"
  seed=#pixel
  diff=diff
  bailout=bailout
  
default:
  title = "CFAP"
  periodicity=0
  method=multipass
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    default=100.0
  endparam

}

CGAP {
init:
  a=#pixel
  b=2*a*a*a+1
  aa3=a*a*3
  z=-a

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="CGAPjulia"
  seed=#pixel
  diff=diff
  bailout=bailout
  
default:
  title = "CGAP"
  periodicity=0
  method=multipass
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    default=100.0
  endparam

}

SteveCubic {
init:
  t=#pixel
  a=(t*t*t-1)/(3*t*t)
  b=2*a*a*a-2*a
  aa3=a*a*3
  z=-a

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="SteveCubicJulia"
  seed=#pixel
  diff=diff
  bailout=bailout
  
default:
  title = "SteveCubic"
  periodicity=0
  method=multipass
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    default=100.0
  endparam

}


CBAPjulia {
init:
  t=@seed
  complex z=#pixel
  t3=3*t
  t2=t*t
  a=(t2+1)/t3
  b=2*a*a*a+(t2-2)/t3
  aa3=a*a*3

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
switch:
  type="CBAP"
  bailout=bailout
  
default:
  title = "CBAPjulia"
  periodicity=0
  method=multipass
  
  param seed
    caption="Seed"
    default=(0,1)
  endparam
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    default=100.0
  endparam

}


CCAPjulia {
init:
  a=@seed
  b=2*a*a*a+a
  aa3=a*a*3
  z=#pixel

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))

switch:
  type="CCAP"
  bailout=bailout
  
default:
  title = "CCAPjulia"
  periodicity=0
  method=multipass
  
  param seed
    caption="Seed"
    default=(0,0)
  endparam
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    default=100.0
  endparam

}


CFAPjulia {

init:
  a=@seed
  b=2*a*a*a-2*a
  aa3=a*a*3
  z=#pixel

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="CFAP"
  bailout=bailout
  
default:
  title = "CFAPjulia"
  periodicity=0
  method=multipass
  
  param seed
    caption="Seed"
    default=(0,0)
  endparam
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    default=100.0
  endparam

}


CGAPjulia {
init:
  a=@seed
  b=2*a*a*a+1
  aa3=a*a*3
  z=#pixel

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="CGAP"
  bailout=bailout
  
default:
  title = "CGAPjulia"
  periodicity=0
  method=multipass
  
  param seed
    caption="Seed"
    default=(-0.5,0)
  endparam
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    default=100.0
  endparam

}


SteveCubicJulia {
init:
  t=@seed
  a=(t*t*t-1)/(3*t*t)
  b=2*a*a*a-2*a
  aa3=a*a*3
  z=#pixel

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="SteveCubic"
  bailout=bailout
  
default:
  title = "SteveCubicJulia"
  periodicity=0
  method=multipass
  
  param seed
    caption="Seed"
    default=(0.75,0)
  endparam
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam

  param bailout
    caption="bailout"
    default=100.0
  endparam

}

HomerCubic {
init:
  a=#pixel
  b=a
  aa3=a*a*3
  IF @M==false
    z=a
  ELSE 
    z=-a
  ENDIF

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))

switch:
  type="HomerCubicJulia"
  seed=#pixel
  diff=diff
  bailout=bailout
  
default:
  title = "HomerCubic"
  periodicity=0
  method=multipass
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
param bailout
  caption="bailout"
  default=100.0
endparam
  
param M
  caption="-a"
  hint="Sets the sign of the initial parameter a. If set it will be negative."
  default=false
endparam

}

HomerCubicJulia {
init:
  a=@seed
  b=a
  aa3=a*a*3
  z=#pixel

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))

switch:
  type="HomerCubic"
  bailout=bailout
  
default:
  title = "HomerCubicJulia"
  periodicity=0
  method=multipass
  
param seed
  caption="Seed"
  default=(0,0)
endparam

 param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
param bailout
  caption="bailout"
  default=100.0
endparam

}

MysticCubic {
init:
  a=#pixel
  b=a-2*a*a*a
  aa3=a*a*3
  z=a
loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))

switch:
  type="MysticCubicJulia"
  seed=#pixel
  diff=diff
  bailout=bailout
  
default:
  title = "MysticCubic"
  periodicity=0
  method=multipass
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    default=100.0
  endparam
  
}

MysticCubicJulia {
init:
  a=@seed
    b=a-2*a*a*a
    aa3=a*a*3
  z=#pixel

loop:
  oldz=z
  z=z*z*z-aa3*z+b
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))

switch:
  type="MysticCubic"
  bailout=bailout
  
default:
  title = "MysticCubicJulia"
  periodicity=0
  method=multipass
  
param seed
  caption="Seed"
  default=(0,0)
endparam

param diff
    caption="Diff-Bailout"
    default=false
endparam
  
param bailout
  caption="bailout"
  default=100.0
endparam

}


Article15 {
;NOTE: This sub-module is written only for 
;pedagogical reasons and does not contribute 
;any new forms that can not be brought out 
;from the standard Mandelbrot formula in 
;Ultra Fractal."Article15" refers to an 
;article in the Chaotic series.

init:
  z=@start
  p=@parameter
  c=#pixel

loop:
  z=z^2+p*z+c

bailout:
  |z|<@bailout

default:
  title = "Article15"
  center = (-0.75,0)
  
param start
  caption = "Starting point"
  default = (0,0)
endparam

param parameter
  caption = "z-coefficient"
  default = (1,0)
endparam

param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100
  endparam

}


Multicorns {

init:
  z=@start
  d=@exponent
  c=#pixel

loop:
  oldz=z
  z=conj(z)^d+c

bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
   switch:
  type="MulticornsJulia"
  seed=#pixel
  exponent=exponent
  diff=diff
  bailout=bailout

default:
  title = "Multicorns"
  center = (0,0)
  
param exponent
  caption = "exponent"
  default = (2,0)
endparam

param start
  caption = "Starting point"
  default = (0,0)
endparam

param diff
    caption="Diff-Bailout"
    default=false
endparam


param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100
  endparam
  

}

MulticornsJulia {
init:

  d=@exponent
  c=@seed
  z=#pixel

loop:
  oldz=z
  z=conj(z)^d+c
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))

switch:
  type="Multicorns"
  bailout=bailout
  
default:
  title = "MulticornsJulia"
  periodicity=0
  method=multipass
  
param seed
  caption="Seed"
  default=(0,0)
endparam

param exponent
    caption="exponent"
    default = (2,0)
 endparam
 
param diff
    caption="Diff-Bailout"
    default=false
endparam
  
param bailout
  caption="bailout"
  default=100.0
endparam

}

Compasses {

init:
  a=#pixel
  z=a
  d=@exponent
  
loop:
  oldz=z
  z=z^d-d*a^(d-1)*z

bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))

  
switch:
  type="CompassJulia"
  seed=#pixel
  exponent=exponent
  diff=diff
  bailout=bailout

default:
  title = "Compasses"
  center = (0,0)
  
param exponent
  caption = "exponent"
  default = (3,0)
endparam

param diff
    caption="Diff-Bailout"
    default=false
endparam

param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100
  endparam

}

CompassJulia {
init:

  d=@exponent
  a=@seed
  z=#pixel

loop:
  oldz=z
  z=z^d-d*a^(d-1)*z
bailout:
    (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))

switch:
  type="Compasses"
  bailout=bailout
  
default:
  title = "CompassJulia"
  periodicity=0
  method=multipass
  
param seed
  caption="Seed"
  default=(0,0)
endparam

param exponent
    caption="exponent"
    default = (3,0)
endparam
  
param diff
    caption="Diff-Bailout"
    default=false
endparam

param bailout
  caption="bailout"
  default=100.0
endparam

}

DeformedMandelbrot {

init:
  complex z=0
  complex oldz=0
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(#pixel)
  float dd=imag(#pixel)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;a-real, a-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;a-real, b-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;a-real, b-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;a-imag, b-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;a-imag, b-imag
    IX=@areal
    IY=@breal
  ELSE                    ;b-real, b-imag
    IX=@areal
    IY=@aimag
  ENDIF
    
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t

      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
  
  IF @PlottedPlane==0      ;a-real, a-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;a-real, b-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;a-real, b-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;a-imag, b-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;a-imag, b-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;b-real, b-imag
    b=cc+dd*1i
  ENDIF


  z=a
      
  loop:
    oldz=z
    z=z*z-2*a*z+b
    
bailout:
(!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="DeformedJulia"
  seed=#pixel
  PlottedPlane=PlottedPlane
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff
  bailout=bailout
  

  
default:
  title = "DeformedMandelbrot"
  periodicity=2
  method=multipass
  
  
  param PlottedPlane
    enum = "1.(a-real,a-imag)" "2.(a-real,b-real)" "3.(a-real,b-imag)" "4.(a-imag,b-real)"   \
           "5.(a-imag,b-imag)" "6.(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"
    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam

  
  param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
     
  }
  
  
DeformedJulia {

init:
  complex z=#pixel
  complex oldz=0+0i
  float t=0
  float aa=0
  complex a=0+0i
  complex b=0+0i
  float cc=real(@seed)
  float dd=imag(@seed)
  float IX=0
  float IY=0
  float resIX=0
  float resIY=0
  float yrot=0
  float xrot=0
  float zrot=0
  
  IF @PlottedPlane==0     ;a-real, a-imag
    IX=@breal
    IY=@bimag
  ELSEIF @PlottedPlane==1 ;a-real, b-real
    IX=@aimag
    IY=@bimag
  ELSEIF @PlottedPlane==2 ;a-real, b-imag
    IX=@aimag
    IY=@breal
  ELSEIF @PlottedPlane==3 ;a-imag, b-real
    IX=@areal
    IY=@bimag
  ELSEIF @PlottedPlane==4 ;a-imag, b-imag
    IX=@areal
    IY=@breal
  ELSE                    ;b-real, b-imag
    IX=@areal
    IY=@aimag
  ENDIF
  
  IF @LocalRot==true
    cc=cc-real(#center)
    dd=dd-imag(#center)
    resIX=IX
    resIY=IY
    IX=0
    IY=0
  ENDIF

    IF @yrot!=0  ;yrot-z
      yrot=(@yrot%360)*pi/180
      t=cabs(cc+IX*1i)      
      aa=atan2(cc+IX*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IX=0
      ELSEIF aa==pi/2
        cc=0
        IX=t
      ELSEIF aa==-pi/2
        cc=0
        IX=-t
      ELSE
        cc=t*cos(aa)
        IX=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrot!=0   ;xrot-z
      xrot=(@xrot%360)*pi/180
      t=cabs(IX+dd*1i)     
      aa=atan2(IX+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IX=-t
        dd=0
      ELSEIF aa==pi/2
        IX=0
        dd=t
      ELSEIF aa==-pi/2
        IX=0
        dd=-t
      ELSE
        IX=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @zrot!=0   ;zrot-xy
      zrot=(@zrot%360)*pi/180
      t=cabs(cc+dd*1i)
      aa=atan2(cc+dd*1i)     
      aa=zrot+aa
      IF abs(aa)==pi
        cc=-t
        dd=0
      ELSEIF aa==pi/2
        cc=0
        dd=t
      ELSEIF aa==-pi/2
        cc=0
        dd=-t
      ELSE
        cc=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
      

    IF @yrott!=0   ;yrot-t
      yrot=(@yrott%360)*pi/180
      t=cabs(cc+IY*1i)      
      aa=atan2(cc+IY*1i)
      aa=yrot+aa
      IF abs(aa)==pi
        cc=-t
        IY=0
      ELSEIF aa==pi/2
        cc=0
        IY=t
      ELSEIF aa==-pi/2
        cc=0
        IY=-t
      ELSE
        cc=t*cos(aa)
        IY=t*sin(aa)
      ENDIF
    ENDIF
      
    IF @xrott!=0   ;xrot-t
      xrot=(@xrott%360)*pi/180
      t=cabs(IY+dd*1i)     
      aa=atan2(IY+dd*1i)
      aa=xrot+aa
      IF abs(aa)==pi
        IY=-t
        dd=0
      ELSEIF aa==pi/2
        IY=0
        dd=t
      ELSEIF aa==-pi/2
        IY=0
        dd=-t
      ELSE
        IY=t*cos(aa)
        dd=t*sin(aa)
      ENDIF
    ENDIF
    
  IF @LocalRot==true
    cc=cc+real(#center)
    dd=dd+imag(#center)
    IX=IX+resIX
    IY=IY+resIY
  ENDIF
    
  
  IF @PlottedPlane==0      ;a-real, a-imag
    a=cc+dd*1i
    b=IX+IY*1i
  ELSEIF @PlottedPlane==1  ;a-real, b-real
    a=cc+IX*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==2  ;a-real, b-imag
    a=cc+IX*1i
    b=IY+dd*1i
  ELSEIF @PlottedPlane==3  ;a-imag, b-real
    a=IX+cc*1i
    b=dd+IY*1i
  ELSEIF @PlottedPlane==4  ;a-imag, b-imag
    a=IX+cc*1i
    b=IY+dd*1i
  ELSE
    a=IX+IY*1i             ;b-real, b-imag
    b=cc+dd*1i
  ENDIF

    
  
loop:
  oldz=z
  z=z*z-2*a*z+b

    
bailout:
  (!@diff && (|z|<@bailout))||(@diff && (|z-oldz|>1/@bailout)&&(|z|<@bailout))
  
switch:
  type="DeformedMandelbrot"
  PlottedPlane=PlottedPlane
  areal=areal
  aimag=aimag
  breal=breal
  bimag=bimag
  xrot=xrot
  yrot=yrot
  xrott=xrott
  yrott=yrott
  zrot=zrot
  LocalRot=LocalRot
  diff=diff

  bailout=bailout
  

default:
  title = "DeformedJulia"
  periodicity=2
  method=multipass
  
   param PlottedPlane
    enum = "1.(a-real,a-imag)" "2.(a-real,b-real)" "3.(a-real,b-imag)" "4.(a-imag,b-real)"   \
           "5.(a-imag,b-imag)" "6.(b-real,b-imag)"
    default=0
    hint="The axis that will be plotted."
  endparam
  
  param areal
    caption=" a-real "
    hint="Value for a-real when a-real is constant (not plotted)."
    default=0.0
  endparam
  
  param aimag
    caption=" a-imag "
    hint="Value for a-imag when a-imag is constant (not plotted)."
    default=0.0
  endparam
  
   param breal
    caption=" b-real "
    hint="Value for b-real when b-real is constant (not plotted)."
    default=0.0
  endparam
  
   param bimag
    caption=" b-imag "
    hint="Value for b-imag when b-imag is constant (not plotted)."
    default=0.0
  endparam
  
 
 param xrot
    caption="x-rotz"
    hint= "Rotates yz-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrot
    caption="y-rotz"
    hint= "Rotates xz-plane in degrees around the y-axis."
    default=0.0
 endparam
 
 param xrott
    caption="x-rott"
    hint= "Rotates yt-plane in degrees around the x-axes."
    default=0.0
 endparam
  
 param yrott
    caption="y-rott"

    hint= "Rotates xt-plane in degrees around the y-axis."
    default=0.0
 endparam
 
  
  param zrot
    caption="z-rot"
    hint= "Rotating xy-plane in degrees around the z-axis."
    default=0.0
  endparam
  
 

   param LocalRot
    caption="Local Rotation"
    hint="Enables Local Rotation."
    default=false
  endparam
  
  
  param diff
    caption="Diff-Bailout"
    default=false
  endparam
  
  param bailout
    caption="bailout"
    hint="Value for bailout"
    default=100.0
  endparam
  
  
  param seed
    caption="Seed"
    default=(0,0)
    hint="Seed for Julia"
  endparam
     
  }