Assymetroscope1 {
;
; Derived from original Kaleidoscope written by Damien M. Jones.
; Symmetrical forms can still be obtained
; However assymetrical mappings of variable distrtion can be achieved
; Low values for "divisor' produce more assymetry - use with different angles
; Evan Bayliss October 2023
transform:
  float r2 = 0.0
  float d = 0.0
  complex r = (0,1) ^ (@angle/90)	; complex rotation vector
  complex c = @symcenter		; assume symmetry center is fixed
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  complex z2 = #pixel - c		; get coordinate relative to symcenter

  ; convert z2 into angle and distance
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    If @extrastep == 0
      r2 = (r2 + #pi * 2)  ; rotate 360 degrees
    else
      r2 = (r2 + #pi * 2) * |@rfunc(r)| ; allows for assymetry
    endif
  ENDIF
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ;elseif (r2 <= #pi/@symorder)
      ; r2 = (#pi*2/@symorder - r2) * (r2*#pi) + |@rfunc(r)|
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    finx = #pixel/@num
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c + finx	; compute point
  ENDIF

default:
  title = "Assymetroscope 1"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order/ Axes of Assymetry"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam
  param extrastep
  caption = "Choice of r2 calculation"
  enum = "original" "modified with function"
  default = 0
  endparam

  func rfunc
  caption = "r variable function"
  default = sin()
  visible = @extrastep == 1
  endfunc

  complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
  param centermove
    caption = "Use Screen Center"
    default = false
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam

  param num
  Caption = "Divisor for init #pixel"
  default = 1000.0
  endparam
}


   Assymetroscope2 {
;
; Derived from original Kaleidoscope written by Damien M. Jones.
; Symmetrical forms can still be obtained
; However assymetrical mappings of variable distrtion can be achieved
; Low values for "divisor' produce more assymetry - use with different angles
; Evan Bayliss October 2023
transform:
  float r2 = 0.0
  float d = 0.0
  complex r = (0,1) ^ (@angle/90)	; complex rotation vector
  complex c = @symcenter		; assume symmetry center is fixed
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  complex z2 = #pixel - c		; get coordinate relative to symcenter

  ; convert z2 into angle and distance
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    If @extrastep == 0
      r2 = (r2 + #pi * 2)  ; rotate 360 degrees
    else
      r2 = (r2 + #pi * 2) * |@rfunc(r)| ; allows for assymetry
    endif
  ENDIF
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ;elseif (r2 <= #pi/@symorder)
      ; r2 = (#pi*2/@symorder - r2) * (r2*#pi) + |@rfunc(r)|
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    finx = #pixel/@num
    If @pix == 0
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c + finx	; compute point
    Elseif @pix == 1
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c + finx + #pixel
    elseif @pix == 2
     #pixel = (cos(r2)*d + flip(@finfunc(r2)*d))/r + c + finx
    elseif @pix ==3
     #pixel = (cos(r2)*d + flip(@finfunc(r2)*d))
    Endif
  ENDIF

default:
  title = "Assymetroscope 2"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order/ Axes of Assymetry"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam
  param extrastep
  caption = "Choice of r2 calculation"
  enum = "original" "modified with function"
  default = 0
  endparam

  func rfunc
  caption = "r variable function"
  default = sin()
  visible = @extrastep == 1
  endfunc

  complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
  param centermove
    caption = "Use Screen Center"
    default = false
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam

  param num
  Caption = "Divisor for init #pixel"
  default = 1000.0
  endparam

  param pix
  caption = "Choice of final pixel formula"
  enum ="(cos(r2)*d + flip(sin(r2)*d))/r + c + finx" \
  "(cos(r2)*d + flip(sin(r2)*d))/r + c + finx + #pixel" \
  "(cos(r2)*d + flip(@finfunc(r2)*d))/r + c + finx" \
  "(cos(r2)*d + flip(@finfunc(r2)*d))"
  default = 0
  endparam

  func finfunc
  caption = "Final pixel calc function"
  default = sin()
  visible = @pix == 2 || @pix == 3
  endfunc

}


KaleidoscopeEBver3 {
;
; Kaleidoscope transformation. Can be used to simulate many
; different kinds of symmetry.
;
; Original written by Damien M. Jones.
; Modified Evan Bayliss Sept 2021
; There is now a choice of formulae for #pixel
; Combining different formulae and angles can produce interesting effects
; This is most complex version - not all choices may work with a particular fractal formula
;
transform:
  float r2 = 0.0
  float d = 0.0
  complex r = (0,1) ^ (@angle/90)	; complex rotation vector
  complex c = @symcenter		; assume symmetry center is fixed
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  complex z2 = #pixel - c		; get coordinate relative to symcenter

  ; convert z2 into angle and distance
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    r2 = r2 + #pi * 2; rotate 360 degrees
  ENDIF
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/(#pi)/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    if @choice == 0
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c 	; compute point
    elseif @choice == 1
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c  + real(@rfunc(r))
    elseif @choice == 2
    #pixel = (cos(r2)*d + flip(@rfunc2(r2)*d))/r + c  + real(@rfunc(r))
    elseif @choice == 3
    #pixel = (cos(r2)*d + flip(@rfunc2(r2)*d))/r + flip((imag(@rfunc(r)*d)))/r  + c
    elseif @choice == 4
    #pixel = (@r2num*r2) + (cos(r2)*d + flip(sin(r2)*d))/r + c 	; compute point
    elseif @choice == 5
    #pixel = (real(z2)/flip(imag(z2))) + (cos(r2)*d + flip(sin(r2)*d))/r + c
    elseif @choice == 6
    float rf = real(@rfunc2(z2))
    float ff = real(flip(imag(@rfunc(z2))))
    #pixel = rf/ff + (cos(r2)*d + flip(sin(r2)*d))/r + c
    ENDIF
  endif

default:
  title = "Kaleidoscope EB ver 3"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam
  complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
 int param choice
 caption = "Choice of index formula"
 enum  = "Standard" "Standard + real(rfunc(r))" "Standard with flip(rfunc(r)) + real(rfunc(r))" "Double flip formula" \
  "Standard formula + r2num*r2" "Standard formula + real(z2)/flip(imag(z2))" "Standard formula + real(rfunc2(z2))/flip(imag(rfunc(z2)))"
 default = 0
 endparam

float param r2num
caption = "Number to multiply r2"
default = 0
endparam
 
func rfunc
 caption = "Function for r"
 default = abs()
 endfunc

 func rfunc2
 caption = "Function for flip(rfunc2(r2)*d))/r"
 default = sin()
 endfunc

 param centermove
    caption = "Use Screen Center"
    default = false
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam
}

KaleidoscopeEBver {
;
; Kaleidoscope transformation. Can be used to simulate many
; different kinds of symmetry.
;
; Original written by Damien M. Jones.
; Modified Evan Bayliss Sept 2021
; There is now a choice of formulae for #pixel
; Combining different formulae and angles can produce interesting effects
; Version 3 is the most complex
;
transform:
  float r2 = 0.0
  float d = 0.0
  complex r = (0,1) ^ (@angle/90)	; complex rotation vector
  complex c = @symcenter		; assume symmetry center is fixed
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  complex z2 = #pixel - c		; get coordinate relative to symcenter

  ; convert z2 into angle and distance  
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    r2 = r2 + #pi * 2; rotate 360 degrees
  ENDIF
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/(#pi)/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    if @choice == 0
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c 	; compute point
    elseif @choice == 1
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c  + real(@rfunc(r))
    elseif @choice == 2
    #pixel = (cos(r2)*d + flip(@rfunc2(r2)*d))/r + c  + real(@rfunc(r))
    ENDIF
  endif

default:
  title = "Kaleidoscope EB ver 1"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam
  complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
 int param choice
 caption = "Choice of index formula"
 enum  = "Standard" "Standard + real(rfunc(r))" "Standard with flip(rfunc(r)) + real(rfunc(r))"
 default = 0
 endparam

 func rfunc
 caption = "Function for r"
 default = abs()
 endfunc

 func rfunc2
 caption = "Function for flip(rfunc2(r2)*d))/r"
 default = sin()
 endfunc
 
 param centermove
    caption = "Use Screen Center"
    default = false
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam
}

KaleidoscopeEBver2 {
;
; Kaleidoscope transformation. Can be used to simulate many
; different kinds of symmetry.
;
; Original written by Damien M. Jones.
; Modified Evan Bayliss Sept 2021
; There is now a choice of formulae for #pixel
; Combining different formulae and angles can produce interesting effects
; Version 3 is the most complex
;
transform:
  float r2 = 0.0
  float d = 0.0
  complex r = (0,1) ^ (@angle/90)	; complex rotation vector
  complex c = @symcenter		; assume symmetry center is fixed
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  complex z2 = #pixel - c		; get coordinate relative to symcenter

  ; convert z2 into angle and distance
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    r2 = r2 + #pi * 2; rotate 360 degrees
  ENDIF
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/(#pi)/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    if @choice == 0
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c 	; compute point
    elseif @choice == 1
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c  + real(@rfunc(r))
    elseif @choice == 2
    #pixel = (cos(r2)*d + flip(@rfunc2(r2)*d))/r + c  + real(@rfunc(r))
    elseif @choice == 3
    #pixel = (cos(r2)*d + flip(@rfunc2(r2)*d))/r + flip((imag(@rfunc(r)*d)))/r  + c
    ENDIF
  endif

default:
  title = "Kaleidoscope EB ver 2"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam
  complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
 int param choice
 caption = "Choice of index formula"
 enum  = "Standard" "Standard + real(rfunc(r))" "Standard with flip(rfunc(r)) + real(rfunc(r))" "Double flip formula"
 default = 0
 endparam

 func rfunc
 caption = "Function for r"
 default = abs()
 endfunc

 func rfunc2
 caption = "Function for flip(rfunc2(r2)*d))/r"
 default = sin()
 endfunc

 param centermove
    caption = "Use Screen Center"
    default = false
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam
}

KaleidoscopeEBver9 {
;
; Kaleidoscope transformation.
;
; Original written by Damien M. Jones.
; Modified Evan Bayliss Oct 2021
; Incorporates Mandelbrot formula as one of the choices
; The result straddles both mapping and formula especiall for "inside" sections
;
transform:
  float r2 = 0.0
  float d = 0.0
  complex r = (0,1) ^ (@angle/90)	; complex rotation vector
  complex c = @symcenter		; assume symmetry center is fixed
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  if @iterchoice == 0
  complex z2 = #pixel - c		; get coordinate relative to symcenter
  else
  complex z2 = #pixel - c
          while iter <= @itnum
          iter = iter + 1
          z2 = z2^@power + #pixel ; Mandelbrot formula
          endwhile
  endif
  ; convert z2 into angle and distance
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    r2 = r2 + #pi * 2; rotate 360 degrees
  ENDIF
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c	; compute point
  ENDIF

default:
  title = "Kaleidoscope EB ver 9"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam
  int param iterchoice
  caption = "Formula for z2"
  enum = "Standard #pixel - c" "z2 = z2^@power + #pixel"
  default = 0
  endparam

  float param power
  caption = "Power value for z2"
  default = 2
  endparam

  int param itnum
  caption = "Iteration number"
  default =1
  endparam

  complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
  param centermove
    caption = "Use Screen Center"
    default = false
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam
}

KPJ1 {
;
; Kaleidoscope mixed with Popcorn Julia
; Evan Bayliss Oct 2021
;
; Original Kaleidoscope Written by Damien M. Jones.
;
transform:
  float r2 = 0.0
  float d = 0.0
  complex r = (0,1) ^ (@angle/90)	; complex rotation vector
  complex c = @symcenter		; assume symmetry center is fixed
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  if @iterchoice == 0
  complex z2 = #pixel - c		; get coordinate relative to symcenter
  else
  complex z2 = #pixel - c
    while iter <= @itnum || |z2| > @bailout
    x = real(z2), y = imag(z2)
    iter = iter +1
    newx = x - @h*fn1((y) + fn2(@k*y)) ; Popcorn Julia (PJ) formula
    newy = y - @h*fn1((x) + fn2(@k*x))
    x = newx, y = newy
    z2 = fn3(x) + fn4(y) ; end PJ
    endwhile
  endif

  ; convert z2 into angle and distance
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    r2 = r2 + #pi * 2; rotate 360 degrees
  ENDIF
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c	; compute point
  ENDIF

default:
  title = "KPJ 1"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam
  int param iterchoice
  caption = "Formula for z2"
  enum = "Standard #pixel - c" "Popcorn Julia formula (PJ)"
  default = 0
  endparam

  float param power
  caption = "Power value for z2"
  default = 2
  endparam

  int param itnum
  caption = "Iteration number"
  hint = "Works best with low iteration values"
  default =1
  endparam

  param h
    caption = "PJ H value"
    default = 0.05
  endparam
  param k
    caption = "PJ K value"
    default = 3.0
  endparam
  param bailout ; does not work well with low values
    caption = "PJ Bailout value"
    default = 1e18
  endparam
  func fn1
    caption = "PJ 1st Function"
    default = sin()
  endfunc
  func fn2
    caption = "PJ 2nd Function"
    default = tan()
  endfunc
  func fn3
    caption = "PJ 3rd Function"
    default = ident()

  endfunc
  func fn4
    caption = "PJ 4th Function"
    default = flip()
  endfunc
  complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
  param centermove
    caption = "Use Screen Center"
    default = false
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam
}
 KAGT1 {
;
; Kaleidoscope mixed with elements from Otto Magus AltGnarlaThotep
; Evan Bayliss Oct 2021
;
; Original Kaleidoscope Written by Damien M. Jones.
;
transform:
  float r2 = 0.0
  float d = 0.0
  complex r = (0,1) ^ (@angle/90)	; complex rotation vector
  complex c = @symcenter		; assume symmetry center is fixed
  int i2 = 0
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  if @iterchoice == 0
  complex z2 = #pixel - c		; get coordinate relative to symcenter
  else
  complex z2 = #pixel - c
    while iter <= @itnum || |z2| > @bailout
    float x = real(z2), float y = imag(z2) ; AltGnarlaThotep (AGT) formula incorporated
    iter = iter +1
    float b = x^2+ y^2
    x=x/b*@p1+real(@p2/10)
    y=y/b*@p1+imag(@p2/10)
    a=x
    if i2==0
    x=x-@p3*real(sin(y+sin(@p4*(y+sin(@p5*y)))))/10
    y=y+@p3*real(sin(a+sin(@p4*(a+sin(@p5*a)))))/10
    i2=i2+1
    else
    x=x-@p6*real(tanh(y+cos(@p7*(y+sin(@p8*y)))))/10
    y=y+@p6*real(tanh(a+cos(@p7*(a+sin(@p8*a)))))/10
    i2=0
    endif
    z2=(fn2(x+flip(y)))^@power+@p9
    z2=51*z2/50 ; end of AGT portion
    endwhile
  endif




  ; convert z2 into angle and distance
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    r2 = r2 + #pi * 2; rotate 360 degrees
  ENDIF
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c	; compute point
  ENDIF

default:
  title = "KAGT 1"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam
  int param iterchoice
  caption = "Formula for z2"
  enum = "Standard #pixel - c" "Alt Gnarlathotep formula (AGT)"
  default = 0
  endparam

  int param itnum
  caption = "Iteration number"
  default = 1
  endparam

   param p1
    caption = "AGT 1st value"
    default = 1.0
  endparam

   param p2
    caption = "AGT 2nd value"
    default = (0,0)
  endparam

   param p3
    caption = "AGT 3rd value"
    default = 0.3
  endparam

   param p4
    caption = "AGT 4th value"
    default = 5.0
  endparam

   param p5
    caption = "AGT 5th value"
    default = 2.0
  endparam

   param p6
    caption = "AGT 6th value"
    default = 0.3
  endparam

 param p7
    caption = "AGT 7th value"
    default = 5.0
  endparam

  param p8
    caption = "AGT 8th value"
    default = 2.0
  endparam

  func fn2
    caption = "AGT Function"
    default = ident()
  endfunc

  param p9
    caption = "AGT 9th (post function) value"
    default = (0,0)
  endparam
  float param power
  caption = "Power value for z2"
  default = 2
  endparam

  param bailout
    caption = "AGT Bailout value"
    default = 1e18
  endparam

  complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
  param centermove
    caption = "Use Screen Center"
    default = false
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam
}

KaleidoscopeEBver3a {
;
; Original written by Damien M. Jones. Modifies Evan Bayliss September 2021
;
transform:
  float r2 = 0.0
  float d = 0.0
  complex r = (0,1) ^ (@angle/90)	; complex rotation vector
  complex c = @symcenter		; assume symmetry center is fixed
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  if @z2choice == 0
  complex z2 = #pixel - c		; get coordinate relative to symcenter
  else
      complex z2 = #pixel -c
      if real(#pixel) <= real(c) && imag(#pixel) <= imag(c)
      z2 = @z2func(z2) + z2
      elseif real(#pixel) <= real(c) && imag(#pixel) >imag(c)
      z2 = -@z2func(z2) + z2
      elseif real(#pixel) > real(c) && imag(#pixel) <= imag(c)
      z2 = @z2func(z2) - z2
      elseif real(#pixel) > real(c) && imag(#pixel) > imag(c)
      z2 = -(@z2func(z2) + z2)
      endif
   endif

  ; convert z2 into angle and distance
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    r2 = r2 + #pi * 2; rotate 360 degrees
  ENDIF
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/(#pi)/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    if @choice == 0
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c 	; compute point
    elseif @choice == 1
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c  + real(@rfunc(r))
    elseif @choice == 2
    #pixel = (cos(r2)*d + flip(@rfunc2(r2)*d))/r + c  + real(@rfunc(r))
    elseif @choice == 3
    #pixel = (cos(r2)*d + flip(@rfunc2(r2)*d))/r + flip((imag(@rfunc(r)*d)))/r  + c
    elseif @choice == 4
    #pixel = (@r2num*r2) + (cos(r2)*d + flip(sin(r2)*d))/r + c 	; compute point
    elseif @choice == 5
    #pixel = (real(z2)/flip(imag(z2))) + (cos(r2)*d + flip(sin(r2)*d))/r + c
    elseif @choice == 6
    float rf = real(@rfunc2(z2))
    float ff = real(flip(imag(@rfunc(z2))))
    #pixel = rf/ff + (cos(r2)*d + flip(sin(r2)*d))/r + c
    ENDIF
  endif

default:
  title = "Kaleidoscope EB ver 3a"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam
  complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
 int param z2choice
 caption = "Choose z2 calculation method"
 enum = "Standard" "Variation with functions"
 default = 0
 endparam

 func z2func
 caption = "Function for z2"
 default =abs()
 endfunc

 int param choice
 caption = "Choice of index formula"
 enum  = "Standard" "Standard + real(rfunc(r))" "Standard with flip(rfunc(r)) + real(rfunc(r))" "Double flip formula" \
  "Standard formula + r2num*r2" "Standard formula + real(z2)/flip(imag(z2))" "Standard formula + real(rfunc2(z2))/flip(imag(rfunc(z2)))"
 default = 0
 endparam

float param r2num
caption = "Number to multiply r2"
default = 0
endparam

func rfunc
 caption = "Function for r"
 default = abs()
 endfunc

 func rfunc2
 caption = "Function for flip(rfunc2(r2)*d))/r"
 default = sin()
 endfunc

 param centermove
    caption = "Use Screen Center"
    default = false
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam
}

KNewtt1 {
;
; Kaleidoscope mixed with Newton
; Evan Bayliss Oct 2021
;
; Original Kaleidoscope Written by Damien M. Jones.
;
transform:
  float r2 = 0.0
  float d = 0.0
  int iter = 0
  complex r = (0,1) ^ (@angle/90)	; complex rotation vector
  complex c = @symcenter		; assume symmetry center is fixed
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  if @iterchoice == 0
  complex z2 = #pixel - c		; get coordinate relative to symcenter
  else
  complex z2 = #pixel - c
    zold =z2
    while iter <= @itnum ;|| |z2 - zold| < @bailout
     iter = iter +1
      zold = z2
    z2 = ((@p1 - 1) * z2^@power + @root) / (@p1 * z2 ^ (@p1 - 1))
    endwhile
  endif

  ; convert z2 into angle and distance
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    r2 = r2 + #pi * 2; rotate 360 degrees
  ENDIF
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c	; compute point
  ENDIF

default:
  title = "KNewt 1"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam
  int param iterchoice
  caption = "Formula for z2"
  enum = "Standard #pixel - c" "Newton Formula"
  default = 0
  endparam

  float param power
  caption = "Power value for z2"
  default = 2
  endparam

  int param itnum
  caption = "Iteration number"
  ;hint = "Works best with low iteration values"
  default =1
  endparam

  param p1
    caption = "Newton p1 (exponent) value"
    default = (3,0)
  endparam

 param root
  caption = "Root value for Newton"
  default =(1,0)
  endparam

   param bailout
    caption = "PJ Bailout value"
    default = 0.00001
  endparam

  complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
  param centermove
    caption = "Use Screen Center"
    default = false
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam
}

KaleidoscopeEBver10b {
;
; Kaleidoscope transformation. Can be used to simulate many
; different kinds of symmetry.
;
; Original ver written by Damien M. Jones.
; Modified Evan Bayliss Nov 2021 and Jan 2022
; Different rotation vector formulae
;
transform:
  float r2 = 0.0
  float d = 0.0
  float xpix = real(#screenpixel)
  float ypix = imag(#screenpixel)
  float xc =real(#center)
  float yc = real(flip(#center))
  tanang = (xpix - xc)/(ypix - yc)
  tanang2 = xpix/ypix
  if @choice == 0
  complex r = (0,1) ^ (@angle/90) ; complex rotation vector
  elseif @choice == 1
  complex r = (0,1) ^ (@angle + |#pixel|/90)	; complex rotation vector
  elseif @choice == 2
  complex r = (0,1) ^ ((@angle*tanang)/90) ; complex rotation vector
  elseif @choice == 3
  complex r = (0,1) ^ ((@angle + atan2(tanang))/90) ; complex rotation vector
  elseif @choice == 4
  complex r = (0,1) ^ (@angle/90) + atan2(tanang)
  elseif @choice == 5
  complex r = @rnum ^ (@angle/90)
  elseif @choice == 6
  complex r = @rnum ^ (@angle + atan2(tanang2))/90
  elseif @choice == 7
  complex r = @rnum ^ (atan2(#pixel))
  endif

  complex c = @symcenter		; assume symmetry center is fixed
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  complex z2 = #pixel - c		; get coordinate relative to symcenter

  ; convert z2 into angle and distance
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    r2 = r2 + #pi * 2; rotate 360 degrees
  ENDIF
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    if @finchoice == 0
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c	; compute point
    else
    #pixel = @finfunc(#pixel) + (cos(r2)*d + flip(sin(r2)*d))/r + c
    endif
  ENDIF

default:
  title = "Kaleidoscope EB ver 10b"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam
    complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
  param centermove
    caption = "Use Screen Center"
    default = true
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param choice
  caption = "Choice of rotation vector formula"
  enum = "complex r = (0,1) ^ (@angle/90)" "complex r = (0,1) ^ (@angle + |#pixel|/90)" "complex r = (0,1) ^ ((@angle*tanang)/90)" \
  "(0,1) ^ ((@angle*atan2(tanang))/90)" "(0,1) ^ (@angle/90) + atan2(tanang)" "@rnum ^ (@angle/90)" "@rnum ^ (@angle + atan2(tanang2))/90" \
  "@rnum ^ (atan2(#pixel))"
  default = 0
  endparam

  complex param rnum
  caption = "Rotation vector constant"
  default =(0,1)
  visible = @choice == 6 || @choice == 5  || @choice ==7
  endparam


  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam
 param finchoice
 caption = "Choice of final pixel formula"
 enum ="(cos(r2)*d + flip(sin(r2)*d))/r + c" "@finfunc(#pixel) + (cos(r2)*d + flip(sin(r2)*d))/r + c"
 default = 0
 endparam

 func finfunc
 caption = "Pixel Function in final formula (Choice 1)"
 default =abs()
 visible = @finchoice == 1
 endfunc

}

KaleidoscopeEBver10a {
;
; Kaleidoscope transformation. Can be used to simulate many
; different kinds of symmetry.
;
; Original ver written by Damien M. Jones.
; Modified Evan Bayliss Nov 2021
; Different rotation vector formulae
;
transform:
  float r2 = 0.0
  float d = 0.0
  float xpix = real(#screenpixel)
  float ypix = imag(#screenpixel)
  float xc =real(#center)
  float yc = real(flip(#center))
  tanang = (xpix - xc)/(ypix - yc)

  if @choice == 0
  complex r = (0,1) ^ (@angle/90) ; complex rotation vector
  elseif @choice == 1
  complex r = (0,1) ^ (@angle + |#pixel|/90)	; complex rotation vector
  elseif @choice == 2
  complex r = (0,1) ^ ((@angle*tanang)/90) ; complex rotation vector
  elseif @choice == 3
  complex r = (0,1) ^ ((@angle + atan2(tanang))/90) ; complex rotation vector
  elseif @choice == 4
  complex r = (0,1) ^ (@angle/90) + atan2(tanang)
  elseif @choice == 5
  complex r = @rnum ^ (@angle/90)
  endif

  complex c = @symcenter		; assume symmetry center is fixed
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  complex z2 = #pixel - c		; get coordinate relative to symcenter

  ; convert z2 into angle and distance
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    r2 = r2 + #pi * 2; rotate 360 degrees
  ENDIF
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    if @finchoice == 0
    #pixel = (cos(r2)*d + flip(sin(r2)*d))/r + c	; compute point
    else
    #pixel = @finfunc(#pixel) + (cos(r2)*d + flip(sin(r2)*d))/r + c
    endif
  ENDIF

default:
  title = "Kaleidoscope EB ver 10a"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam

  param choice
  caption = "Choice of rotation vector formula"
  enum = "complex r = (0,1) ^ (@angle/90)" "complex r = (0,1) ^ (@angle + |#pixel|/90)" "complex r = (0,1) ^ ((@angle*tanang)/90)" \
  "(0,1) ^ ((@angle*atan2(tanang))/90)" "(0,1) ^ (@angle/90) + atan2(tanang)" "@rnum ^ (@angle/90)"
  default = 0
  endparam

  complex param rnum
  caption = "Rotation vector constant"
  default =(0,1)
  endparam

  complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
  param centermove
    caption = "Use Screen Center"
    default = false
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam
 param finchoice
 caption = "Choice of final pixel formula"
 enum ="(cos(r2)*d + flip(sin(r2)*d))/r + c" "@finfunc(#pixel) + (cos(r2)*d + flip(sin(r2)*d))/r + c"
 default = 0
 endparam

 func finfunc
 caption = "Pixel Function in final formula (Choice 1)"
 default =abs()
 endfunc

}

KPJ1AmendedVer3 {
;
; Kaleidoscope mixed with Popcorn Julia
; Evan Bayliss Oct 2021
;Power for z2 incorporated
; "While iter..." line altered after suggestion from Jim Blue
; Altered #pixel line

; Original Kaleidoscope Written by Damien M. Jones.
;
transform:
  float r2 = 0.0
  float d = 0.0
  complex r = (0,1) ^ (@angle/90)	; complex rotation vector
  complex c = @symcenter		; assume symmetry center is fixed
  IF (@centermove)			; relative symmetry center requested
    c = #center				; symmetry center is image center
  ENDIF
  if @iterchoice == 0
  complex z2 = #pixel - c		; get coordinate relative to symcenter
  else
  complex z2 = #pixel - c
    while iter <= @itnum && |z2| < @bailout
    x = real(z2), y = imag(z2)
    iter = iter +1
    newx = x - @h*fn1((y) + fn2(@k*y)) ; Popcorn Julia (PJ) formula
    newy = y - @h*fn1((x) + fn2(@k*x))
    x = newx, y = newy
    z2 = fn3(x) + fn4(y) + z2^@power ; end PJ
    endwhile
  endif

  ; convert z2 into angle and distance
  r2 = atan2(z2)
  IF (r2 < 0); negative angle (we want 0 < atan < pi*2)
    r2 = r2 + #pi * 2; rotate 360 degrees
  ENDIF
    r2 = r2 + r2*(atan2(|#pixel|))
  d = cabs(z2)				; distance from symcenter

  IF (@symorder > 0)			; Zero symmetry disables the transform.
    ; apply symmetry
    IF (@symreflect == 0)		; reflective
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      IF (r2 > #pi/@symorder)		; upper half of the range
        r2 = #pi*2/@symorder - r2	; reflect angle
      ENDIF
    ELSEIF (@symreflect == 1)		; left symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
    ELSEIF (@symreflect == 2)		; right symmetry
      r2 = r2 - floor(r2*@symorder/#pi/2)*#pi*2/@symorder
      r2 = #pi*2/@symorder - r2		; always reflect this
    ELSEIF (@symreflect == 3)		; slice-only symmetry
      IF (r2 > #pi*2/@symorder)		; outside of slice
        r2 = 0				; reset angle
	#solid = true			; this is outside now
      ENDIF
    ENDIF
    #pixel =  (cos(r2)*d + flip(sin(r2)*d))/r + c	; compute point
  ENDIF

default:
  title = "KPJ 1 Amended Version 3"
  helpfile = "Uf*.chm"
  helptopic = "Html/transformations/standard/kaleidoscope.html"

  param symorder
    caption = "Symmetry Order"
    default = 8.0
    hint = "Indicates the number of reflected components. \
            Use 0 to temporarily disable symmetry."
  endparam
  param symreflect
    caption = "Symmetry Mode"
    default = 0
    enum = "reflective" "left" "right" "slice only"
    hint = "Style of symmetry.  Reflective will always be \
            seamless; left and right may not be.  If Slice \
	    is selected, only the section that will be \
	    mirrored will be shown."
  endparam
  int param iterchoice
  caption = "Formula for z2"
  enum = "Standard #pixel - c" "Popcorn Julia formula (PJ)"
  default = 0
  endparam

  float param power
  caption = "Power value for z2"
  default = 2
  endparam

  int param itnum
  caption = "Iteration number"
  hint = "Works best with low iteration values"
  default =1
  endparam

  param h
    caption = "PJ H value"
    default = 0.05
  endparam
  param k
    caption = "PJ K value"
    default = 3.0
  endparam
  param bailout ; does not work well with low values
    caption = "PJ Bailout value"
    default = 1e18
  endparam
  func fn1
    caption = "PJ 1st Function"
    default = sin()
  endfunc
  func fn2
    caption = "PJ 2nd Function"
    default = tan()
  endfunc
  func fn3
    caption = "PJ 3rd Function"
    default = ident()

  endfunc
  func fn4
    caption = "PJ 4th Function"
    default = flip()
  endfunc
  complex param symcenter
    caption = "Center"
    default = #center
    enabled = !@centermove
    hint = "Sets the center of symmetry.  If Use Screen \
            Center is set, this item is ignored."
  endparam
  param centermove
    caption = "Use Screen Center"
    default = false
    hint = "If set, symmetry will be around the center of \
            the window, regardless of the Symmetry Center \
	    setting."
  endparam
  param angle
    caption = "Rotation angle"
    default = 0.0
    hint = "Sets how much to rotate the fractal (in degrees) \
            before applying symmetry. Can be used to select \
            a slice of the fractal."
  endparam
}