This digital works is created exclusively from fractals, with 0% AI generated. It can therefore be converted into a set of functions and parameters that can be the basis for the training of an AI.

The mathematical formulas and parameter combinations corresponding to each fractal are presented below. In each case, the numerical characters have been replaced by ■ to prevent unauthorized reproduction. If you are interested in using the full data set to train an AI, please contact Philippe.

Fractal_■■■_B {
fractal:
  title="Fractal_■■■_B" width=■■■■ height=■■■■ layers=■
  credits="Philoxerax;■/■■/■■■■"
layer:
  caption="Background" opacity=■■ visible=no mergemode=lighten
mapping:
  center=-■.■■■■■■■■■■■■■■/■.■■■■■■■■■■■■ magn=■.■■■■■■■ angle=■■.■■■■
formula:
  maxiter=■■■ filename="mt.ufm" entry="mt-barnsleyish-j" p_c=■/■.■■
  p_threshold=■ p_bailout=■.■ f_fn■=cos
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  smooth=yes rotation=■■ index=■ color=■■■■■■■ index=■■ color=■■■■■■■■
  index=■■ color=■■■■■■■■ index=■■ color=■ index=■■ color=■■■■■■■■
  index=■■ color=■■■■■■■■ index=■■ color=■■■■■■■■ index=■■
  color=■■■■■■ index=■■ color=■■■■■■■ index=■■ color=■■■■■■■■ index=■■
  color=■■■■■■■ index=■■ color=■■■■■■ index=■■ color=■■■■■■■ index=■■
  color=■■■■■■■ index=■■ color=■■■■■■■■ index=■■ color=■■■■■■■■
  index=■■ color=■■■■■■■■ index=■■ color=■■■■■■■ index=■■ color=■■■■■■
  index=■■■ color=■■■■■■■ index=■■■ color=■■■■■■■ index=■■■
  color=■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■
  index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■
  color=■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■■
  index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■ index=■■■
  color=■■■■■■■■ index=■■■ color=■■■■■■■ index=■■■ color=■■■■■■■
  index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■
  color=■■■■■■■■ index=■■■ color=■ index=■■■ color=■■■■■■■■ index=■■■
  color=■■■■■■■■ index=■■■ color=■■■■■■■ index=■■■ color=■■■■■■■■
  index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■ index=■■■
  color=■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■
  index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■
  color=■■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■
  index=-■■■ color=■■■■■■■■ index=-■■ color=■■■■■■■ index=-■■
  color=■■■■■■■■ index=-■■ color=■■■■■■■■ index=-■■ color=■■■■■■
  index=-■■ color=■■■■■■■ index=-■■ color=■■■■■■■■ index=-■■
  color=■■■■■■■ index=-■■ color=■■■■■■■■ index=-■■ color=■■■■■■■■
  index=-■■ color=■■■■■■■■ index=-■■ color=■■■■■■■ index=-■■
  color=■■■■■■■ index=-■■ color=■■■■■■■ index=-■■ color=■■■■■■■
  index=-■■ color=■■■■■■■ index=-■ color=■■■■■■■ index=-■
  color=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■ mergemode=overlay
mapping:
  center=-■■.■■■■■■■■■/■■.■■■■■■■■■ magn=■.■■■■■■■■ angle=■.■■■■
formula:
  maxiter=■■■ filename="lkm■.ufm" entry="fourier-popcorn"
  p_control_type=basic p_bailout=■■■■ p_hall=■.■■■/■
  p_functypeall="sin general" p_powerall=■/■ p_ntermall=■■
  p_slopeall=■/■ f_funcall=tanh p_hx=■.■/■ p_vartypexin=y
  p_functypexin="cos odd pos" p_powerxin=■/■ p_ntermxin=■■
  f_funcxin=cos p_vartypexout=y p_functypexout="cos odd pos"
  p_powerxout=■/■ p_ntermxout=■■ p_slopexout=■/■ f_funcxout=cos
  p_hy=■.■/■ p_vartypeyin=x p_functypeyin="sin odd pos" p_poweryin=■/■
  p_ntermyin=■■ f_funcyin=sin p_vartypeyout=x
  p_functypeyout="sin odd pos" p_poweryout=■/■ p_ntermyout=■■
  p_slopeyout=■/■ f_funcyout=sin
inside:
  transfer=none solid=■■■■■■■■■■
outside:
  transfer=linear
gradient:
  smooth=yes rotation=-■■■ index=■■ color=■■■■■■■ index=■■■ color=■■■
  index=-■■■ color=■■■■■■■ index=-■■ color=■■■■■■■ index=-■
  color=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Background" opacity=■■■
mapping:
  center=-■■.■■■■■■■■■■/■■.■■■■■■■■■ magn=■.■■■■■■■■ angle=■■■
formula:
  maxiter=■■■ filename="lkm■.ufm" entry="fourier-popcorn"
  p_control_type=basic p_bailout=■■■■ p_hall=■.■■■/■
  p_functypeall="sin general" p_powerall=■/■ p_ntermall=■■
  p_slopeall=■/■ f_funcall=tanh p_hx=■.■/■ p_vartypexin=y
  p_functypexin="cos odd pos" p_powerxin=■/■ p_ntermxin=■■
  f_funcxin=cos p_vartypexout=y p_functypexout="cos odd pos"
  p_powerxout=■/■ p_ntermxout=■■ p_slopexout=■/■ f_funcxout=cos
  p_hy=■.■/■ p_vartypeyin=x p_functypeyin="sin odd pos" p_poweryin=■/■
  p_ntermyin=■■ f_funcyin=sin p_vartypeyout=x
  p_functypeyout="sin odd pos" p_poweryout=■/■ p_ntermyout=■■
  p_slopeyout=■/■ f_funcyout=sin
inside:
  transfer=none solid=■■■■■■■■■■
outside:
  transfer=linear
gradient:
  smooth=yes rotation=-■■■ index=■■ color=■■■■■■■ index=■■■ color=■■■
  index=-■■■ color=■■■■■■■ index=-■■ color=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
}

mt-barnsleyish-j { ; Mark Townsend, ■■ May ■■■■
init:
  z = #pixel
loop:
  if real(z) >= @threshold
    z = @fn■(z + ■) ■ -@c
  else  
    z = @fn■(z - ■) ■ @c
  endif  
bailout:
  |z| < @bailout
default:
  title = "Barnsleyish Julia"
  param c
    caption = "Julia Seed"
    default = (■.■, ■.■■)
  endparam  
  param threshold
    caption = "Threshold"
    default = ■.■
  endparam  
  param bailout
    caption = "Bailout Value"
    default = ■.■
  endparam  
  func fn■
    caption = "Function"
    default = cos()
  endfunc  
switch:
  type = "mt-barnsleyish-m"  
  bailout = bailout
  threshold = threshold
  fn■ = fn■
}

fourier-popcorn { ; Kerry Mitchell ■■May■■■■
;
; This is a complex-valued implementation and generalization
; of Cliff Pickover's "popcorn" algorithm.  His method iterates
; ■ real variables like this:
;
; xnew = xold - h ■ sin(a■y + tan(b■y))
; ynew = yold - h ■ sin(a■x + tan(b■x))
;
; where a = ■. The current method generalizes the above by:
;   using truncated Fourier series instead of just single sin or tan function
;   allowing for complex values of a (slope)
;   having the same Fourier series parameters (basic controls) or
;   having different parameters for the ■ series (x inner, x outer,
;     y inner, and y outer)
;
init:
  complex temp=(■,■)
  complex tempx=(■,■)
  complex tempy=(■,■)
  complex temp■=(■,■)
  complex temp■x=(■,■)
  complex temp■y=(■,■)
  complex tempin=(■,■)
  complex tempinx=(■,■)
  complex tempiny=(■,■)
  complex tempout=(■,■)
  complex tempoutx=(■,■)
  complex tempouty=(■,■)
  complex x=real(#pixel)
  complex y=imag(#pixel)
  complex xnew=(■,■)
  complex ynew=(■,■)
  complex z=#pixel
  int iterm=■
  int jterm=■
  int parity=■
loop:
;
; basic controls
;
  if(@control_type=="basic")
;
; choose what inner variable to use
;
  tempinx=y
  tempiny=x
;
; compute the inner Fourier series
;
  tempx=■
  tempy=■
  iterm=■
  while(iterm<@ntermall)
    iterm=iterm+■
    if(@functypeall=="sin odd pos")
      jterm=■■iterm-■
      tempx=tempx+sin(tempinx■jterm)/(jterm^@powerall)
      tempy=tempy+sin(tempiny■jterm)/(jterm^@powerall)
    elseif(@functypeall=="cos odd pos")
      jterm=■■iterm-■
      tempx=tempx+cos(tempinx■jterm)/(jterm^@powerall)
      tempy=tempy+cos(tempiny■jterm)/(jterm^@powerall)
    elseif(@functypeall=="sin all pos")
      jterm=iterm
      tempx=tempx+sin(tempinx■jterm)/(jterm^@powerall)
      tempy=tempy+sin(tempiny■jterm)/(jterm^@powerall)
    elseif(@functypeall=="cos all pos")
      jterm=iterm
      tempx=tempx+cos(tempinx■jterm)/(jterm^@powerall)
      tempy=tempy+cos(tempiny■jterm)/(jterm^@powerall)
    elseif(@functypeall=="sin odd alt")
      jterm=■■iterm-■
      parity=(iterm%■)■■-■
      tempx=tempx+parity■sin(tempinx■jterm)/(jterm^@powerall)
      tempy=tempy+parity■sin(tempiny■jterm)/(jterm^@powerall)
    elseif(@functypeall=="cos odd alt")
      jterm=■■iterm-■
      parity=(iterm%■)■■-■
      tempx=tempx+parity■cos(tempinx■jterm)/(jterm^@powerall)
      tempy=tempy+parity■cos(tempiny■jterm)/(jterm^@powerall)
    elseif(@functypeall=="sin all alt")
      jterm=iterm
      parity=(iterm%■)■■-■
      tempx=tempx+parity■sin(tempinx■jterm)/(jterm^@powerall)
      tempy=tempy+parity■sin(tempiny■jterm)/(jterm^@powerall)
    elseif(@functypeall=="cos all alt")
      jterm=iterm
      parity=(iterm%■)■■-■
      tempx=tempx+parity■cos(tempinx■jterm)/(jterm^@powerall)
      tempy=tempy+parity■cos(tempiny■jterm)/(jterm^@powerall)
    elseif(@functypeall=="sin general")
      jterm=iterm
      tempx=tempx+@funcall(jterm)■sin(tempinx■jterm)/(jterm^@powerall)
      tempy=tempy+@funcall(jterm)■sin(tempiny■jterm)/(jterm^@powerall)
    elseif(@functypeall=="cos general")
      jterm=iterm
      tempx=tempx+@funcall(jterm)■cos(tempinx■jterm)/(jterm^@powerall)
      tempy=tempy+@funcall(jterm)■cos(tempiny■jterm)/(jterm^@powerall)
    endif
  endwhile
;
; choose what outer variable to use
;
  tempoutx=y
  tempouty=x
;
; compute the outer Fourier series
;
  temp■x=■
  temp■y=■
  iterm=■
  while(iterm<@ntermall)
    iterm=iterm+■
    if(@functypeall=="sin odd pos")
      jterm=■■iterm-■
      temp■x=temp■x+sin((@slopeall■tempoutx+tempx)■jterm)/(jterm^@powerall)
      temp■y=temp■y+sin((@slopeall■tempouty+tempy)■jterm)/(jterm^@powerall)
    elseif(@functypeall=="cos odd pos")
      jterm=■■iterm-■
      temp■x=temp■x+cos((@slopeall■tempoutx+tempx)■jterm)/(jterm^@powerall)
      temp■y=temp■y+cos((@slopeall■tempouty+tempy)■jterm)/(jterm^@powerall)
    elseif(@functypeall=="sin all pos")
      jterm=iterm
      temp■x=temp■x+sin((@slopeall■tempoutx+tempx)■jterm)/(jterm^@powerall)
      temp■y=temp■y+sin((@slopeall■tempouty+tempy)■jterm)/(jterm^@powerall)
    elseif(@functypeall=="cos all pos")
      jterm=iterm
      temp■x=temp■x+cos((@slopeall■tempoutx+tempx)■jterm)/(jterm^@powerall)
      temp■y=temp■y+cos((@slopeall■tempouty+tempy)■jterm)/(jterm^@powerall)
    elseif(@functypeall=="sin odd alt")
      jterm=■■iterm-■
      parity=(iterm%■)■■-■
      temp■x=temp■x+parity■sin((@slopeall■tempoutx+tempx)■jterm)/(jterm^@powerall)
      temp■y=temp■y+parity■sin((@slopeall■tempouty+tempy)■jterm)/(jterm^@powerall)
    elseif(@functypeall=="cos odd alt")
      jterm=■■iterm-■
      parity=(iterm%■)■■-■
      temp■x=temp■x+parity■cos((@slopeall■tempoutx+tempx)■jterm)/(jterm^@powerall)
      temp■y=temp■y+parity■cos((@slopeall■tempouty+tempy)■jterm)/(jterm^@powerall)
    elseif(@functypeall=="sin all alt")
      jterm=iterm
      parity=(iterm%■)■■-■
      temp■x=temp■x+parity■sin((@slopeall■tempoutx+tempx)■jterm)/(jterm^@powerall)
      temp■y=temp■y+parity■sin((@slopeall■tempouty+tempy)■jterm)/(jterm^@powerall)
    elseif(@functypeall=="cos all alt")
      jterm=iterm
      parity=(iterm%■)■■-■
      temp■x=temp■x+parity■cos((@slopeall■tempoutx+tempx)■jterm)/(jterm^@powerall)
      temp■y=temp■y+parity■cos((@slopeall■tempouty+tempy)■jterm)/(jterm^@powerall)
    elseif(@functypeall=="sin general")
      jterm=iterm
      temp■x=temp■x+@funcall(jterm)■sin((@slopeall■tempoutx+tempx)■jterm)/(jterm^@powerall)
      temp■y=temp■y+@funcall(jterm)■sin((@slopeall■tempouty+tempy)■jterm)/(jterm^@powerall)
    elseif(@functypeall=="cos general")
      jterm=iterm
      temp■x=temp■x+@funcall(jterm)■cos((@slopeall■tempoutx+tempx)■jterm)/(jterm^@powerall)
      temp■y=temp■y+@funcall(jterm)■cos((@slopeall■tempouty+tempy)■jterm)/(jterm^@powerall)
    endif
  endwhile
  xnew=x+@hall■temp■x
  ynew=y+@hall■temp■y
  x=xnew
  y=ynew
  z=x+flip(y)
;
; advanced controls
;
  else
;
; x equation
;
;   choose what inner variable to use
;
  if(@vartypexin=="x")
    tempin=x
  elseif(@vartypexin=="y")
    tempin=y
  elseif(@vartypexin=="x+y")
    tempin=x+y
  elseif(@vartypexin=="y-x")
    tempin=y-x
  elseif(@vartypexin=="x■y")
    tempin=x■y
  elseif(@vartypexin=="y/x")
    tempin=y/x
  endif
;
;   compute the inner Fourier series
;
  temp=■
  iterm=■
  while(iterm<@ntermxin)
    iterm=iterm+■
    if(@functypexin=="sin odd pos")
      jterm=■■iterm-■
      temp=temp+sin(tempin■jterm)/(jterm^@powerxin)
    elseif(@functypexin=="cos odd pos")
      jterm=■■iterm-■
      temp=temp+cos(tempin■jterm)/(jterm^@powerxin)
    elseif(@functypexin=="sin all pos")
      jterm=iterm
      temp=temp+sin(tempin■jterm)/(jterm^@powerxin)
    elseif(@functypexin=="cos all pos")
      jterm=iterm
      temp=temp+cos(tempin■jterm)/(jterm^@powerxin)
    elseif(@functypexin=="sin odd alt")
      jterm=■■iterm-■
      parity=(iterm%■)■■-■
      temp=temp+parity■sin(tempin■jterm)/(jterm^@powerxin)
    elseif(@functypexin=="cos odd alt")
      jterm=■■iterm-■
      parity=(iterm%■)■■-■
      temp=temp+parity■cos(tempin■jterm)/(jterm^@powerxin)
    elseif(@functypexin=="sin all alt")
      jterm=iterm
      parity=(iterm%■)■■-■
      temp=temp+parity■sin(tempin■jterm)/(jterm^@powerxin)
    elseif(@functypexin=="cos all alt")
      jterm=iterm
      parity=(iterm%■)■■-■
      temp=temp+parity■cos(tempin■jterm)/(jterm^@powerxin)
    elseif(@functypexin=="sin general")
      jterm=iterm
      temp=temp+@funcxin(jterm)■sin(tempin■jterm)/(jterm^@powerxin)
    elseif(@functypexin=="cos general")
      jterm=iterm
      temp=temp+@funcxin(jterm)■cos(tempin■jterm)/(jterm^@powerxin)
    endif
  endwhile
;
;   choose what outer variable to use
;
  if(@vartypexout=="x")
    tempout=x
  elseif(@vartypexout=="y")
    tempout=y
  elseif(@vartypexout=="x+y")
    tempout=x+y
  elseif(@vartypexout=="y-x")
    tempout=y-x
  elseif(@vartypexout=="x■y")
    tempout=x■y
  elseif(@vartypexout=="y/x")
    tempout=y/x
  endif
;
;   compute the outer Fourier series
;
  temp■=■
  iterm=■
  while(iterm<@ntermxout)
    iterm=iterm+■
    if(@functypexout=="sin odd pos")
      jterm=■■iterm-■
      temp■=temp■+sin((@slopexout■tempout+temp)■jterm)/(jterm^@powerxout)
    elseif(@functypexout=="cos odd pos")
      jterm=■■iterm-■
      temp■=temp■+cos((@slopexout■tempout+temp)■jterm)/(jterm^@powerxout)
    elseif(@functypexout=="sin all pos")
      jterm=iterm
      temp■=temp■+sin((@slopexout■tempout+temp)■jterm)/(jterm^@powerxout)
    elseif(@functypexout=="cos all pos")
      jterm=iterm
      temp■=temp■+cos((@slopexout■tempout+temp)■jterm)/(jterm^@powerxout)
    elseif(@functypexout=="sin odd alt")
      jterm=■■iterm-■
      parity=(iterm%■)■■-■
      temp■=temp■+parity■sin((@slopexout■tempout+temp)■jterm)/(jterm^@powerxout)
    elseif(@functypexout=="cos odd alt")
      jterm=■■iterm-■
      parity=(iterm%■)■■-■
      temp■=temp■+parity■cos((@slopexout■tempout+temp)■jterm)/(jterm^@powerxout)
    elseif(@functypexout=="sin all alt")
      jterm=iterm
      parity=(iterm%■)■■-■
      temp■=temp■+parity■sin((@slopexout■tempout+temp)■jterm)/(jterm^@powerxout)
    elseif(@functypexout=="cos all alt")
      jterm=iterm
      parity=(iterm%■)■■-■
      temp■=temp■+parity■cos((@slopexout■tempout+temp)■jterm)/(jterm^@powerxout)
    elseif(@functypexout=="sin general")
      jterm=iterm
      temp■=temp■+@funcxout(jterm)■sin((@slopexout■tempout+temp)■jterm)/(jterm^@powerxout)
    elseif(@functypexout=="cos general")
      jterm=iterm
      temp■=temp■+@funcxout(jterm)■cos((@slopexout■tempout+temp)■jterm)/(jterm^@powerxout)
    endif
  endwhile
  xnew=x+@hx■temp■
;
; y equation
;
;   choose what inner variable to use
;
  if(@vartypeyin=="x")
    tempin=x
  elseif(@vartypeyin=="y")
    tempin=y
  elseif(@vartypeyin=="x+y")
    tempin=x+y
  elseif(@vartypeyin=="y-x")
    tempin=y-x
  elseif(@vartypeyin=="x■y")
    tempin=x■y
  elseif(@vartypeyin=="y/x")
    tempin=y/x
  endif
;
;   compute the inner Fourier series
;
  temp=■
  iterm=■
  while(iterm<@ntermyin)
    iterm=iterm+■
    if(@functypeyin=="sin odd pos")
      jterm=■■iterm-■
      temp=temp+sin(tempin■jterm)/(jterm^@poweryin)
    elseif(@functypeyin=="cos odd pos")
      jterm=■■iterm-■
      temp=temp+cos(tempin■jterm)/(jterm^@poweryin)
    elseif(@functypeyin=="sin all pos")
      jterm=iterm
      temp=temp+sin(tempin■jterm)/(jterm^@poweryin)
    elseif(@functypeyin=="cos all pos")
      jterm=iterm
      temp=temp+cos(tempin■jterm)/(jterm^@poweryin)
    elseif(@functypeyin=="sin odd alt")
      jterm=■■iterm-■
      parity=(iterm%■)■■-■
      temp=temp+parity■sin(tempin■jterm)/(jterm^@poweryin)
    elseif(@functypeyin=="cos odd alt")
      jterm=■■iterm-■
      parity=(iterm%■)■■-■
      temp=temp+parity■cos(tempin■jterm)/(jterm^@poweryin)
    elseif(@functypeyin=="sin all alt")
      jterm=iterm
      parity=(iterm%■)■■-■
      temp=temp+parity■sin(tempin■jterm)/(jterm^@poweryin)
    elseif(@functypeyin=="cos all alt")
      jterm=iterm
      parity=(iterm%■)■■-■
      temp=temp+parity■cos(tempin■jterm)/(jterm^@poweryin)
    elseif(@functypeyin=="sin general")
      jterm=iterm
      temp=temp+@funcyin(jterm)■sin(tempin■jterm)/(jterm^@poweryin)
    elseif(@functypeyin=="cos general")
      jterm=iterm
      temp=temp+@funcyin(jterm)■cos(tempin■jterm)/(jterm^@poweryin)
    endif
  endwhile
;
;   choose what outer variable to use
;
  if(@vartypeyout=="x")
    tempout=x
  elseif(@vartypeyout=="y")
    tempout=y
  elseif(@vartypeyout=="x+y")
    tempout=x+y
  elseif(@vartypeyout=="y-x")
    tempout=y-x
  elseif(@vartypeyout=="x■y")
    tempout=x■y
  elseif(@vartypeyout=="y/x")
    tempout=y/x
  endif
;
;   compute the outer Fourier series
;
  temp■=■
  iterm=■
  while(iterm<@ntermyout)
    iterm=iterm+■
    if(@functypeyout=="sin odd pos")
      jterm=■■iterm-■
      temp■=temp■+sin((@slopeyout■tempout+temp)■jterm)/(jterm^@poweryout)
    elseif(@functypeyout=="cos odd pos")
      jterm=■■iterm-■
      temp■=temp■+cos((@slopeyout■tempout+temp)■jterm)/(jterm^@poweryout)
    elseif(@functypeyout=="sin all pos")
      jterm=iterm
      temp■=temp■+sin((@slopeyout■tempout+temp)■jterm)/(jterm^@poweryout)
    elseif(@functypeyout=="cos all pos")
      jterm=iterm
      temp■=temp■+cos((@slopeyout■tempout+temp)■jterm)/(jterm^@poweryout)
    elseif(@functypeyout=="sin odd alt")
      jterm=■■iterm-■
      parity=(iterm%■)■■-■
      temp■=temp■+parity■sin((@slopeyout■tempout+temp)■jterm)/(jterm^@poweryout)
    elseif(@functypeyout=="cos odd alt")
      jterm=■■iterm-■
      parity=(iterm%■)■■-■
      temp■=temp■+parity■cos((@slopeyout■tempout+temp)■jterm)/(jterm^@poweryout)
    elseif(@functypeyout=="sin all alt")
      jterm=iterm
      parity=(iterm%■)■■-■
      temp■=temp■+parity■sin((@slopeyout■tempout+temp)■jterm)/(jterm^@poweryout)
    elseif(@functypeyout=="cos all alt")
      jterm=iterm
      parity=(iterm%■)■■-■
      temp■=temp■+parity■cos((@slopeyout■tempout+temp)■jterm)/(jterm^@poweryout)
    elseif(@functypeyout=="sin general")
      jterm=iterm
      temp■=temp■+@funcyout(jterm)■sin((@slopeyout■tempout+temp)■jterm)/(jterm^@poweryout)
    elseif(@functypeyout=="cos general")
      jterm=iterm
      temp■=temp■+@funcyout(jterm)■cos((@slopeyout■tempout+temp)■jterm)/(jterm^@poweryout)
    endif
  endwhile
  ynew=y+@hy■temp■
  x=xnew
  y=ynew
  z=x+flip(y)
  endif
bailout:
  |z|<@bailout
default:
  title="Fourier Popcorn"
  heading
    text="Uses Cliff Pickover's Popcorn routine, substituting Fourier \
      series for the sine and tangent functions."
  endheading
;
; general parameters
;
  heading
    caption="General parameters"
  endheading
  param control_type
    caption="control type"
    default=■
    enum="basic" "advanced"
  endparam
  float param bailout
    caption="bailout value"
    default=■■■■
  endparam
;
; basic parameters
;
  heading
    caption="Fourier series parameters"
    visible=(@control_type=="basic")
  endheading
  complex param hall
    caption="step size"
    default=■.■
    visible=(@control_type=="basic")
  endparam
  param functypeall
    caption="function type"
    default=■
    enum="sin odd pos" "cos odd pos" "sin all pos" "cos all pos" \
      "sin odd alt" "cos odd alt" "sin all alt" "cos all alt" \
      "sin general" "cos general"
    visible=(@control_type=="basic")
  endparam
  complex param powerall
    caption="power"
    default=■
    visible=(@control_type=="basic")
  endparam
  int param ntermall
    caption="# terms"
    default=■■
    min=■
    visible=(@control_type=="basic")
  endparam
  complex param slopeall
    caption="slope"
    default=■
    visible=(@control_type=="basic")
  endparam
  func funcall
    caption="function"
    default=tan()
    visible=((@control_type=="basic")&&((@functypeall=="sin general")\
      ||(@functypeall=="cos general")))
  endfunc
;
; advanced parameters
;
; x inner parameters
;
  heading
    caption="x inner parameters"
    visible=(@control_type=="advanced")
  endheading
  complex param hx
    caption="step size"
    default=■.■
    visible=(@control_type=="advanced")
  endparam
  param vartypexin
    caption="inner variable type"
    default=■
    enum="x" "y" "x+y" "y-x" "x■y" "y/x"
    visible=(@control_type=="advanced")
  endparam
  param functypexin
    caption="function type"
    default=■
    enum="sin odd pos" "cos odd pos" "sin all pos" "cos all pos" \
      "sin odd alt" "cos odd alt" "sin all alt" "cos all alt" \
      "sin general" "cos general"
    visible=(@control_type=="advanced")
  endparam
  complex param powerxin
    caption="power"
    default=■
    visible=(@control_type=="advanced")
  endparam
  int param ntermxin
    caption="# terms"
    default=■■
    min=■
    visible=(@control_type=="advanced")
  endparam
  func funcxin
    caption="function"
    default=cos()
    visible=((@control_type=="advanced")&&((@functypexin=="sin general")\
      ||(@functypexin=="cos general")))
  endfunc
;
; x outer parameters
;
  heading
    caption="x outer parameters"
    visible=(@control_type=="advanced")
  endheading
  param vartypexout
    caption="outer variable type"
    default=■
    enum="x" "y" "x+y" "y-x" "x■y" "y/x"
    visible=(@control_type=="advanced")
  endparam
  param functypexout
    caption="function type"
    default=■
    enum="sin odd pos" "cos odd pos" "sin all pos" "cos all pos" \
      "sin odd alt" "cos odd alt" "sin all alt" "cos all alt" \
      "sin general" "cos general"
    visible=(@control_type=="advanced")
  endparam
  complex param powerxout
    caption="power"
    default=■
    visible=(@control_type=="advanced")
  endparam
  int param ntermxout
    caption="# terms"
    default=■■
    min=■
    visible=(@control_type=="advanced")
  endparam
  complex param slopexout
    caption="slope"
    default=■
    visible=(@control_type=="advanced")
  endparam
  func funcxout
    caption="function"
    default=cos()
    visible=((@control_type=="advanced")&&((@functypexout=="sin general")\
      ||(@functypexout=="cos general")))
  endfunc
;
; y inner parameters
;
  heading
    caption="y inner parameters"
    visible=(@control_type=="advanced")
  endheading
  complex param hy
    caption="step size"
    default=■.■
    visible=(@control_type=="advanced")
  endparam
  param vartypeyin
    caption="inner variable type"
    default=■
    enum="x" "y" "x+y" "y-x" "x■y" "y/x"
    visible=(@control_type=="advanced")
  endparam
  param functypeyin
    caption="function type"
    default=■
    enum="sin odd pos" "cos odd pos" "sin all pos" "cos all pos" \
      "sin odd alt" "cos odd alt" "sin all alt" "cos all alt" \
      "sin general" "cos general"
    visible=(@control_type=="advanced")
  endparam
  complex param poweryin
    caption="power"
    default=■
    visible=(@control_type=="advanced")
  endparam
  int param ntermyin
    caption="# terms"
    default=■■
    min=■
    visible=(@control_type=="advanced")
  endparam
  func funcyin
    caption="function"
    default=sin()
    visible=((@control_type=="advanced")&&((@functypeyin=="sin general")\
      ||(@functypeyin=="cos general")))
  endfunc
;
; y outer parameters
;
  heading
    caption="y outer parameters"
    visible=(@control_type=="advanced")
  endheading
  param vartypeyout
    caption="outer variable type"
    default=■
    enum="x" "y" "x+y" "y-x" "x■y" "y/x"
    visible=(@control_type=="advanced")
  endparam
  param functypeyout
    caption="function type"
    default=■
    enum="sin odd pos" "cos odd pos" "sin all pos" "cos all pos" \
      "sin odd alt" "cos odd alt" "sin all alt" "cos all alt" \
      "sin general" "cos general"
    visible=(@control_type=="advanced")
  endparam
  complex param poweryout
    caption="power"
    default=■
    visible=(@control_type=="advanced")
  endparam
  int param ntermyout
    caption="# terms"
    default=■■
    min=■
    visible=(@control_type=="advanced")
  endparam
  complex param slopeyout
    caption="slope"
    default=■
    visible=(@control_type=="advanced")
  endparam
  func funcyout
    caption="function"
    default=sin()
    visible=((@control_type=="advanced")&&((@functypeyout=="sin general")\
      ||(@functypeyout=="cos general")))
  endfunc
}