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 In each case, the numerical characters have been replaced by ■ to prevent unauthorized reproduction.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, please contact Philippe.

Fractal_■■■_C {
fractal:
  title="Fractal_■■■_C" width=■■■■ height=■■■■ layers=■
  credits="Philoxerax;■/■/■■■■"
layer:
  caption="Background" opacity=■■ mergemode=overlay precision=■
mapping:
  center=■.■■■■■■■■■■■■/-■.■■■■■■■■■■■■■■ magn=■■.■■■■■■
  angle=-■■.■■■■
formula:
  maxiter=■■■ percheck=off filename="asz.ufm" entry="andrextrandom-■"
  p_base=-■.■■/-■.■ p_base■=■.■■/■.■■ p_random_strength=■.■
  p_bailout=■E■ p_bailout_mode="|z/c|" p_zc_mode=Multiply
  p_zc_absolute=no p_zc_inverse=no p_ztype=Real p_scatter=yes
  f_function■=cos f_function■=ident
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=■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■ mergemode=overlay
mapping:
  center=■.■■■■■■■■■■■■■/■.■■■■■■■■■■■■■ magn=■■.■■■■■■
  angle=-■■■.■■■■
formula:
  maxiter=■■■ filename="mt.ufm" entry="mt-■■■■■■a" p_bailout=■■■■.■
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  smooth=yes rotation=-■■■ index=■■ color=■ index=■■ color=■ index=■■■
  color=■■■■■■ index=-■■■ color=■■■■■■■■ index=■■■ color=■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■■ mergemode=lighten
mapping:
  center=■.■■■■■■■■■■■■■■/-■.■■■■■■■■■■■■■■ magn=■■.■■■■■■
  angle=-■■■.■■■■
formula:
  maxiter=■■■ filename="mt.ufm" entry="mt-■■■■■■a" p_bailout=■■■■.■
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  smooth=yes rotation=-■■■ index=■■ color=■ index=■■ color=■
  index=-■■■ color=■■■■■■■ index=■■■ color=■■■■■■■ index=-■■
  color=■■■■■■■■ index=■■■ color=■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Background" opacity=■■ mergemode=screen
mapping:
  center=■.■■■■■■■■■■■■■■/■.■■■■■■■■■■■■■■ magn=■■.■■■■■■
  angle=-■■■.■■■■
formula:
  maxiter=■■■ filename="mt.ufm" entry="mt-■■■■■■a" p_bailout=■■■■.■
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  smooth=yes rotation=-■■■ index=■■ color=■ index=■■ color=■
  index=-■■■ color=■■■■■■■ index=■■■ color=■■■■■■■■ index=-■■
  color=■■■■■■■■ index=■■■ color=■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■ mergemode=green
mapping:
  center=-■.■■■■■■■■■■■■■■■/-■.■■■■■■■■■■■■■■ magn=■■■■.■■■■
  angle=-■■.■■■■
formula:
  maxiter=■■■ filename="lkm■.ufm" entry="extra-foam"
  p_pixel_type="all in" p_wq=yes p_zc=yes p_circuit_type=series
  p_bailout=■■■■ p_qinit=■/■ p_cinit=■/■ p_winit=■/■ p_zinit=■/■
  p_wpowerinw=■/■ p_zpowerinw=-■.■■■■■/■ p_wpowerinz=■/■
  p_zpowerinz=■/■
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  smooth=yes rotation=-■■ index=■■■ color=■■■■■■■■ index=■■■ color=■
  index=■■■ color=■■■■■■■■ index=-■ color=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■ mergemode=red
mapping:
  center=-■.■■■■■■■■■■■■■■■/-■.■■■■■■■■■■■■■■ magn=■■■■.■■■■
  angle=-■■.■■■■
formula:
  maxiter=■■■ filename="lkm■.ufm" entry="extra-foam"
  p_pixel_type="all in" p_wq=yes p_zc=yes p_circuit_type=series
  p_bailout=■■■■ p_qinit=■/■ p_cinit=■/■ p_winit=■/■ p_zinit=■/■
  p_wpowerinw=■/■ p_zpowerinw=-■/■ p_wpowerinz=■/■ p_zpowerinz=■/■
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  smooth=yes rotation=-■■ index=■■ color=■■■■■■■■ index=■■■
  color=■■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■
  index=-■■ color=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■■
mapping:
  center=-■.■■■■■■■■■■■■■■/-■.■■■■■■■■■■■■■■ magn=■■■■.■■■
  angle=-■■.■■■■
formula:
  maxiter=■■■ filename="lkm■.ufm" entry="extra-foam"
  p_pixel_type="all in" p_wq=yes p_zc=yes p_circuit_type=series
  p_bailout=■■■■ p_qinit=■/■ p_cinit=■/■ p_winit=■/■ p_zinit=■/■
  p_wpowerinw=■/■ p_zpowerinw=-■/■ p_wpowerinz=■/■ p_zpowerinz=■/■
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=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
}

 ;(c) by Andras Szolek
; The formula is the same as Andrextrandom-■, only the
; defaults are the different. I made two for the easy
; switching.

init:
  z = #pixel
  random = z+(#random/(■/(@random_strength/■■■)))
  c = z-#pixel^■/■+@base*@base■+■.■■
  zc = ■

 if @zc_mode == ■
  zc = z*c
 elseif @zc_mode == ■
  zc = z/c
 elseif @zc_mode == ■
  zc = z+c
 elseif @zc_mode == ■
  zc = z-c
 elseif @zc_mode == ■
  zc = z^c
 endif

 if @zc_mode == ■ && @zc_inverse == true
  zc = c/z
 elseif @zc_mode == ■ && @zc_inverse == true
  zc = c-z
 elseif @zc_mode == ■ && @zc_inverse == true
  zc = c^z
 endif

 if @zc_absolute == true
  zc = |zc|
 endif

 b = ■

loop:

  z = z/(@function■(random))/(zc)+@base
  z = z*(zc)+random
  c = (z+c)*■+@base

  z = @function■(z*(sqrt(c*@base■)/@bailout)+zc)

 if @scatter == true
  z = z+((@base■-@base)/■■■)+zc
  c = c-((c/flip(c))/(c*real(c)))-zc
 endif

 if imag(z)>■
  z = real(z+@base)
 elseif imag(z)>■
  z = flip(z+@base)
 elseif imag(z)<■   z = imag(z+@base)  elseif real(z)>■
  z = flip(z+@base)
 elseif real(z)>■
  z = real(z+@base)
  endif
  
 if @scatter == true
 if real(z)*imag(z) < flip(z)
  z = real(z)/imag(z)
 endif
 endif

 if @ztype == ■
  z = real(z)
 elseif @ztype == ■
  z = imag(z)
 endif

 if @bailout_mode == ■
  b = z*c
 elseif @bailout_mode == ■
  b = |z*c|
 elseif @bailout_mode == ■
  b = z/c
 elseif @bailout_mode == ■
  b = |z/c|
 elseif @bailout_mode == ■
  b = z+c
 elseif @bailout_mode == ■
  b = |z*c|
 elseif @bailout_mode == ■
  b = z-c
 elseif @bailout_mode == ■
  b = |z-c|
 elseif @bailout_mode == ■
  b = z
 elseif @bailout_mode == ■
  b = |z|
 elseif @bailout_mode == ■■
  b = c
 elseif @bailout_mode == ■■
  b = |c|
 else
  b = z*c
 endif

bailout:
  b <= @bailout/■■

default:
 title = "Andrextrandom - Switch #■"

 param base
  caption = "Base, ''Seed'' #■"
  default = (-■.■■,-■.■)
 endparam

 param base■
  caption = "Base, ''Seed'' #■"
  default = (■.■■,■.■■)
  endparam

 param random_strength
  caption = "Random-intensity"
  default = ■.■
  min = ■.■
 endparam

 param bailout
  caption = "Bailout"
  default = ■E■
 endparam

 param bailout_mode
  caption = "Bailout Mode"
  hint = "The bailout-process : ''this value'' < \   ''bailout parameter /variant/''"   enum = "z*c" "|z*c|" "z/c" "|z/c|" "z+c" "|z+c|"\   "z-c" "|z-c|" "z" "|z|" "c" "|c|"   default = ■  endparam  param zc_mode   caption = "ZC - Mode"   enum = "Multiply" "Division" "Add" "Subtract"\   "Product"  endparam  param zc_absolute   caption = "ZC - Absolute"   hint = "It gives an absolute-result to the z ? c"   default = false  endparam  param zc_inverse   caption = "ZC - Inverse"   hint = "This function is working in ''Division'', \   ''Subtract'' and ''Product'' ZC-Modes. How does \   it works? z/c -> c/z, z-c -> c-z and z^c -> c^z"
  default = false
 endparam

 param ztype
  caption = "Z Type"
  enum = "Real" "Imag"
 endparam

 param scatter
  caption = "Scatter"
  default = true
 endparam

 func function■
  caption = "Function #■"
  default = cos()
 endfunc

 func function■
  caption = "Function #■"
  default = ident()
 endfunc

 periodicity = ■

switch:
 type = "andrextrandom-■"
 base = #pixel
 random_strength = random_strength
 bailout = bailout
 bailout_mode = bailout_mode
 zc_mode = zc_mode
 zc_absolute = zc_absolute
 zc_inverse = zc_inverse
 ztype = ztype
 scatter = scatter
 function■ = function■
 function■ = function■
}

mt-■■■■■■a { ; Mark Townsend ■■ Jul ■■■■
init:
  z = ■
  int iter = ■
loop:
  z = z^iter + iter * #pixel
  iter = iter + ■
bailout:
 |z| < @bailout
default:
  title = "■■■■■■a"
  param bailout
    caption = "Bailout value"
    default = ■■■■.■
  endparam  
}

mt-modulate-j { ; Mark Townsend, ■■ Jul ■■■■
init:
  z = #pixel
  int iter = ■
loop:
  iter = iter + ■
  z = z^■ + ((iter % @m)* @c)
bailout:
  |z| < @bailout
default:
  title = "Modulate Julia"
  param c
    caption = "Julia seed"
    default = (-■.■,■)
  endparam  
  param m
    caption = "Modulate"
    default = ■
  endparam  
  param bailout
    caption = "Bailout value"
    default = ■■■■.■
  endparam  
switch:
  type = "mt-modulate-m"  
  m = m
  bailout = bailout
}

extra-foam { ; Kerry Mitchell ■■ June ■■■■
;
; Generalization of "Mandelbrot Foam" from fractal forums
; https://fractalforums.org/fractal-mathematics-and-new-theories/■■/mandelbrot-foam-math/■■■■/msg■■■■#msg■■■■
; original:
;   w = a*w/z
;   z = z^■ + w^■ + c
;
; powers of w and z in w and z formulas are parameters
;
; added parallel/series modes:
;   parallel: compute new w and new z independently
;   series: compute new w and use that for new z
;
; pixel_type parameter allows the pixel to represent either complex parameter (or both) or the initial values
;   of either complex variable (or both).
;
init:
  complex q=(■,■)
  complex c=(■,■)
  complex w=(■,■)
  complex wnew=(■,■)
  complex z=(■,■)
  complex znew=(■,■)
;
; Use pixel value to set parameters (like a Mandelbrot set) and/or
;   initialize variables (like a Julia set)
;
  if(@pixel_type=="q")
    q=#pixel
    c=@cinit
    if(@wq==true)
      w=q
    else
      w=@winit
    endif
    if(@zc==true)
      z=c
    else
      z=@zinit
    endif
  elseif(@pixel_type=="c")
    q=@qinit
    c=#pixel
    if(@wq==true)
      w=q
    else
      w=@winit
    endif
    if(@zc==true)
      z=c
    else
      z=@zinit
    endif
  elseif(@pixel_type=="q = c")
    q=#pixel
    c=#pixel
    if(@wq==true)
      w=q
    else
      w=@winit
    endif
    if(@zc==true)
      z=c
    else
      z=@zinit
    endif
  elseif(@pixel_type=="initial w")
    q=@qinit
    c=@cinit
    w=#pixel
    if(@zc==true)
      z=c
    else
      z=@zinit
    endif
  elseif(@pixel_type=="initial z")
    q=@qinit
    c=@cinit
    if(@wq==true)
      w=q
    else
      w=@winit
    endif
    z=#pixel
  elseif(@pixel_type=="w = z")
    q=@qinit
    c=@cinit
    w=#pixel
    z=#pixel
  elseif(@pixel_type=="all in")
    q=#pixel
    c=#pixel
    w=#pixel
    z=#pixel
  endif
loop:
;
; Series: compute new w and use that for new z.
; Parallel: compute new w and new z independently.
;
  if(@circuit_type=="series")
    w=q*w^@wpowerinw*z^@zpowerinw
    z=z^@zpowerinz+w^@wpowerinz+c
  elseif(@circuit_type=="parallel")
    wnew=q*w^@wpowerinw*z^@zpowerinw
    znew=z^@zpowerinz+w^@wpowerinz+c
    w=wnew, z=znew
  endif
bailout:
  |z|<@bailout
default:
  title="Extra Foam"
;
; General Parameters
;
  heading
    caption="General Parameters"
  endheading
  param pixel_type
    caption="pixel type"
    default=■
    enum="q" "c" "q = c" "initial w" "initial z" "w = z" "all in"
  endparam
  bool param wq
    caption="w = q"
    default=true
    visible=((@pixel_type=="q")||(@pixel_type=="c")||(@pixel_type=="q = c")||(@pixel_type=="initial z"))
  endparam
  bool param zc
    caption="z = c"
    default=true
    visible=((@pixel_type=="q")||(@pixel_type=="c")||(@pixel_type=="q = c")||(@pixel_type=="initial w"))
  endparam
  param circuit_type
    caption="circuit type"
    default=■
    enum="series" "parallel"
  endparam
  float param bailout
    caption="bailout"
    default=■■■■
  endparam
;
; Initializations
;
  heading
    caption="Initializations"
  endheading
  complex param qinit
    caption="q"
    default=(■,■)
    visible=((@pixel_type=="c")||(@pixel_type=="initial w")||(@pixel_type=="initial z")||(@pixel_type=="w = z"))
  endparam
  complex param cinit
    caption="c"
    default=(■,■)
    visible=((@pixel_type=="q")||(@pixel_type=="initial w")||(@pixel_type=="initial z")||(@pixel_type=="w = z"))
  endparam
  complex param winit
    caption="initial w"
    default=(■,■)
    visible=((@wq==false)&&(@pixel_type!="initial w")&&(@pixel_type!="w = z"))
  endparam
  complex param zinit
    caption="initial z"
    default=(■,■)
    visible=((@zc==false)&&(@pixel_type!="initial z")&&(@pixel_type!="w = z"))
  endparam
;
; Variable Powers
;
  heading
    caption="Variable Powers"
  endheading
  complex param wpowerinw
    caption="w power in w"
    default=■
  endparam
  complex param zpowerinw
    caption="z power in w"
    default=-■
  endparam
  complex param wpowerinz
    caption="w power in z"
    default=■
  endparam
  complex param zpowerinz
    caption="z power in z"
    default=■
  endparam
}