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 In each case, the numerical characters have been replaced by ■ to prevent unauthorized reproduction.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_■■■_D {
fractal:
  title="Fractal_■■■_D" width=■■■■ height=■■■■ layers=■
  credits="Philoxerax;■■/■■/■■■■"
layer:
  caption="Layer ■" opacity=■■■ mergemode=overlay
mapping:
  center=-■.■■■■■■■■■■■■■/-■.■■■■■■■■■■■■ magn=■■.■■■■■■
  angle=■■■.■■■■
formula:
  maxiter=■■■■ percheck=off filename="dmj.ufm"
  entry="dmj-PhoenixDNovaMandel" p_start=■/■ p_power■=■/■ p_power■=■/■
  p_coeff■=■/■ p_coeff■=-■/■ p_induct=-■.■/■ p_bailout=■.■■■■■
  p_usecritical=no p_relax=■/■
inside:
  transfer=linear
outside:
  transfer=linear
gradient:
  comments="Use with Lighting coloring algorithm." smooth=yes
  rotation=■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■■ mergemode=overlay
mapping:
  center=-■.■■■■■■■■■■■■/-■.■■■■■■■■■■■■ magn=■■.■■■■■■ angle=■■■.■■■■
formula:
  maxiter=■■■■ percheck=off filename="dmj.ufm"
  entry="dmj-PhoenixDNovaMandel" p_start=■/■ p_power■=■/■ p_power■=■/■
  p_coeff■=■/■ p_coeff■=-■/■ p_induct=-■.■/■ p_bailout=■.■■■■■
  p_usecritical=no p_relax=■/■
inside:
  transfer=linear
outside:
  transfer=linear
gradient:
  comments="Use with Lighting coloring algorithm." smooth=yes
  rotation=■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■■ mergemode=difference
mapping:
  center=■.■■■■■■■■■/-■.■■■■■■■■■ magn=■.■■■■■■■■
formula:
  maxiter=■■■ percheck=off filename="mt.ufm" entry="mt-zeepop-m"
  p_h=■.■/■ p_bailout=■■■ p_epsilon=■E-■ f_fn■=atan f_fn■=abs
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=■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■■ mergemode=overlay
mapping:
  center=■.■■■■■■■■■■■/-■.■■■■■■■■■■■■ magn=■■.■■■■■■
formula:
  maxiter=■■■ percheck=off filename="mt.ufm" entry="mt-zeepop-j"
  p_c=■/■ p_h=■.■■■/■ p_bailout=■■ p_epsilon=■E-■ f_fn■=cabs f_fn■=tan
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=■■■
layer:
  caption="Background" opacity=■■■
mapping:
  center=■.■■■■■■■■■■■/-■.■■■■■■■■■■■■ magn=■■.■■
formula:
  maxiter=■■■ percheck=off filename="mt.ufm" entry="mt-zeepop-j"
  p_c=■/■ p_h=■.■/■ p_bailout=■■ p_epsilon=■E-■ f_fn■=cabs f_fn■=tan
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=■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
}

dmj-PhoenixDNovaMandel {
;
; This is the DoubleNova fractal (Mandelbrot form),
; a modified Newtonian-style fractal.
;
; This variant includes an inductive component similar
; to the Phoenix fractal.
;
init:
  complex zold = (■,■)
  complex y = (■,■)
  
  z = @start
  IF (@usecritical)
    z = ( -((@power■-■)■@power■■@coeff■) / \
           ((@power■-■)■@power■■@coeff■) ) ^ (■/(@power■-@power■))
  ENDIF
  
loop:
  y = zold
  zold = z
  z = z - (@coeff■■z^@power■ + @coeff■■z^@power■ - ■) ■ @relax / \
          (@coeff■■@power■■z^(@power■-■) + @coeff■■@power■■z^(@power■-■)) + #pixel + @induct■y
  
bailout:
  |z - zold| > @bailout
  
default:
  title = "PhoenixDoubleNova (Mandelbrot)"
  helpfile = "dmj-pub\dmj-pub-uf-pdn.htm"
  maxiter = ■■■■
  periodicity = ■
  center = (-■.■,■)
  magn = ■.■
  
  param start
    caption = "Start Value"
    default = (■,■)
    hint = "Starting value for each point.  You can use this to \
            'perturb' the fractal."
  endparam
  param power■
    caption = "Primary Exponent"
    default = (■,■)
    hint = "Defines the primary exponent for the equation."
  endparam
  param power■
    caption = "Secondary Exponent"
    default = (■,■)
    hint = "Defines the secondary exponent for the equation."
  endparam
  param coeff■
    caption = "Primary Scale"
    default = (■,■)
    hint = "Defines the coefficient (multiplier) for the \
            primary exponent term."
  endparam
  param coeff■
    caption = "Secondary Scale"
    default = (-■,■)
    hint = "Defines the coefficient (multiplier) for the \
            secondary exponent term."
  endparam
  param induct
    caption = "Phoenix Distortion"
    default = (-■.■,■)
    hint = "Sets how 'strong' the previous iteration's effect should be \
            on the fractal."
  endparam
  param bailout
    caption = "Bailout"
    default = ■.■■■■■
    hint = "Bailout value; smaller values will cause more \
            iterations to be done for each point."
  endparam
  param usecritical
    caption = "Use Critical Point"
    default = false
    hint = "If set, a critical point for the function will \
            be used in place of the Start Value."
  endparam
  param relax
    caption = "Relaxation"
    default = (■,■)
    hint = "This can be used to slow down the convergence of \
            the formula."
  endparam

switch:
  type = "dmj-PhoenixDNovaJulia"
  seed = #pixel
  power■ = @power■
  power■ = @power■
  coeff■ = @coeff■
  coeff■ = @coeff■
  bailout = @bailout
  relax = @relax
}

mt-zeepop-m { ; Mark Townsend, ■ May ■■■■
init:
  c = #pixel
  z = sqr(■ - #pixel)
  oldz = ■
loop:
  oldz = z
  z = z - @h ■ @fn■(z + @fn■(c ■ z))
bailout:
  |z - oldz| > @epsilon
default:
  title = "Zeepop Mset"
  periodicity  = ■
  param h
    caption = "Step Size"
    default = (■.■,■)
  endparam       
  param bailout
    caption = "Bailout Value"
    default = ■■■
  endparam       
  param epsilon
    caption = "Epsilon"
    default = ■e-■
  endparam       
  func fn■
    caption = "Function #■"
    default = sin()
  endfunc  
  func fn■
    caption = "Function #■"
    default = tan()
  endfunc  
switch:
  type = "mt-zeepop-j"
  c = #pixel
  h = h
  fn■ = fn■
  fn■ = fn■
  bailout = bailout
  epsilon = epsilon
}

mt-zeepop-m { ; Mark Townsend, ■ May ■■■■
init:
  c = #pixel
  z = sqr(■ - #pixel)
  oldz = ■
loop:
  oldz = z
  z = z - @h ■ @fn■(z + @fn■(c ■ z))
bailout:
  |z - oldz| > @epsilon
default:
  title = "Zeepop Mset"
  periodicity  = ■
  param h
    caption = "Step Size"
    default = (■.■,■)
  endparam       
  param bailout
    caption = "Bailout Value"
    default = ■■■
  endparam       
  param epsilon
    caption = "Epsilon"
    default = ■e-■
  endparam       
  func fn■
    caption = "Function #■"
    default = sin()
  endfunc  
  func fn■
    caption = "Function #■"
    default = tan()
  endfunc  
switch:
  type = "mt-zeepop-j"
  c = #pixel
  h = h
  fn■ = fn■
  fn■ = fn■
  bailout = bailout
  epsilon = epsilon
}