mjd_Julia { ; 20000401
; Made by Mark jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
;
; This is not exactly what i like to call "inventive" ...
init:
  z = pixel
  if @dis == 0
    d = @seed
  else
    d = #pixel
  endif
loop:
  z = @fnz2(#z^@power) * @fnc2(d^@power2) + @fnc(@seed)
bailout:
  |z| <= @bailout
default:
  title="fn(z^p)*fn(d^p)+fn(c) Julia"
  maxiter=400

  param seed    
    caption="Julia seed"
    default=(.6,.5)
  endparam
  param dis      
    caption="d=?"
    default=0,enum="Seed""Pixel"
  endparam
  param power    
    caption="Power (z)"
    default=(3,0)
  endparam
  param power2
    caption="Power (pixel)"
    default=(-1,0)
  endparam
  param bailout  
    caption="Bailout"
    default=64.0
  endparam
  func fnz2
    caption="Function of z^p1"
    default=sin()
  endfunc
  func fnc2
    caption="Function of c^p2"
    default=cos()
  endfunc
  func fnc
    caption="Function of c"
    default=sin()
  endfunc
switch:
  type="mjd_Mandel"
  start=#pixel
  dis=@dis
  power=@power
  power2=@power2
  bailout=@bailout
  fnz2=@fnz2
  fnc2=@fnc2
  fnc=@fnc
}

;##################################################################

mjd_Mandel { ; 20000401
; Made by Mark jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
;
; It's of no use to have these, but anyway ...
init:
  z = @start + #pixel
  if @dis == 0
    d = #pixel
  else
    d = @start
  endif
loop:
  z = @fnz2(#z^@power) * @fnc2(d^@power2) + @fnc(#pixel)
bailout:
  |z| <= @bailout
default:
  title="fn(z^p)*fn(d^p)+fn(c) Mandel"
  maxiter=400

  param start  
    caption="Perturbation"    
    default=(0,0)  
  endparam
  param dis    
    caption="d=?"             
    default=0
    enum="Pixel""Perturbation"
  endparam
  param power  
    caption="Power (z)"       
    default=(3,0)  
  endparam
  param power2 
    caption="Power (pixel)"   
    default=(-1,0) 
  endparam
  param bailout
    caption="Bailout"         
    default=64.0   
  endparam
  func fnz2    
    caption="Function of z^p1"
    default=sin()  
  endfunc
  func fnc2    
    caption="Function of c^p2"
    default=cos()  
  endfunc
  func fnc     
    caption="Function of c"   
    default=sin()  
  endfunc
switch:
  type="mjd_Julia"
  seed=#pixel
  dis=@dis
  power=@power
  power2=@power2
  bailout=@bailout
  fnz2=@fnz2
  fnc2=@fnc2
  fnc=@fnc
}

;##################################################################

mjd_Lambda { ; 20000401
; Made by Mark jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
;
; So boring to have these formulas in my database ...
init:
  z = #pixel
loop:
  z = @fnz(#z)*(1-#z)*@fnc(@seed)
bailout:
  |z| <= @bailout
default:
  title="fn(z)*(1-z)*fn(c) Julia"
  center=(.5,0)
  maxiter=400

  param seed   
    caption="Lambda Seed"  
    default=(.85,.6)
  endparam
  param bailout
    caption="Bailout"      
    default=64.0    
  endparam
  func  fnz    
    caption="Function of Z"
    default=sin()   
  endfunc
  func  fnc    
    caption="Function of C"
    default=sin()   
  endfunc
switch:
  type="mjd_LambdaMan"
  start=#pixel
  bailout=@bailout
  fnz=@fnz
  fnc=@fnc  
}

;##################################################################

mjd_LambdaMan { ; 20000401
; Made by Mark jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
;
; I wonder if anyone even uses these formulas ...
init:
  z = @start+.5
loop:
  z = @fnz(#z)*(1-#z)*@fnc(#pixel)
bailout:
  |z| <= @bailout
default:
  title="fn(z)*(1-z)*fn(c) Mandel"
  center=(1,0)
  magn=0.5
  maxiter=400

  param start  
    caption="Perturbation" 
    default=(0,0)
  endparam
  param bailout
    caption="Bailout"      
    default=64.0 
  endparam
  func  fnz    
    caption="Function of Z"
    default=sin()
  endfunc
  func  fnc    
    caption="Function of C"
    default=sin()
  endfunc
switch:
  type="mjd_Lambda"
  seed=#pixel
  bailout=@bailout
  fnz=@fnz
  fnc=@fnc  
}

;##############################################################################

mjd-julia-mandel { ;20000416
; Made by Mark jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
;
; Last modification 20000418
; Optimized for speed 20010121
init:
  complex oc=(0,0) ;orbit center
  float or=0       ;orbit cabs
  float oang=0     ;orbut atan2

  complex c = #pixel
  int i=0
  while (i<@juliter)
    c=@julfn(c)^@jpower+@seed
    if @jrecip
      c=recip(c)
    endif
    i=i+1
  endwhile

  c=(c-@center)/@size
  if @invers>0
    c=@invers/c
  endif
  c=c+c*@random*(#random-(.5,.5))

  #z=@start
loop:
  #z=#z^@mpower + c
  if @otype=="Twist" ;=change angle
    oc=#z-@ocenter
    or=cabs(oc)
    oang=atan2(oc)+@oamount*exp(-or/@osize)
    #z=or*exp(flip(oang))+@ocenter
  elseif @otype=="Scare" ;=change distance
    oc=#z-@ocenter
    or=cabs(oc)/@oamount
    oang=atan2(oc)
    or=or+@osize/(1/or+or)
    #z=@oamount*or*exp(flip(oang))+@ocenter
  endif
bailout:
  |#z| <= @bailout
default:
  title = "Mjd-Julia-Mandel"
  precision=30
  center=(0,0)
  param juliter
    caption="Julia iterations"
    default=3
    min=0
    hint="Number of julia iterations before mandel is being calculated"
  endparam

  heading
    caption="Julia parameters"
  endheading
  param seed
    caption="Seed"
    default=(.3,.6)
    hint="Switch to browse this param"
  endparam
  param jpower
    caption="Power"
    default=(2,0)
    hint="Power of the julia iterations"
  endparam
  param jrecip
    caption="Julia inverse"
    default=false
    hint="Inverse every iteration of julia set (try this! with mandel inversion)"
  endparam
  func julfn
    caption="Julia function"
    default=ident()
    hint="Function applied to every mandel iteration (Try Sin or Tan)"
  endfunc

  heading
    caption="Mandel parameters"
  endheading
  param start
    caption="Perturbation"
    default=(0,0)
    hint="Mandel start value (perturbation)"
  endparam
  param center
    caption="Center"
    default=(0,0)
    hint="Center of mandel set after julia iterations"
  endparam
  param size
    caption="Magnitude"
    default=(1,0)
    min=1e-20
    hint="Magnify mandel set after julia iterations"
  endparam
  param invers
    caption="Inversion"
    default=0.0
    min=0
    hint="Inversion radius of mandelbrot set (0=off)"
  endparam
  param mpower
    caption="Power"
    default=(2,0)
    hint="Power of the mandel iterations"
  endparam
  param bailout
    caption="Bailout"
    default=1e+20
    min=1
    hint="Bailout value for mandel iterations"
  endparam

  heading
    caption="Orbit fool parameters"
  endheading
  param otype
    caption="Orbit fool type"
    enum="none" "Twist" "Scare"
    default=0
  endparam
  heading
    caption="Twist parameters"
    visible=@otype=="Twist"
  endheading
  heading
    caption="Scare parameters"
    visible=@otype=="Scare"
  endheading
  param ocenter
    caption="Orbit fool center"
    default=(0,0)
    hint="Center of the orbit fool origin"
    visible=@otype=="Twist" || @otype=="Scare"
  endparam
  param osize
    caption="Orbit fool size"
    default=0.2
    min=0
    hint="Size or decay of orbit fool"
    visible=@otype=="Twist" || @otype=="Scare"
  endparam
  param oamount
    caption="Orbit fool threshold"
    default=1.0
    hint="Amount of orbit fooling -- try negative values for inverse results"
    visible=@otype=="Twist" || @otype=="Scare"
  endparam

  heading
    caption="Other parameters"
  endheading
  param random
    caption="Randomness"
    default=0.0
    hint="Randomness of start value of mandelbrot set"
  endparam
switch:
  type="mjd-mandel-julia"
  @seed=#pixel
  @maniter=@juliter
  @mpower=@jpower
  @mrecip=@jrecip

  @start=@start
  @center=@center
  @size=@size
  @invers=@invers
  @jpower=@mpower

  @otype=@otype
  @ocenter=@ocenter
  @osize=@osize
  @oamount=@oamount

  @bailout=@bailout
  @random=@random
  @julfn=@manfn
}

;##############################################################################

mjd-mandel-julia { ;20000416
; Made by Mark jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
;
; Last modofication 20000418
; Optimized for speed 20010121
init:
  complex oc=(0,0) ;orbit center
  float or=0       ;orbit cabs
  float oang=0     ;orbut atan2

  #z = @start
  int p=-1
  while p<@maniter
    #z=@manfn(#z)^@mpower+#pixel
    if @mrecip
      #z=recip(#z)
    endif
    p=p+1
  endwhile

  #z=(#z-@center)/@size

  if @invers>0
    #z=@invers/#z
  endif

  complex c=@seed+@seed*@random*(#random-(.5,.5))
loop:
  #z=#z^@jpower + c
  if @otype==1     ;Orbit fool: Twist (=change angle)
    oc=#z-@ocenter
    or=cabs(oc)
    oang=atan2(oc)+@oamount*exp(-or/@osize)
    #z=or*exp(flip(oang))+@ocenter
  elseif @otype==2 ;Orbit fool: Scare (=change distance)
    oc=#z-@ocenter
    or=cabs(oc)/@oamount
    oang=atan2(oc)
    or=or+@osize/(1/or+or)
    #z=@oamount*or*exp(flip(oang))+@ocenter
  endif
bailout:
  |#z|<=@bailout
default:
  title = "Mjd-Mandel-Julia"
  center=(-.5,0)
  
  param maniter
    caption="Mandel iterations"
    default=3
    min=0
    hint="Number of mandel iterations before Julia is being calculated"
  endparam

  heading
    caption="Mandel parameters"
  endheading
  param start
    caption="Perturbation"
    default=(0,0)
    hint="Mandel start value (perturbation)"
  endparam
  param mpower
    caption="Power"
    default=(2,0)
    hint="Power of the mandel iterations"
  endparam
  param mrecip
    caption="Inverse"
    default=false
    hint="Inverse every iteration of mandel set (try this! with julia inversion)"
  endparam
  func manfn
    caption="Mandel function"
    default=ident()
    hint="Function applied to every mandel iteration (Try Sin or Tan. Try Cabs with maniter>=5 for an egg)"
  endfunc
  
  heading
    caption="Julia parameters"
  endheading
  param seed
    caption="Seed"
    default=(.3,.6)
    hint="Switch to browse this param"
  endparam
  param center
    caption="Center"
    default=(0,0)
    hint="Center julia set after mandel iterations"
  endparam
  param size
    caption="Magnitude"
    default=(1,0)
    min=1e-20
    hint="Magnify julia set after mandel iterations"
  endparam
  param invers
    caption="Inversion"
    default=0.0
    min=0
    hint="Inversion radius of julia set (0=off)"
  endparam
  param jpower
    caption="Power"
    default=(2,0)
    hint="Power of the julia iterations"
  endparam
  param bailout
    caption="Bailout"
    default=1e+20
    min=1.0
    hint="Bailout value for julia iterations"



  endparam

  heading
    caption="Orbit fool parameters"
  endheading
  param otype
    caption="Orbit fool type"
    enum="none" "Twist" "Scare"
    default=0
  endparam
  heading
    caption="Twist parameters"
    visible=@otype=="Twist"
  endheading
  heading
    caption="Scare parameters"
    visible=@otype=="Scare"
  endheading
  param ocenter
    caption="Orbit fool center"
    default=(0,0)
    hint="Center of the orbit fool origin"
    visible=@otype=="Twist" || @otype=="Scare"
  endparam
  param osize
    caption="Orbit fool size"
    default=.2
    min=0
    hint="Size or decay of orbit fool"
    visible=@otype=="Twist" || @otype=="Scare"
  endparam
  param oamount
    caption="Orbit fool threshold"
    default=1.0
    hint="Amount of orbit fooling -- try negative values for inverse results"
    visible=@otype=="Twist" || @otype=="Scare"
  endparam

  heading
    caption="Other parameters"
  endheading
  param random
    caption="Randomness"
    default=0.0
    hint="Randomness of seed value of julia set"
  endparam
switch:
  type="mjd-julia-mandel"
  @start=@start
  @juliter=@maniter
  @jpower=@mpower
  @jrecip=@mrecip

  @seed=#pixel
  @center=@center
  @size=@size
  @invers=@invers
  @jpower=@mpower

  @otype=@otype
  @ocenter=@ocenter
  @osize=@osize
  @oamount=@oamount

  @bailout=@bailout
  @random=@random
  @julfn=@manfn
}

;##############################################################################

3FunctionsJulia { ;20000424
; Made by Mark jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
;
; Optimized for speed 20010122
init:
  #z = #pixel
loop:
  #z=@fn1(#z*@f1)*@w1+#z*(1-@w1)
  #z=@fn2(#z*@f2)*@w2+#z*(1-@w2)
  #z=@fn3(#z*@f3)*@w3+#z*(1-@w3)+@seed
bailout:
  |#z| <= @bailout
default:
  title = "3 functions (julia)"
  
  param f1
    caption="Function 1 factor"
    default=1.0
  endparam
  param f2
    caption="Function 2 factor"
    default=1.0
  endparam
  param f3
    caption="Function 3 factor"
    default=1.0
  endparam
  param w1
    caption="Function 1 weight"
    default=1.0
    min=0
    max=1
  endparam
  param w2
    caption="Function 2 weight"
    default=1.0
    min=0
    max=1
  endparam
  param w3
    caption="Function 3 weight"
    default=1.0
    min=0
    max=1
  endparam

  param seed
    caption="Julia seed"
    default=(.5,0)
  endparam
  param bailout
    caption="Bailout"
    default=4.0
  endparam

  func fn1
    caption="Function A"
    default=sinh()
  endfunc
  func fn2
    caption="Function B"
    default=log()
  endfunc
  func fn3
    caption="Function C"
    default=atan()
  endfunc
switch:
  type="3FunctionsMandel"
  start=#pixel
  bailout=@bailout
  f1=@f1
  f2=@f2
  f3=@f3
  w1=@w1
  w2=@w2
  w3=@w3
  fn1=@fn1
  fn2=@fn2
  fn3=@fn3
}

;##############################################################################

3FunctionsMandel { ;20000424
; Made by Mark jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
;
; Optimized for speed 20010122
init:
  #z = @start
loop:
  #z=@fn1(#z*@f1)*@w1+#z*(1-@w1)
  #z=@fn2(#z*@f2)*@w2+#z*(1-@w2)
  #z=@fn3(#z*@f3)*@w3+#z*(1-@w3)+#pixel
bailout:
  |#z| <= @bailout
default:
  title = "3 functions (mandel)"

  param f1
    caption="Function 1 factor"
    default=1.0
  endparam
  param f2
    caption="Function 2 factor"
    default=1.0
  endparam
  param f3
    caption="Function 3 factor"
    default=1.0
  endparam
  param w1
    caption="Function 1 weight"
    default=1.0
    min=0
    max=1
  endparam
  param w2
    caption="Function 2 weight"
    default=1.0
    min=0
    max=1
  endparam
  param w3
    caption="Function 3 weight"
    default=1.0
    min=0
    max=1
  endparam

  param start
    caption="Perturbation"
    default=(.5,0)
  endparam
  param bailout
    caption="Bailout"
    default=4.0
  endparam

  func fn1
    caption="Function A"
    default=sinh()
  endfunc
  func fn2
    caption="Function B"
    default=log()
  endfunc
  func fn3
    caption="Function C"
    default=atan()
  endfunc
switch:
  type="3FunctionsJulia"
  seed=#pixel
  bailout=@bailout
  f1=@f1
  f2=@f2
  f3=@f3
  w1=@w1
  w2=@w2
  w3=@w3
  fn1=@fn1
  fn2=@fn2
  fn3=@fn3
}

;##################################################################

RandomPrimeMethod { ;20010113
; Made by Mark jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
;
init:
  float x=0
  float y=0
  int u=@prime1
  int v=@prime2
  int r=0
  bool noprime=true
  
  #z=@fnc(#pixel)
loop:
  x=(real(#z)%1)*u
  y=(imag(#z)%1)*v
  
  u=trunc(x)
  v=trunc(y)
  x=x-u
  y=y-v

  ;be sure u and v are odd numbers
  if u%2==0
    u=u+1
  endif
  if v%2==0
    v=v+1
  endif

  noprime=true
  while noprime ;search the first larger prime number (59.92% chance for success, else it's odd enough)
    r=u%30
    if r==1 || r==7 || r==11 || r==13 || r==17 || r==19 || r==27 || r==29
      u=u-2
      noprime=false
    endif
    u=u+2
  endwhile

  noprime=true
  while noprime ;search the first larger prime number (59.92% chance for success, else it's odd enough)
    r=v%30
    if r==1 || r==7 || r==11 || r==13 || r==17 || r==19 || r==27 || r==29
      v=v-2
      noprime=false
    endif


    v=v+2
  endwhile

  #z=abs(fn1(x+flip(y))^2*(0,1)^(@rot/90))
bailout:
  |u+v| >@bailout
default:
  title = "Random (prime method)"
  center=(2,1.5)

  param rot
    caption="Rotation step"
    default=20.0
  endparam
  param prime1
    caption="Initial prime 1"
    default=12347
  endparam
  param prime2
    caption="Initial prime 2"
    default=13577
  endparam
  param bailout
    caption="Bailout"
    default=8.0
    min=4
  endparam
  
  func fn1
    caption="Standard function"
    default=cotan()
  endfunc
  func fnc
    caption="pixel function (pre)"
    default=abs()
  endfunc
}

;##############################################################################

WeirdFormula(XAXIS) { ;20000428
; Made by Mark jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
;
; Optimized for speed 20010122
init:
  complex efk=0
  complex efg=0
  complex dg=0
  complex fdg=0
  complex dgj=0
  complex dgf=0
  complex fgh=0
  complex fh=0
  complex gfh=0
  complex bfh=0
  complex bh=0
  #z=#pixel*4
loop:
  float gh=real(#z)
  float ek=imag(#z)
  efk=#pi/2-acos((sqr(@ef)+sqr(@fk)-sqr(ek))/2/@ef/@fk)
  efg=#pi-efk
  dg=sqrt(sqr(@df)+sqr(@fg)-2*@df*@fg*cos(efg))
  fdg=#pi/2-acos((sqr(@df)+sqr(dg)-sqr(@fg))/2/@df/dg)
  dgj=#pi/2-acos((sqr(dg)+sqr(@gj)-sqr(@dj))/2/dg/@gj)
  dgf=#pi-efg-fdg
  fgh=dgf+dgj
  fh=sqrt(sqr(@fg)+sqr(gh)-2*@fg*gh*cos(fgh))
  gfh=#pi/2-acos((sqr(@fg)+sqr(fh)-sqr(gh))/2/@fg/fh)
  bfh=efg-gfh
  bh=sqrt(sqr(@bf)+sqr(fh)-2*@bf*fh*cos(bfh))
  #z=fh+flip(bh)
bailout:
  |#z|>=@bailout
default:
  title = "Weird formula"
  center=(0,0)

  param ef
    default=3.0
  endparam
  param fk
    default=3.0
  endparam
  param fg
    default=3.0
  endparam
  param df
    default=13.0
  endparam
  param dj
    default=3.0
  endparam
  param gj
    default=14.0
  endparam
  param bf
    default=14.0
  endparam
  param bailout
    caption="Bailout"
    default=8.0
  endparam
}

Pixel--F { ;20010123
; Made by Mark jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
;
; Combination of Mark Townsend's Pixel formula

; with "inside" option, and Samuel Monnier's
; "Pixel (2 iterations) formula.
;
; This formula is expanded with basic figures.
; This means, if a pixel falls within the figure, it
; is inside, and other pixels are outside.
init:
  bool done=false
  int i=0
  #z = #pixel
  
  if @mode!="All Outside"
    if @figure=="Circle"
      if @mode=="Figure negative"
        if cabs(#z)>@size, i=-#maxiter, endif
      else
        if cabs(#z)<@size, i=-#maxiter, endif
      endif
    elseif @figure=="Square"
      complex zz=abs(#z)
      if @mode=="Figure negative"
        if real(zz)>@size || imag(zz)>@size, i=-#maxiter, endif
      else
        if real(zz)<@size && imag(zz)<@size, i=-#maxiter, endif
      endif
    elseif @figure=="Diamond"
      complex zz=abs(#z)
      if @mode=="Figure negative"
        if real(zz)+imag(zz)>@size, i=-#maxiter, endif
      else
        if real(zz)+imag(zz)<@size, i=-#maxiter, endif
      endif
    elseif @figure=="Cardioid"
      complex zz=#z/@size/(4/3)
      float u=2*real(zz)
      float v=sqr(u)+sqr(2*imag(zz))
      float w=v-u+0.25
      if @mode=="Figure negative"
        if w-sqrt(w)+u-.5>0, i=-#maxiter, endif
      else
        if w-sqrt(w)+u-.5<0, i=-#maxiter, endif
      endif
    endif
  endif
loop:  
  if @mode!=1
    i=i+1
    if i==@outiter
      done=true
    endif
  endif  
bailout:
  done==false
default:
  title = "Pixel--F"
  maxiter=2
  param mode
    caption="Mode"
    enum="All Outside" "All Inside" "Figure" "Figure negative"
    default=0
  endparam
  param outiter
    caption="Outside iterations"
    default=2
  endparam
  param figure
    caption="Figure"
    enum="Circle" "Square" "Diamond" "Cardioid"
    default=0
  endparam
  param size
    caption="Size of figure"
    default=1.0
    min=1e-30
  endparam
}

Squaref{
; Made by Mark Jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
init:
  float x=real(#pixel)
  float y=imag(#pixel)
  float xx=0
  
  int i=0

  float a1=0
  float a2=0
  float a3=0
  float b1=0
  float b2=0
  float b3=0
  float c1=0
  float c2=0
  float c3=0
  float d1=0
  float d2=0
  float d3=0

  float e1=1
  float f1=0
  float e2=-1
  float f2=0
  float e3=0
  float f3=-1

  if @t1==0
    a1=.5
    d1=.5
  elseif @t1==1
    b1=-.5
    c1=.5
  elseif @t1==2
    a1=-.5
    d1=-.5
  elseif @t1==3
    b1=.5
    c1=-.5
  elseif @t1==4
    a1=-.5
    d1=.5
  elseif @t1==5
    b1=.5
    c1=.5
  elseif @t1==6
    a1=.5
    d1=-.5
  elseif @t1==7
    b1=-.5
    c1=-.5
  endif

  if @t2==0
    a2=.5
    d2=.5
  elseif @t2==1
    b2=-.5
    c2=.5
  elseif @t2==2
    a2=-.5
    d2=-.5
  elseif @t2==3
    b2=.5
    c2=-.5
  elseif @t2==4
    a2=-.5
    d2=.5
  elseif @t2==5
    b2=.5
    c2=.5
  elseif @t2==6
    a2=.5
    d2=-.5
  elseif @t2==7
    b2=-.5
    c2=-.5
  endif

  if @t3==0
    a3=.5
    d3=.5
  elseif @t3==1
    b3=-.5
    c3=.5
  elseif @t3==2
    a3=-.5
    d3=-.5
  elseif @t3==3
    b3=.5
    c3=-.5
  elseif @t3==4
    a3=-.5
    d3=.5
  elseif @t3==5
    b3=.5
    c3=.5
  elseif @t3==6
    a3=.5
    d3=-.5
  elseif @t3==7
    b3=-.5
    c3=-.5
  endif
loop:
  xx=x
  if x>=abs(y)
    if b1==0
      x=(x-e1)/a1
      y=(y-f1)/d1
    else
      x=(y-f1)/c1
      y=(xx-e1)/b1
    endif
  elseif -x>=abs(y)
    if b2==0
      x=(x-e2)/a2
      y=(y-f2)/d2
    else
      x=(y-f2)/c2
      y=(xx-e2)/b2
    endif
  elseif y<0
    if b3==0
      x=(x-e3)/a3
      y=(y-f3)/d3
    else
      x=(y-f3)/c3
      y=(xx-e3)/b3
    endif
  endif  
  z=x+flip(y)
  i=i+1
bailout:
  (@mode==0 && cabs(z)/i>@bailout) || \
  (@mode==1 && |z|/i>@bailout) || \
  (@mode==2 && (abs(real(z))+abs(imag(z)))/i>@bailout) || \
  (@mode==3 && abs(real(z))/(100/3)+abs(imag(z))/i>@bailout)
default:
  title="Squaref"
  method=multipass
  periodicity=0
  magn=.75
  
  param bailout
    caption="Bailout"
    default=.02
  endparam
  param mode
    caption="Bailout mode"
    enum="Cabs""Cabs^2""Abs""Spike"
    default=2
  endparam
  param t1
    caption="T1: Right square"
    enum="mirror=0 rot=0"\
         "mirror=0 rot=90"\
         "mirror=0 rot=180"\
         "mirror=0 rot=270"\
         "mirror=1 rot=0"\
         "mirror=1 rot=90"\
         "mirror=1 rot=180"\
         "mirror=1 rot=270"
    default=1
  endparam
  param t2
    caption="T2: Left square"
    enum="mirror=0 rot=0"\
         "mirror=0 rot=90"\

         "mirror=0 rot=180"\
         "mirror=0 rot=270"\
         "mirror=1 rot=0"\
         "mirror=1 rot=90"\
         "mirror=1 rot=180"\
         "mirror=1 rot=270"
    default=4
  endparam
  param t3
    caption="T3: Lower square"
    enum="mirror=0 rot=0"\
         "mirror=0 rot=90"\
         "mirror=0 rot=180"\
         "mirror=0 rot=270"\
         "mirror=1 rot=0"\
         "mirror=1 rot=90"\
         "mirror=1 rot=180"\
         "mirror=1 rot=270"
    default=0
  endparam
switch:
  type="®FormulaMaker"
  @start=#pixel
  @bailout=bailout
  @fn1=fn1
  @fn2=fn2
}

Attractors{ ;20010211
; Made by Mark Jeronimus <Mark.Jeronimus@hva.nl>
; ® 2000 Mark Jeronimus
;
;#####################################################################
;
;I made this formula because I saw Ron Barnett's "Strange Attractors"
;formula, and I was a bit puzzled by the bailout method he used. And
;I was also irritated by the fact you have to enter the standard
;values for each formula seperately. So I grabbed a lot of strange
;attractor formulas together, and normal attractor formulas too, and
;started creating a formula which uses a real orbit trap and a *lot*
;additional coloring methods. Later, I added an inside coloring, which
;colors according to the last orbit's position. Then I added iteration
;skip, bailout, 3d color modes, pixel start modes and 3d rotation
;modes. And ofcourse all kinds of attractor default's.
;
;#####################################################################
;
;This formula knows 2 modes of coloring:
;
;<O: Outside coloring mode>
;* Outside coloring, which is triggered when the orbit traps into an
;  orbit trap or if the orbit bails out. If the orbit traps into the
;  orbit trap, the color accumulator becomes filled with the color
;  produced by the current "Inside coloring mode". If the maxiter is
;  reached AND the pixel has hit the trap, the pixel automatically
;  bails out and the content from the color accumulator is stored into
;  the real part of #z. -- One exception: If the coloring mode "Orbit
;  position" is selected, #z becomes the last position of the orbit.
;  This is the only case in which imag(#z) becomes filled.
;
;  If the trap radius is 0.0 and bailout is 0.0, the pixel will never
;  become 'outside'.
;
;<I: Inside coloring mode>
;* Inside coloring, which is active when the maxiter is reached and
;  there are no orbits cached in the orbit trap. This mode stores the
;  color produced by the "Outside coloring mode" into the real part
;  if #z. --Also the same exception here: If the coloring mode "Orbit
;  position" is selected, #z becomes the last position of the orbit.
;
;The 3D coloring modes (except 3D Orbit distance) can only be used
;  with true 3D formulas. These are listed in the table. If 3D orbit
;  distance is selected on a 2D formula, the Z depth which also
;  includes the calculation, is constant and equal to the entered
;  "Manual Z start" parameter.
;
;<Param presets>
;Each formula knows at least one set of predefenied parameters, which
;  are stored in the formula, so every attractor comes as it is meant
;  to look like. These definitions can include A, B, C, D and dt. If
;  the "Manual" setting is selected, the parameters can be entered in
;  the parameter entries "Param A".."Param dt".
;
;<O: Limit hits (0=off)>
;If the Outside coloring mode "Number of hits" is selected, the color
;  accumulator keeps track of the number of hits. If this number
;  exceeds this entered number, it is set equal to this number, and
;  the pixel bails out. If this mode is 0, the pixel color is not
;  limited, and can wrap around the gradient.
;
;<O: Bailout>
;If bailout > 0.0, the and the orbit radius exceeds the this value, it
;  immediately becomes outside, and the color accumulator is used for
;  coloring. If the color accumulator was not written to, the outside
;  color is 0.
;  If the bailout <0.0, the pixel bails out on a bsis of orbit speed
;  (like oldz-#z) and if the speed is smaller than the entered value,
;  the pixel immediately bails out. (same rules here too)
;
;<O: Iteration skip>
;The number of iterations to wait before applying any kind of outside
;  coloring.
;
;<S: Orbit start>
;This determines the start of the orbit AFTER rotating and BEFORE
;  iterating the formula.
;* It knows "Attractor default" as standard setting. See
;  the table for the standard settings.
;* "Zero  means that the start is (0,0,0)
;* "One" means that the start is (1,1,1)
;* "Manual" means that every x/y/z is entered manually.
;* "Manual (relative)" means that the entered x/y/z values are added
;  to the attractor's default values.
;* "Manual (scaling)" means that the entered x/y/z values are
;  multiplied to the attractor's default values.
;
;<R: 3D orbit view>
;This parameter determines the rotation of 3D formulas. Rotation of
;  the initial orbit always occures before the mutating orbit start
;  options and before any 'default start' options other than 'pixel'
;  (see table) i.e. if the default start is different from pixel then
;  the initial orbit is not rotated.
;  If the option "Manual rotation" is selected, the rotations along
;  the X, Y and Z axis are entered manually (in degrees).
;
;Mark Jeronimus
;
;Thanks to the Beta-testers:
;  Pat Goltz
;  Bob margolis
;  David Makin
;  Faye Williams
;  Kenneth Childress
;
;#####################################################################
;                            | Parameters| Presets| default start*|3D
;--------------------------------------------------------------------
;Chip                        | A,B,C     | 1      | pixel         |
;Dynamic system              | A,B,dt    | 1      | pixel         |
;Gingerbreadman              | A,B,C     | 1      | pixel         |
;Gnarl                       | A,B,C,dt  | 4      | pixel         |
;Henon                       | A,B,C     | 1      | pixel         |
;Hopalong                    | A,B,C     | 1      | pixel         |
;Implicit Euler approximation| A,B,dt    | 1      | pixel         |
;Kamtorus                    | A,dt      | 2      | pixel         |
;Latoocarfian                | A,B,C,D   | 2      | pixel         |
;Latoocarfian InvX           | A,B,C,D   | 1      | pixel         |
;Lorenz3d                    | A,B,C,dt  | 1      | (.5,20,1)**   | *
;Lorenz3d1                   | A,B,C,dt  | 1      | (1,1,1)**     | *
;Lorenz3d3                   | A,B,C,dt  | 1      | (1,1,1)**     | *
;Lorenz3d4                   | A,B,C,dt  | 1      | (1,1,1)**     | *
;Martin                      | A         | 1      | pixel         |
;Mira                        | A,B       | 10     | pixel         |
;Peitgen                     | A,B       | 1      | pixel         |
;Pickover                    | A,B,C,D   | 1      | pixel *       | *
;Popcorn                     | A,dt      | 1      | pixel         |
;Quadruptwo                  | A,B,C     | 2      | pixel         |
;Rossler3d (front)           | A,B,C,dt  | 1      | (1,1,1)**     | *
;Threeply                    | A,B,C     | 1      | pixel+c***    |
;Unity                       | A         | 3      | pixel         |
;Verhulst                    | A         | 3      | pixel         |
;Vine                        | A,dt      | 1      | pixel         |
;Vine2                       | A,B,dt    | 1      | pixel         |
;VineX                       | A,B,dt    | 1      | pixel         |
;VinePwr                     | A,B,dt    | 1      | pixel         |
;Volterra-Lotka              | A,B       | 1      | pixel         |
;
;*) If the formula is 2D, or if the start is pixel, then Z is always
;   equal to the entered "Manual Z start"
;**) Only if "Orbit trap radius" > 0, else pixel
;***) c=0+0i If "Inside coloring" = "off", else c=9.125+3,875i
;
;#####################################################################
;
;Last update: 2000/02/11
;  Repaired and optimized the Volterra-Lotka formula, which i totally
;  forgot to implement. The formula was there, but was not working
;  right.
;
;Release date: 2000/02/11
;
;#####################################################################
;
init:
  ;source
  float x = real(#pixel)
  float y = imag(#pixel)
  float zz = @zstart

  ;previous-iteration vars
  complex oldz=#pixel
  complex oldz2=(0,0)
  float oldrad=0

  ;temporary vars
  int i=0
  float xx=0
  float yy=0
  float rad=0
  float temp=0
  float temp2=0
  complex tempz=(0,0)
  complex tempc=(0,0)


  ;result buffers
  float lasthit=0
  complex lastz=(0,0)

  ;per-pixel vars
  int iter=0
  int pixelhits=0
  bool done=false

  ;per-fractal vars
  float a=@pa
  float b=@pb
  float c=@pc
  float d=@pd
  float dt=@pdt

  ;Rotate start position if nessecary
  if @type>=10 && @type<=13 || @type==17 || @type==20
    if @view==1     ;xz top
      temp=zz
      zz=y
      y=temp
    elseif @view==2 ;zy right
      temp=zz
      zz=x
      x=temp
    elseif @view==3 ;yz right flip
      temp=zz
      zz=y
      y=x
      x=temp
    elseif @view==4 ;rotation
      #z=(x+flip(y)) * 1i^(-@rotz/90)                  ;(x,y)
      y=imag(z)
      #z=(real(#z)+flip(zz)) * 1i^(-imag(@rotxy)/90)  ;(x,z)
      x=real(x)
      #z=(imag(#z)+flip(y)) * 1i^(-real(@rotxy)/90)    ;(z,y)
      zz=real(#z)
      y=imag(#z)
    endif
  endif

  ;select start
  if @start==1      ;zero
    x=y=zz=0
  elseif @start==2  ;one
    x=y=zz=1
  elseif @start==3  ;manual
    x=real(@xystart)
    y=imag(@xystart)
    zz=@zstart
  elseif @start==4  ;manual relative
    x=x+real(@xystart)
    y=y+imag(@xystart)
    zz=@zstart
  elseif @start==5  ;manual scaling
    x=x*real(@xystart)
    y=y*imag(@xystart)
    zz=@zstart
  elseif @start>5    ;attractor defaults
    if @type==10
      if @dist>0
        x=.5
        y=20
        zz=1
      endif
    elseif @type==11
      if @dist>0
        x=y=zz=1
      endif
    elseif @type==12
      if @dist>0
        x=y=zz=1
      endif
    elseif @type==13
      if @dist>0
        x=y=zz=1
      endif
    elseif @type==20
      if @dist>0
        x=y=zz=1
      endif
    elseif @type==21
      if @incol>0
        x=x+9.125
        y=y-3.875
      endif
    endif
  endif

  if @preset>0
    if @type==0
      a=-15
      b=-19
      c=1
    elseif @type==1  ;Dynamic system
      a=1
      b=3
      dt=.1
    elseif @type==2  ;Gingerbreadman
      a=1
      b=1
      c=1
    elseif @type==3  ;Gnarl
      if @preset==1
        a=8
        b=5
        c=0
        dt=0.1
      elseif @preset==2
        a=1
        b=2.7
        c=2.7
        dt=0.1
      elseif @preset==3
        a=1
        b=3
        c=2
        dt=0.1
      else
        a=1
        b=3
        c=6
        dt=0.1
      endif
    elseif @type==4  ;Henon
      a=1
      b=1.4
      c=.3
    elseif @type==5  ;Hopalong
      a=.4
      b=1
      c=0
    elseif @type==6  ;Implicit euler approximation
      a=1
      b=3
      dt=.1
    elseif @type==7  ;Kamtorus
      if @preset==1
        a=1.3
        dt=.05
      else
        a=acos(.24)
        dt=.05
      endif
    elseif @type==8  ;Latoocarfian
      if @preset==1
        a=-2.5
        b=1
        c=.75
        d=.75
      else
        a=-.966918
        b=2.879879
        c=.765145
        d=.744728
      endif
    elseif @type==9  ;Latoocarfian2
      a=-1.25
      b=1
      c=1.5
      d=1.5
    elseif @type==10  ;Lorenz3d
      a=5
      b=15
      c=1
      dt=.02
    elseif @type==11 ;Lorenz3d1
      a=5
      b=15
      c=1
      dt=.02
    elseif @type==12 ;Lorenz3d3
      a=10
      b=28
      c=2.66
      dt=.02
    elseif @type==13 ;Lorenz3d4
      a=10
      b=28
      c=2.66
      dt=.02
    elseif @type==14 ;Martin
      a=3.14
    elseif @type==15 ;Mira
      if @preset==1
        a=.3
        b=1
      elseif @preset==2
        a=-.05
        b=1
      elseif @preset==3
        a=.18
        b=1
      elseif @preset==4
        a=-.48
        b=.93
      elseif @preset==5
        a=.31
        b=1
      elseif @preset==6
        a=.32
        b=1
      elseif @preset==7
        a=-.4
        b=1
      elseif @preset==8
        a=-.4
        b=.99
      elseif @preset==9
        a=-.2
        b=1
      elseif @preset==10
        a=.3
        b=.999
      endif
    elseif @type==16 ;Peitgen
      a=.37
      b=.4
    elseif @type==17 ;Pickover
      a=2.24
      b=.43
      c=-.65
      d=-2.43
    elseif @type==18 ;Popcorn
      a=3
      dt=.05
    elseif @type==19 ;Quadrupto
      if @preset==1
        a=34
        b=1
        c=5
      else
        a=35
        b=1
        c=7
      endif
    elseif @type==20 ;Rossler3d
      a=.2
      b=.2
      c=5.7
      dt=.04
    elseif @type==21 ;Threeply
      a=-55
      b=-1
      c=-42
    elseif @type==22 ;Unity
      if @preset==1
        a=2
      elseif @preset==2
        a=1.71
      else
        a=1.75
      endif
    elseif @type==23 ;Verhulst
      if @preset==1
        a=1.95
      elseif @preset==2
        a=1.7
      else
        a=1.6
      endif
    elseif @type==24 ;Vine
      a=2.7
      dt=.1
    elseif @type==25 ;Vine2
      a=2.7
      b=2.7
      dt=.1
    elseif @type==26 ;VineX
      a=2.7
      b=3
      dt=.1
    elseif @type==27 ;VinePwr
      a=2.7
      b=2
      dt=.1
    elseif @type==28 ;Volterra-Lotka
      a=.3695
      b=.739
    endif
  endif

  if @type==7      ;Kantorus
    c=cos(a)
    d=sin(a)
  elseif @type==15 ;Mira
    c=2-2*a
    temp=x*x
    d=a*x+c*temp/(1+temp)
  elseif @type==16 ;Peitgen
    c=#pi/b-1
    d=a*b
  elseif @type==21 ;Threeply
    d=cos(b)
    b=sin(a+b+c)
  endif
loop:
  if @type==0      ;Chip
    if x==0
      x=1e-50
    endif
    xx=x
    x=y-x/abs(x)*cos(sqr(log(abs(b*x-c)))) \
               *atan(sqr(log(abs(c*x-b))))
    y=a-xx
  elseif @type==1  ;Dynamic system
    yy=y
    y=y+dt*sin(x +a*sin(b*x))
    x=x-dt*sin(yy+a*sin(b*yy))
  elseif @type==2  ;Gingerbreadman
    xx=x
    x=a-y+b*sin(x)
    y=c*xx
  elseif @type==3  ;Gnarl
    xx=x
    x=x-dt*sin(a*y +sin(b*(y +sin(c*y ))))
    y=y+dt*sin(a*xx+sin(b*(xx+sin(c*xx))))
  elseif @type==4  ;Henon
    xx=x
    x=a+y-b*x*x
    y=c*xx
  elseif @type==5  ;Hopalong
    if x==0
      x=1e-50
    endif
    xx=x
    x=y-x/abs(x)*sqrt(abs(b*x-c))
    y=a-xx
  elseif @type==6  ;Implicit euler approximation
    y=y+dt*sin(x+a*sin(b*x))
    x=x-dt*sin(y+a*sin(b*y))
  elseif @type==7  ;Kamtorus
    xx=x
    x = c*x - d*(y-x*x)
    y = d*xx+ c*(y-xx*xx)
  elseif @type==8  ;Latoocarfian
    xx=x
    x=c*sin(b*x)+sin(b*y)
    y=d*sin(a*y)+sin(a*xx)
  elseif @type==9  ;Latoocarfian invx
    xx=x
    x=c*sin(b*x)-sin(b*y)
    y=d*sin(a*y)+sin(a*xx)
  elseif @type==10 ;Lorenz3d
    xx=x
    yy=y
    x =x +dt*a*(y-x)
    y =y +dt*(xx*(b-zz)-y)
    zz=zz+dt*(xx*yy-c*zz)
  elseif @type==11 ;Lorenz3d1

    ;Original formula:
    ;  norm = sqrt(x(n)^2 + y(n)^2)
    ;  x(n+1) = x(n) + (-a*dt-dt)*x(n)
    ;               + (a*dt-b*dt)*y(n)
    ;               + (dt-a*dt)*norm
    ;               + y(n)*dt*z(n)
    ;  y(n+1) = y(n) + (b*dt-a*dt)*x(n)
    ;               - (a*dt+dt)*y(n)
    ;               + (b*dt+a*dt)*norm
    ;               - x(n)*dt*z(n)
    ;               - norm*z(n)*dt
    ;  z(n+1) = z(n) +(y(n)*dt/2)
    ;               - c*dt*z(n)
    ;
    ;Optimized one:

    #z=x+flip(y)
    tempc=(a+b-zz+flip(1-a))*cabs(#z)
    tempz=flip(#z)*zz
    #z=#z*(b-a+flip(1+a))

    zz=zz+dt*(y/2 - c*zz)
    x =x +dt*(imag(tempc) + real(tempz) - imag(#z))
    y =y +dt*(real(tempc) - imag(tempz) + real(#z))

  elseif @type==12 ;Lorenz3d3

    ;original formula:
    ;  norm = sqrt(x(n)^2 + y(n)^2)
    ;  x(n+1) = x(n) + (-(a*dt+dt)*x(n)
    ;               + (a*dt-b*dt+z(n)*dt)*y(n))/3
    ;               + ((dt-a*dt)*(x(n)^2-y(n)^2)
    ;               + 2*(b*dt+a*dt-z(n)*dt)*x(n)*y(n))/(3*norm)
    ;  y(n+1) = y(n) +((b*dt-a*dt-z(n)*dt)*x(n)
    ;               - (a*dt+dt)*y(n))/3
    ;               + (2*(a*dt-dt)*x(n)*y(n)
    ;               + (b*dt+a*dt-z(n)*dt)*(x(n)^2-y(n)^2))/(3*norm)
    ;  z(n+1) = z(n) +(3*x(n)*dt*x(n)*y(n)
    ;               -y(n)*dt*y(n)^2)/2
    ;               - c*dt*z(n)
    ;
    ;Optimized one:

    #z=x+flip(y)
    tempz=flip(#z^2)*(b+a-zz+flip(a-1))/3/cabs(#z)
    #z=#z*(b-a-zz+flip(a+1))/3

    zz=zz+dt*((3*x^2-y^2)*y/2 - c*zz)
    x =x +dt*(real(tempz) - imag(#z))
    y =y +dt*(imag(tempz) + real(#z))

  elseif @type==13 ;Lorenz3d4

    ;Original formula:
    ;  x(n+1) = x(n) +(-a*dt*x(n)^3
    ;   + (2*a*dt+b*dt-z(n)*dt)*x(n)^2*y(n)
    ;   + (a*dt-2*dt)*x(n)*y(n)^2
    ;   + (z(n)*dt-b*dt)*y(n)^3) / (2 * (x(n)^2+y(n)^2))
    ;  y(n+1) = y(n) +((b*dt-z(n)*dt)*x(n)^3
    ;   + (a*dt-2*dt)*x(n)^2*y(n)
    ;    + (-2*a*dt-b*dt+z(n)*dt)*x(n)*y(n)^2
    ;    - a*dt*y(n)^3) / (2 * (x(n)^2+y(n)^2))
    ;  z(n+1) = z(n) +(2*x(n)*dt*x(n)^2*y(n)
    ;   - 2*x(n)*dt*y(n)^3
    ;   - c*dt*z(n))
    ;
    ;Optimized one:

    #z=x+flip(y)
    xx=x^3
    yy=y^3
    temp2=zz-b
    tempz=dt*.5/|#z|*(flip(#z*(a-2+flip(a+a-temp2))*x*y) \
      -(xx+flip(yy))*(a+flip(temp2)))

    zz=zz+dt*(2*(xx*y-x*yy) - c*zz)
    x=x+real(tempz)
    y=y+imag(tempz)

  elseif @type==14 ;Martin
    xx=x
    x=y-sin(x)
    y=a-xx
  elseif @type==15 ;Mira
    xx=x
    x=b*y+d
    temp=x*x
    d=a*x+c*temp/(1+temp)
    y=d-xx



  elseif @type==16 ;Peitgen
    xx=x
    if x<=0
      x=(2-a)*x - y
    elseif x>=b
      x=(2-a)*x - y - d
    else
      x=(2-a*c)*x - y
    endif
    y=xx
  elseif @type==17 ;Pickover
    xx=x
    x=sin(a*y)-zz*cos(b*x)
    y=zz*sin(c*xx)-cos(d*y)
    zz=sin(xx)
  elseif @type==18 ;Popcorn
    xx=x
    x=x-dt*sin(y+tan(a*y))
    y=y-dt*sin(xx+tan(a*xx))
  elseif @type==19 ;Quadrupto
    if x==0
      x=1e-50
    endif
    xx=x
    x=y-x/abs(x)*sin(log(abs(b*x-c))) \
           *atan(sqr(log(abs(c*x-b))))
    y=a-xx
  elseif @type==20 ;Rossler3d
    xx=x
    x=x-dt*(y+zz)
    y=y+dt*(xx+a*y)
    zz=zz+dt*(b+(xx-c)*zz)
  elseif @type==21 ;Threeply
    if x==0
      x=1e-50
    endif
    xx=x
    x=y-x/abs(x)*(abs(sin(x)*d+c-x*b))
    y=a-xx
  elseif @type==22 ;Unity
    temp=a-|x+flip(y)|
    y=temp*x
    x=temp*y
  elseif @type==23 ;Verhulst
    xx=x
    x=y
    y=a*y*(1-xx^2)
  elseif @type==24 ;Vine
    xx=x
    x=x-dt*sin(y+sin(a*y))
    y=y+dt*sin(xx+sin(a*xx))
  elseif @type==25 ;Vine2
    xx=x
    x=x-dt*sin(y+sin(b*(y+sin(a*y))))
    y=y+dt*sin(xx+sin(b*(xx+sin(a*xx))))
  elseif @type==26 ;VineX
    xx=y
    yy=x
    int i=0
    while i<round(b)
      xx=y+sin(a*xx)
      yy=x+sin(a*yy)
      i=i+1
    endwhile
    x=x-dt*sin(xx)
    y=y+dt*sin(yy)
  elseif @type==27 ;VinePwr
    xx=x
    x=x-dt*sin(y^b+sin(a*y))
    y=y+dt*sin(xx^b+sin(a*xx))
  elseif @type==28 ;Volterra-Lotka
    ;Original formula:
    ; x = x+a * (x-xy + ((x+b*(x-xy))-(x+b*(x-xy))*(y+b*(xy-y))) )
    ; y = y+a * (xy-y + ((x+b*(x-xy))*(y+b*(xy-y))-(y+b*(xy-y))) )
    ;
    ;Optimized one:

    rad=x*y
    xx=x-rad
    yy=rad-y
    temp=(x+b*xx)
    temp2=(y+b*yy)
    rad=temp*temp2
    x=x+a*(xx+(temp-rad))
    y=y+a*(yy+(rad-temp2))
  endif

  ;is lorenz3d or pickover or rossler3d ?
  if @type>=10 && @type<=13 || @type==17 || @type==20

    if @view==1     ;xz top
      #z=x+flip(zz)
    elseif @view==2 ;zy right
      #z=zz+flip(y)
    elseif @view==3 ;yz right flip
      #z=y+flip(zz)
    elseif @view==4 ;manual rotation
      #z=(zz+flip(y)) * 1i^(real(@rotxy)/90)          ;(z,y)
      temp=imag(#z)
      #z=(x+flip(real(#z))) * 1i^(imag(@rotxy)/90)    ;(x,z)
      #z=(real(#z)+flip(temp)) * 1i^(@rotz/90) ;(x,y)
    else            ;xy front
      #z=x+flip(y)
    endif

  else
    #z=x+flip(y)
  endif

  iter=iter+1

  ;is Orad or Test ?
  if @outcol==2 || @incol==2
    rad=cabs(#z)
  endif

  if iter>@skip
    if @bailout>0
      if |#z|>@bailout
        done=true
      endif
    elseif @bailout<0
      if |#z-oldz|<-@bailout
        done=true
      endif
    endif

    if cabs(#pixel-#z)<@dist

      pixelhits=pixelhits+1

      if @outcol==0      ;Hits
        if @limit>0
          lasthit=pixelhits/@limit
          if lasthit>.99
            lasthit=.99
            done=true
          endif
        else
          lasthit=pixelhits/20
        endif
      elseif @outcol==1  ;Ospeed
        lasthit=cabs(oldz-#z)
      elseif @outcol==2  ;Orad
        lasthit=abs(oldrad-rad)
      elseif @outcol==3  ;Oang
        lasthit=abs(atan2(-#z/oldz)+#pi)*(0.9975/#pi/2)
      elseif @outcol==4  ;Odir
        lasthit=abs(atan2(-(#z-oldz)/(oldz-oldz2))+#pi)*(0.9975/#pi/2)
      elseif @outcol==5  ;Odist
        lasthit=cabs(#z-#pixel)*100
      elseif @outcol==6  ;Ang
        lastz=abs(atan2(-#z)+#pi)*(0.9975/#pi/2)
      elseif @outcol==7  ;Dir
        lastz=abs(atan2(-#z+oldz)+#pi)*(0.9975/#pi/2)
      elseif @outcol==8  ;Opos
        lastz=#z
      elseif @outcol==9  ;Depth
        lasthit=10+zz
      elseif @outcol==10 ;3Dist
        lasthit=sqrt(|#z|+zz^2)*100
      elseif @outcol==11 ;XZpos
        lastz=x+flip(zz)
      elseif @outcol==12 ;YZpos
        lastz=y+flip(zz)
      endif

    endif

  endif

  ;if last iter is reached and there are
  ;no pixel hits, the pixel becomes 'inside'
  if iter==#maxiter || done

    if pixelhits>0 || done
      ;is Ang or Dir or Opos or XZpos or YZpos ?
      if @outcol>=6 && @outcol<=8 || @outcol==11 || @outcol==12
        #z=lastz
      else
        #z=lasthit
      endif
      done=true
    else
      if @incol==0      ;Off
        #z=(0,0)
      elseif @incol==1  ;Ospeed
        #z=cabs(oldz-#z)
      elseif @incol==2  ;Orad
        #z=abs(oldrad-rad)
      elseif @incol==3  ;Oang
        #z=abs(atan2(-#z/oldz)+#pi)*(0.9975/#pi/2)
      elseif @incol==4  ;Odir
        #z=abs(atan2(-(#z-oldz)/(oldz-oldz2))+#pi)*(0.9975/#pi/2)
      elseif @incol==5  ;Odist
        #z=cabs(#z-#pixel)
      elseif @incol==6  ;Ang
        #z=abs(atan2(-#z)+#pi)*(0.9975/#pi/2)
      elseif @incol==7  ;Dir
        #z=abs(atan2(-#z+oldz)+#pi)*(0.9975/#pi/2)
;      elseif @incol==8  ;Opos
;        #z=#z
      elseif @incol==9  ;Depth
        #z=10+zz
      elseif @incol==10 ;3Dist
        #z=sqrt(|#z|+zz^2)
      elseif @incol==11 ;XZpos
        #z=real(#z)+flip(zz)
      elseif @incol==12 ;YZpos
        #z=imag(#z)+flip(zz)
      endif
    endif

  endif

  ;is Odir ?
  if @outcol==4 || @incol==4
    oldz2=oldz
  endif

  ;is Orad or Rad?
  if @outcol==2 || @incol==2
    oldrad=rad
  endif

  ;is Ospeed or Oang or Odir or bailout<0
  if @outcol==1 || @outcol==3 || @outcol==4 || @outcol==7 || \
    @incol==1  || @incol==3 ||  @incol==4 || @incol==7 || \
    @bailout<0
    oldz=#z
  endif
bailout:
  done==false
default:
  title = "Attractors"
  center = (0.0, 0.0)
  magn=0.75
  maxiter = 100
  periodicity = 0
  method = multipass

  param type
    caption="Attractor type"
    enum="Chip" \
         "Dynamic system" \
         "Gingerbreadman" \
         "Gnarl" \
         "Hénon" \
         "Hopalong" \
         "Implicit Euler approximation" \
         "Kamtorus" \
         "Latööcarfian" \
         "Latööcarfian InvX" \
         "Lorenz3d" \
         "Lorenz3d (1 lobe)" \
         "Lorenz3d (3 lobes)" \
         "Lorenz3d (4 lobes)" \
         "Martin" \
         "Mira" \
         "Peitgen" \
         "Pickover" \
         "Popcorn" \
         "Quadruptwo" \
         "Rossler3d" \
         "Threeply" \
         "Unity" \
         "Verhulst" \
         "Vine" \
         "Vine2" \
         "VineX" \
         "VinePwr" \
         "Volterra-Lotka"
    hint="See ''mjd.txt'' for a table of what every attractor uses \
      (defaults, parameters, functions etc.)"
    default=0
  endparam

  param preset
    caption="Param preset"
    enum="Manual" \
         "Default 1" \

         "Default 2" \
         "Default 3" \
         "Default 4" \
         "Default 5" \
         "Default 6" \
         "Default 7" \
         "Default 8" \
         "Default 9" \
         "Default 10"
    hint="Not all attractors use all the default options. In fact, \
      the only attractor that uses more than 3 defaults is ''Mira'', \
      which uses all."
    default=1
  endparam

  param incol
    caption="I: Inside coloring"
    enum="Off" \
         "Last orbit speed" \
         "Last orbit rad. speed" \
         "Last orbit ang. speed" \
         "Last orbit dir. speed" \
         "Last orbit distance" \
         "Last orbit angle" \
         "Last orbit direction" \
         "Last orbit position" \
         "Last 3D orbit depth" \
         "Last 3D orbit distance" \
         "Last 3D orbit XZ pos" \
         "Last 3D orbit YZ pos"
    hint="The 3D options except for 'distance' will only wirk with \
      Pickover, Lorenz3D and Rossler3D attractors."
    default=5
  endparam
  param outcol
    caption="O: Outside coloring"
    enum="Number of hits" \
         "Orbit speed" \
         "Orbit radial speed" \
         "Orbit angular speed" \
         "Orbit directional speed" \
         "Orbit distance" \
         "Orbit angle" \
         "Orbit direction" \
         "Orbit position" \
         "3D orbit depth" \
         "3D orbit distance" \
         "3D orbit XZ position" \
         "3D orbit YZ position"
    default=0
    hint="In order to turn off outside coloring, set Pixel trap \
      radius and Bailout to zero"
  endparam

  param limit
    caption="O: Limit hits (0=off)"
    default=20
    hint="When the Outside coloring mode ''Number of hits'' is \
      selected, the pixel is colored in relation to the number of \
      times the orbit is trapped. To prevent colors from wrapping, \
      this number of hits and above become color index 399."
  endparam

  param dist
    caption="O: Pixel trap radius"
    default=0.0
    hint="If the orbit comes this close to the pixel, the outside \
      coloring value is calculated. Then, when bailed out or when \
      maxiter is reached, the pixel becomes ''outside'' and the value \
      is passed to the outside coloring."
  endparam

  param bailout
    caption="O: Bailout"
    default=0.0
    hint="Use negative values to bailout on a |z-oldz| basis."
  endparam

  param skip
    caption="O: Iteration skip"
    default=0
    hint="The number of iterations to skip before checking any kind \
      of outside"
  endparam

  param pa
    caption="Param A"
    default=1.0
  endparam
  param pb
    caption="Param B"
    default=1.0
  endparam
  param pc
    caption="Param C"
    default=1.0
  endparam
  param pd
    caption="Param D"
    default=1.0
  endparam
  param pdt
    caption="Param dt"
    default=0.1
  endparam

  param start
    caption="S: Orbit start"
    enum="Pixel (except Z)" \
         "Zero" \
         "One" \
         "Manual" \
         "Manual (relative)" \
         "Manual (scaling)" \
         "Attractor Default"
    default=6
  endparam
  param xystart
    caption="S: Manual XY start"
    default=(0,0)
  endparam
  param zstart
    caption="S: Manual Z start"
    default=0.0
  endparam

  param view
    caption="R: 3D orbit view"
    enum="(X,Y) Front" \
         "(X,Z) Top" \
         "(Z,Y) Right" \
         "(Y,Z) Right, flipped" \
         "Manual rotation"
    default=0
    hint="Only available for Pickover, Lorenz3D and Rossler3D \
      attractors."
  endparam

  param rotxy
    caption="R: Manual XY rotation"
    default=(60,30)
    hint="Only active when 3D orbit view is set to Manual"
  endparam
  param rotz
    caption="R: Manual Z rotation"
    default=0.0
    hint="Only active when 3D orbit view is set to Manual"
  endparam
}

c[z²+1/z²]J { ;20010118
; Made by Mark Jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
init:
  #z=#pixel
loop:
  complex z2=#z^2
  #z=@seed*(z2 + 1/z2)
bailout:
  |#z|<@bailout
default:
  title="c(z²+1/z²) Julia"
  magn=.5
  param seed
    caption="Julia seed"
    default=(.58,0)
  endparam
  param bailout
    caption="Bailout"
    default=4.0
  endparam
switch:
  type="c[z²+1/z²]M"
  @start=#pixel
  @bailout=bailout
  @fnz=fnz
}

c[z²+1/z²]M { ;20010109
; Made by Mark Jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
;
; Last modification: 20010118 added julia type and switch
init:
  #z=@start
  complex c=#pixel
loop:
  complex z2=#z^2
  #z=c*(z2 + 1/z2)
bailout:
  |#z|<@bailout
default:
  title="c(z²+1/z²) Mandel"
  magn=2
  param start
    caption="Perturbation"
    default=(1,0)
  endparam
  param bailout
    caption="Bailout"
    default=4.0
  endparam
switch:
  type="c[z²+1/z²]J"
  @seed=#pixel
  @bailout=bailout
  @fnz=fnz
}

c+pi*sinzJ{ ;20010118
; Made by Mark Jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
init:
  #z=#pixel
loop:
  #z=@seed+#pi*@fnz(#z)
bailout:
  |imag(#z)|<@bailout
default:
  title="c+pi*fnz Julia"
  magn=0.666666666666666666666666666666667
  param seed
    caption="Julia seed"
    default=(1,.2)
  endparam
  param bailout
    caption="Bailout"
    default=15.0
  endparam
  func fnz
    caption="z function"
    default=sin()
  endfunc
switch:
  type="c+pi*sinzM"
  @start=#pixel
  @bailout=bailout
  @fnz=fnz
}

c+pi*sinzM{ ;20010109
;Made by Mark Jeronimus <Mark.Jeronimus@hva.nl>
;© 2000 Mark Jeronimus
;Last modification: 20010118 added julia type and switch
init:
  #z=@start
loop:
  #z=#pixel+#pi*@fnz(#z)
bailout:
  |imag(#z)|<@bailout
default:
  title="c+pi*fnz Mandel"
  magn=0.666666666666666666666666666666667
  param start
    caption="Perturbation"
    default=(1.57079632679489661923132169163975,0)
  endparam
  param bailout
    caption="Bailout"
    default=15.0
  endparam
  func fnz
    caption="z function"
    default=sin()
  endfunc
switch:
  type="c+pi*sinzJ"
  @seed=#pixel
  @bailout=bailout
  @fnz=fnz
}

Octageo1Map{ ;
; Made by Mark Jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
init:
  bool x=false
  bool y=false
  bool xy=false
  bool yx=false
  float rot=0

  #z=@start
loop:
  x=real(#z)>0
  y=imag(#z)>0
  xy=imag(#z)+real(#z)>0
  yx=imag(#z)-real(#z)>0
  
  if x && yx
    rot=.75
  elseif y && !yx
    rot=.25
  elseif !y && xy
    rot=3.75
  elseif x && !xy
    rot=3.25
  elseif !x && !yx
    rot=2.75
  elseif !y && yx
    rot=2.25
  elseif y && !xy
    rot=1.75
  else
    rot=1.25
  endif
  #z=#z+#pixel*1i^rot
  #z=sqr(#z)+@seed
bailout:
  |#z|<@bailout
default:
  title="Octageo1 Map"
  method=multipass
  param start
    caption="Mandel Map"
    default=(0,0)
  endparam
  param seed
    caption="Julia seed"
    default=(0,0)
  endparam
  param bailout
    caption="Bailout"
    default=65536.0
  endparam
switch:
  type="Octageo2Mandel"
  start=start
  shift=#pixel
  bailout=bailout  
}

Octageo2Mandel{ ;
; Made by Mark Jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
init:
  bool x=false
  bool y=false
  bool xy=false
  bool yx=false
  float rot=0

  #z=@start
loop:
  x=real(#z)>0
  y=imag(#z)>0
  xy=imag(#z)+real(#z)>0
  yx=imag(#z)-real(#z)>0
  
  if x && yx
    rot=.75
  elseif y && !yx
    rot=.25
  elseif !y && xy
    rot=3.75
  elseif x && !xy
    rot=3.25
  elseif !x && !yx
    rot=2.75
  elseif !y && yx
    rot=2.25
  elseif y && !xy
    rot=1.75
  else
    rot=1.25
  endif
  #z=#z+@shift*1i^rot
  #z=sqr(#z)+#pixel
bailout:
  |#z|<@bailout
default:
  title="Octageo2 Mandel"
  method=multipass
  param start
    caption="Mandel Map"
    default=(0,0)
  endparam
  param shift
    caption="Orbit shift"
    default=(0,0)
  endparam
  param bailout
    caption="Bailout"
    default=65536.0
  endparam
switch:
  type="Octageo3Julia"
  seed=#pixel
  shift=shift
  bailout=bailout  
}

Octageo3Julia{ ;
; Made by Mark Jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
init:
  bool x=false
  bool y=false
  bool xy=false
  bool yx=false
  float rot=0

  #z=#pixel
loop:
  x=real(#z)>0
  y=imag(#z)>0
  xy=imag(#z)+real(#z)>0
  yx=imag(#z)-real(#z)>0
  
  if x && yx
    rot=.75
  elseif y && !yx
    rot=.25
  elseif !y && xy
    rot=3.75
  elseif x && !xy
    rot=3.25
  elseif !x && !yx
    rot=2.75
  elseif !y && yx
    rot=2.25
  elseif y && !xy
    rot=1.75
  else
    rot=1.25
  endif
  #z=#z+@shift*1i^rot
  #z=sqr(#z)+@seed
bailout:
  |#z|<@bailout
default:
  title="Octageo3 Julia"
  method=multipass
  param seed
    caption="Julia seed"
    default=(0,0)
  endparam
  param shift
    caption="Orbit shift"
    default=(0,0)
  endparam
  param bailout
    caption="Bailout"
    default=65536.0
  endparam
switch:
  type="Octageo1Map"
  start=#pixel
  seed=seed
  bailout=bailout  
}

fn(z-p)fn(z+p)+cJ {; 20040119
; Made by Mark Jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
init:
  z=#pixel
loop:
  z=fn1(z+@p)*fn2(z-@p)+@start
bailout:
  |z|<@bailout
default:
  title = "fn(z-p)fn(z+p)+c Julia"
  param start
    caption="Seed"
    default=(0,0)
  endparam
  param p
    caption="Parameter"
    default=(0.3,0.6)
  endparam
  param bailout
    default=4
  endparam
  func fn1
    default=sin()
  endfunc
  func fn2
    default=sin()
  endfunc
switch:
  type="fn(z-p)fn(z+p)+cM"
  p=@p
  bailout=@bailout
}

fn(z-p)fn(z+p)+cM {; 20040119
; Made by Mark Jeronimus <Mark.Jeronimus@hva.nl>
; © 2000 Mark Jeronimus
init:
  z=#pixel+@start
  c=#pixel
loop:
  z=fn1(z+@p)*fn2(z-@p)+c
bailout:
  |z|<@bailout
default:
  title = "fn(z-p)fn(z+p)+c Mandel"
  param start
    default=(0,0)
  endparam
  param p
    caption="Parameter"
    default=(.3,.6)
  endparam
  param bailout
    default=4
  endparam
  func fn1
    default=sin()
  endfunc
  func fn2
    default=sin()
  endfunc
switch:
  type="fn(z-p)fn(z+p)+cJ"
  start=#pixel
  p=@p
  bailout=@bailout
}