comment {
Formulas by Felipe Gallegos Montero
Viņa del Mar, Chile. 2003
}

FG-1 {
 ; Egg shaped fractal
init:
z=#pixel
shift=0
shifter=@shiftval
loop:
z= #pixel+z*z*z
If shifter==0 ;resets counter
shifter=@shiftval
EndIf
If shift==shifter ;shifting algorithm section
z= @F/(z*z*z*#pixel)
z=@FN(z*#pixel)
shift=shift-1
shifter=shift
Else
z=@F*(z*z*z*#pixel)
z=@FN(z/#pixel)
shift=shift+1
EndIf
bailout:
|z|<10
default:
title= "Shifting Egg"
complex param F
default= 1.0
endparam
param shiftval
caption= "Iteration change value"
Hint= "This is for setting \
how many times a formula \
is iterated, until the the formula is changed."
default= 3.0
Endparam
complex func FN
caption= "Inside Shape"
default= cos()
endfunc
}

FG-2{;Resembles a spiny wheel
init:
z=C=#pixel
counter=0
MX=#maxiter/2
loop:
z= 2*C
z=z*z*z*C*(z*@x)
If real(counter)<real(MX)
z=@FN(z^@X)*(@X^C)
Else
z=@FN(@X^z)*(C^@X)
EndIf
counter=counter+1
bailout:
|z|<100
default:
title= "Wheel"
complex param X
default= 3.0
endparam
complex func FN
caption= "Function"
default= cos()
endfunc
}

FG-3{
init:
z=@F/#pixel
C=#pixel
loop:
z=@FN(z/#pixel)*(@F*C)
C=z+C
bailout:
|z|<@Bail
default:
title= "Cross"
complex func FN
caption= "Function"
endfunc
param Bail
caption= "Bailout Value"
default= 100
endparam
complex param F
default= 1
endparam
}

FG-4{ ;With FN=cos() is like a
;combination of normal 
;mandelbrot and cuadratic
;mandelbrots
init:
z=C=#pixel
loop:
z=@FN(z*z)*@F*C
bailout:
|z|<10
default:
title= "Cross-Brot"
complex param F
caption= "Shaping"
default= 1.0
endparam
complex func FN
caption= "Shape function"
default= cos()
endfunc
switch:
type= "FG-7"
julseed=#pixel
F=F
FN=FN
}

FG-5{; From VARiable-mandelBROT
;create the Mandelbrot that you want.
;Version 2.0
init:
z=@Start
C=#pixel
FRM= z+z
NP=1
NE=1
NG=1
If @VNP==true
  NP=#PI
Endif
If @VNE==true
  NE=#E
Endif
If @VNG==true
  NG=5 ^0.5 *0.5 +0.5
Endif
loop:
If @Exline==true
If @ExLTA == "Z=Z+Pixel"
    z=z+C
  Elseif @ExLTA ==  "Z=FN(Z^Exponent)"
    z=@FN2(z^@Exp)
  Elseif @ExLTA == "Z=Z*Pixel"
    z=z*C
  Elseif @ExLTA ==  "Z=FN(Pixel^Exponent)"
    z=@FN2(C^@Exp)
  Elseif @ExLTA == "Z=FN(Z+Pixel^Exponent)"
    z=@FN2(z+C^@Exp)
  Endif
Endif
If @Ftype=="z+z"
  FRM= z+z
 Elseif @Ftype=="z*z"
  FRM= z*z
 Elseif @Ftype=="z^z"
  FRM= z^z
 Elseif @Ftype=="z+x"
  FRM= z+@x
 Elseif @Ftype=="z-x"
  FRM= z-@x
 Elseif @Ftype=="z*x"
  FRM= z*@x
 Elseif @Ftype=="z/x"
  FRM= z/@x
 Elseif @Ftype=="z^x"
  FRM= z^@x
Endif
If @MPS==true 
  z=@FN(FRM)*(NP*NE*NG)*C
 Else
  z=@FN(FRM)*(NP*NE*NG)+C
Endif
If @Exline==true
If @ExLTB == "Z=Z+Pixel"
    z=z+C
  Elseif @ExLTB ==  "Z=FN(Z^Exponent)"
    z=@FN2(z^@Exp)
  Elseif @ExLTB == "Z=Z*Pixel"
    z=z*C
  Elseif @ExLTB ==  "Z=FN(Pixel^Exponent)"
    z=@FN2(C^@Exp)
  Elseif @ExLTB == "Z=FN(Z+Pixel^Exponent)"
    z=@FN2(z+C^@Exp)
  Endif
Endif
bailout:
|@FNB2(@FNB(z))|<@Bail
default:
title= "Var-Brot"
param Ftype
caption= "Fractal formula"
enum= "z+z" "z*z" "z^z" "z+x" "z-x" "z*x" "z-x" "z/x" "z^x"
hint= "Selects the fractal formula"
endparam
bool param Exline
caption= "Extra lines"
default= true
hint= "Enables extra lines"
endparam
bool param MPS
Caption= "Multiplicate by Pixel?"
default= true
hint = "enables the multiplication Z*Pixel"
endparam
complex param Start
default= 0
hint= "Mandelbrot z start  value"
endparam
complex param X
caption= "X value"
default= 2
endparam
complex func FN
caption= "Function"
endfunc
heading
enabled= @Exline==true
caption= "Special line options"
endheading
param ExLTA
enabled= @Exline==true
enum= "Z=Z+Pixel" "Z=FN(Z^Exponent)" \
      "Z=Z*Pixel" "Z=FN(Pixel^Exponent)" \
      "Z=FN(Z+Pixel^Exponent)"
default= 0
caption= "First extra line type"
hint= "Selects the first extra line formula"
endparam
param ExLTB
enabled= @Exline==true
enum= "Z=Z+Pixel" "Z=FN(Z^Exponent)" \
      "Z=Z*Pixel" "Z=FN(Pixel^Exponent)" \
      "Z=FN(Z+Pixel^Exponent)"
default= 1
caption= "Second extra line type"
hint= "Selects the second extra line formula"
endparam
complex param Exp
enabled= @Exline==true
caption= "Exponent"
default= 3
endparam
complex func FN2
enabled= @Exline==true
caption= "Function"
default= ident()
endfunc
heading
caption= "Bailout functions"
endheading
float param Bail
caption= "Bailout Value"
default= 4
endparam
complex func FNB
caption= "First bailout function"
default= ident()
endfunc
complex func FNB2
caption= "Second bailout function"
default= ident()
endfunc
heading
caption= "Special numbers"
endheading
param VNP
caption= "PI"
default= false
hint= "Multiplies the formula with PI"
endparam
param VNE
caption= "E"
default= false
hint= "Multiplies the formula with E"
endparam
param VNG
caption= "Golden number"
default= false
hint= "Multiplies the formula with the golden number (PHI)"
endparam
switch:
type="FG-8"
Exline=Exline
ExLTA=ExLTA
ExLTB=ExLTB
MPS=MPS
julseed=#pixel
Ftype=Ftype
VNP=VNP
VNE=VNE
VNG=VNG
x=x
Exp=Exp
Bail=Bail
FN=FN
FN2=FN2
FNB=FNB
FNB2=FNB2
}

FG-7{ ;Cross-Brot Julia version
init:
z=#pixel
C=@Julseed
loop:
z=@FN(z*z)*@F*C
bailout:
|z|<10
default:
title= "Cross-Jul"
complex param Julseed
caption= "Julia seed"
default= (-0.45625,0.8)
endparam
complex param F
caption= "Shaping"
default= 1.0
endparam
complex func FN
caption= "Shape function"
default= cos()
endfunc
switch:
type= "FG-4"
F=F
FN=FN
}

FG-8{; From VARiable-JUlia
;create the Julia that you want.
;Version 2.0
init:
z=#pixel
C=@Julseed
FRM= z+z
NP=1
NE=1
NG=1
If @VNP==true
  NP=#PI
Endif
If @VNE==true
  NE=#E
Endif
If @VNG==true
  NG=5 ^0.5 *0.5 +0.5
Endif
loop:
If @Exline==true
If @ExLTA == "Z=Z+Julia Seed"
    z=z+C
  Elseif @ExLTA ==  "Z=FN(Z^Exponent)"
    z=@FN2(z^@Exp)
  Elseif @ExLTA == "Z=Z*Julia Seed"
    z=z*C
  Elseif @ExLTA ==  "Z=FN(Julia Seed^Exponent)"
    z=@FN2(C^@Exp)
  Elseif @ExLTA == "Z=FN(Z+Julia Seed^Exponent)"
    z=@FN2(z+C^@Exp)
  Endif
Endif
If @Ftype=="z+z"
  FRM= z+z
 Elseif @Ftype=="z*z"
  FRM= z*z
 Elseif @Ftype=="z^z"
  FRM= z^z
 Elseif @Ftype=="z+x"
  FRM= z+@x
 Elseif @Ftype=="z-x"
  FRM= z-@x
 Elseif @Ftype=="z*x"
  FRM= z*@x
 Elseif @Ftype=="z/x"
  FRM= z/@x
 Elseif @Ftype=="z^x"
  FRM= z^@x
Endif
If @MPS==true 
  z=@FN(FRM)*(NP*NE*NG)*C
 Else
  z=@FN(FRM)*(NP*NE*NG)+C
Endif
If @Exline==true
If @ExLTB == "Z=Z+Julia Seed"
    z=z+C
  Elseif @ExLTB ==  "Z=FN(Z^Exponent)"
    z=@FN2(z^@Exp)
  Elseif @ExLTB == "Z=Z*Julia Seed"
    z=z*C
  Elseif @ExLTB ==  "Z=FN(Julia Seed^Exponent)"
    z=@FN2(C^@Exp)
  Elseif @ExLTB == "Z=FN(Z+Julia Seed^Exponent)"
    z=@FN2(z+C^@Exp)
  Endif
Endif
bailout:
|@FNB2(@FNB(z))|<@Bail
default:
title= "Var-Jul"
complex param Julseed
caption= "Julia Seed"
default= (-0.08125 , 0.53125)
endparam
param Ftype
caption= "Fractal formula"
enum= "z+z" "z*z" "z^z" "z+x" "z-x" "z*x" "z-x" "z/x" "z^x"
hint= "Selects the fractal formula"
endparam
bool param Exline
caption= "Extra lines"
default= true
endparam
bool param MPS
Caption= "Multiplicate by Julia Seed?"
default= true
hint= "Enables the multiplication Z*Seed"
endparam
complex param X
caption= "X value"
default= 2
endparam
complex func FN
caption= "Function"
endfunc
heading
enabled= @Exline==true
caption= "Special line options"
endheading
param ExLTA
enabled= @Exline==true
enum= "Z=Z+Julia Seed" "Z=FN(Z^Exponent)" \
      "Z=Z*Julia Seed" "Z=FN(Julia Seed^Exponent)" \
      "Z=FN(Z+Julia Seed^Exponent)"
default= 0
caption= "First extra line type"
hint= "Selects the first extra line formula"
endparam
param ExLTB
enabled= @Exline==true
enum= "Z=Z+Julia Seed" "Z=FN(Z^Exponent)" \
      "Z=Z*Julia Seed" "Z=FN(Julia Seed^Exponent)" \
      "Z=FN(Z+Julia Seed^Exponent)"
default= 1
caption= "Second extra line type"
hint= "Selects the second extra line formula"
endparam
complex param Exp
enabled= @Exline==true
caption= "Exponent"
default= 3
endparam
complex func FN2
enabled= @Exline==true
caption= "Function"
default= ident()
endfunc
heading
caption= "Bailout functions"
endheading
float param Bail
caption= "Bailout Value"
default= 4
endparam
complex func FNB
caption= "First bailout function"
default= ident()
endfunc
complex func FNB2
caption= "Second bailout function"
default= ident()
endfunc
heading
caption= "Special numbers"
endheading
param VNP
caption= "PI"
default= false
hint= "Multiplies the formula with PI"
endparam
param VNE
caption= "E"
default= false
hint= "Multiplies the formula with E"
endparam
param VNG
caption= "Golden number"
default= false
hint= "Multiplies the formula with the golden number (PHI)"
endparam
switch:
type="FG-5"
Exline=Exline
ExLTA=ExLTA
ExLTB=ExLTB
MPS=MPS
Ftype=Ftype
VNP=VNP
VNE=VNE
VNG=VNG
x=x
Exp=Exp
Bail=Bail
FN=FN
FN2=FN2
FNB=FNB
FNB2=FNB2
}
FG-9{ ;Julia version of Flipper
init:
z=#pixel
C=@Julseed
Flp=z*C
Flp2=flip(Flp)
loop:
A=Flp*z*@X
z=C*z*z  
If Flp==z*C
z=@FN(A^z)*(C*z)*@X
Flp=Flp2
Else
z=@FN(z^A)*(C*z)*@X
Flp=z*C
EndIf
z=@X+(z+z+z)*C
bailout:
|z|<100
default:
Title= "Flipper-Julia"
complex param Julseed
caption= "Julia-seed"
default= (0.275,0.3375)
endparam
complex param X
default= 2
endparam
complex func FN
caption= "Function"
default= Ident()
endfunc
switch:
type= "FG-6"
X=X
FN=FN
}

FG-10{ ;Based on the ecuation for finding
;the values on first, second and 
;third grade ecuations
init:
z=0
loop:
If @Ecu=="First grade"
EC=(@A*z)+@B
Elseif @Ecu=="Second grade"
EC= ((@A^2)*z)+(@B*z)+@C
Else
EC= ((@A^3)*z)+((@B^2)*z)+(@C*z)+@D
Endif
z= z*EC*#pixel
z= @FN(EC)+(z*#pixel)
bailout:
|z|<10
default:
title= "Ecuation Mandelbrot"
param Ecu
caption= "Ecuation"
enum= "First grade" "Second grade" "Third grade"
endparam
complex param A
caption= "A variable"
default= 2
endparam
complex param B
caption= "B variable"
default= 2
endparam
complex param C
caption= "C variable"
default= 2
endparam
complex param D
caption= "D variable"
default= 2
endparam
complex func FN
caption= "Function"
endfunc
switch:
type= "FG-11"
julseed=#pixel
Ecu=Ecu
A=A
B=B
C=C
D=D
FN=FN
}

FG-11{ ;Based on the ecuation for finding
;the values on first, second and 
;third grade ecuations
init:
z=#pixel
loop:
If @Ecu=="First grade"
EC=(@A*z)+@B
Elseif @Ecu=="Second grade"
EC= ((@A^2)*z)+(@B*z)+@C
Else
EC= ((@A^3)*z)+((@B^2)*z)+(@C*z)+@D
Endif
z= z*EC*@Julseed
z= @FN(EC)+(z*@Julseed)
bailout:
|z|<10
default:
title= "Ecuation Julia"
param Ecu
caption= "Ecuation"
enum= "First grade" "Second grade" "Third grade"
endparam
complex param Julseed
caption= "Julia seed"
endparam
complex param A
caption= "A variable"
default= 2
endparam
complex param B
caption= "B variable"
default= 2
endparam
complex param C
caption= "C variable"
default= 2
endparam
complex param D
caption= "D variable"
default= 2
endparam
complex func FN
caption= "Function"
endfunc
switch:
type= "FG-10"
Ecu=Ecu
A=A
B=B
C=C
D=D
FN=FN
}

FG-12{
init:
z=0
OldC=0
loop:
C=#pixel
z=z*@FN((C+OldC)^@Exp)
z=(z^@Exp)*(cabs(C)+abs(OldC))+z
z=@FN(C+OldC)+z
OldC=C
bailout:
|z*C|<100
default:
title= "Strange-Brot"
complex param Exp
caption= "Exponent"
default= 3
endparam
complex func FN
caption= "Function"
default= ident()
endfunc
switch:
type= "FG-13"
julseed=#pixel
Exp=Exp
FN=FN
}

FG-13{
init:
z=#pixel
OldC=0
loop:
C=@Julseed
z=z*@FN((C+OldC)^@Exp)
z=(z^@Exp)*(cabs(C)+abs(OldC))+z
z=@FN(C+OldC)+z
OldC=C
bailout:
|z*C|<100
default:
title= "Strange-Jul"
complex param Julseed
caption= "Julia seed"
default= (0.04375,0.46875)
endparam
complex param Exp
caption= "Exponent"
default= 3
endparam
complex func FN
caption= "Function"
default= ident()
endfunc
switch:
type= "FG-12"
Exp=Exp
FN=FN
}

FG-14{ ; Experimenting with
; different counter styles.
init:
z=0
C=#pixel
CntSt=@countstop
counter=CntSt
Oldcount=0
Oldercount=1
loop:
If counter==Cntst
 If @CntStl=="Inverse linear" ;resetting counter
 Cntst=1
 counter=@countstop
 Elseif @CntStl=="Fibonacci"
 counter=1
 Oldcount=0
 Oldercount=1
 Else
 counter=1
 Endif
z=z^@FN(counter)+C
Else 
z=z^@FN(counter)+C
endif
If @CntStl=="Linear"
counter=counter+1
Elseif @CntStl=="Inverse linear"
counter=counter-1
Elseif @CntStl=="Fibonacci"
Counter=OlderCount+OldCount
OlderCount=OldCount
Oldcount=Counter
Endif
bailout:
|z|<100
default:
title= "Counter-Brot"
maxiter=1000
param CntStl
caption= "Counter style"
enum= "Linear" "Inverse linear" "Fibonacci"
endparam
int param countstop
caption= "Counter stop"
default= 5
endparam
complex func FN
caption= "Cunter function"
default= ident()
endfunc
switch:
type= "FG-15"
Julseed=#pixel
FN=FN
CntStl=CntStl
countstop=countstop
}

FG-15{ ; Experimenting with
; different counter styles.
init:
z=#pixel
C=@Julseed
CntSt=@countstop
counter=CntSt
Oldcount=0
Oldercount=1
loop:
If counter==Cntst
 If @CntStl=="Inverse linear" ;resetting counter
 Cntst=1
 counter=@countstop
 Elseif @CntStl=="Fibonacci"
 counter=1
 Oldcount=0
 Oldercount=1
 Else
 counter=1
 Endif
z=z^@FN(counter)+C
Else 
z=z^@FN(counter)+C
endif
If @CntStl=="Linear"
counter=counter+1
Elseif @CntStl=="Inverse linear"
counter=counter-1
Elseif @CntStl=="Fibonacci"
Counter=OlderCount+OldCount
OlderCount=OldCount
Oldcount=Counter
Endif
bailout:
|z|<100
default:
title= "Counter-Jul"
maxiter=1000
param CntStl
caption= "Counter style"
enum= "Linear" "Inverse linear" "Fibonacci"
endparam
Int param countstop
caption= "Counter stop"
default= 5
endparam
complex func FN
caption= "Cunter function"
default= ident()
endfunc
complex param Julseed
caption= "Julia seed"
default= (-0.525,0.24375)
endparam
switch:
type= "FG-14"
FN=FN
CntStl=CntStl
countstop=countstop
}

FG-6 {
 ; This formula changes
;if a value is "Flipped" or not.
init:
z=C=#pixel
Flp=z*C
Flp2=flip(Flp)
loop:
A=Flp*z*@X
z=C*z*z  
If Flp==z*C
z=@FN(A^z)*(C*z)*@X
Flp=Flp2
Else
z=@FN(z^A)*(C*z)*@X
Flp=z*C
EndIf
z=@X+(z+z+z)*C
bailout:
|z|<100
default:
title="Flipper-Brot"
complex param X
default= 2
endparam
complex func FN
caption= "Function"
default= Ident()
endfunc
switch:
type= "FG-9"
Julseed=#pixel
X=X
FN=FN
}