Fractal 087 D – Lust

Part of ENCOUNTER series – 07 2022

attraction . desire . diamonds . lust . red . satin . sex . silk
Fractal 087 D | Lust
Fractal 087 D zoom1

Fractal 087 D – zoom level 1

Fractal 087 D zoom2

Fractal 087 D – zoom level 2

Data

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 In each case, the numerical characters have been replaced by ■ to prevent unauthorized reproduction.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 087 D - Lust - Part of ENCOUNTER series - 07.2022

Fractal 087 D | Lust

Fractal_■■■_D {
fractal:
  title="Fractal_■■■_D" width=■■■■ height=■■■■ layers=■
  credits="Philoxerax;■/■■/■■■■" antialiasing=yes
layer:
  caption="Background" opacity=■■■ mergemode=lighten
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=sqr
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="Red" opacity=■■ mergemode=red
mapping:
  center=-■.■■■■■■■■■■■■/■.■■■■■■■■■■ magn=■■.■■■■■■ angle=■.■■■■
formula:
  maxiter=■■■■ percheck=off filename="dmj.ufm" entry="dmj-NovaMandel"
  p_start=■/■ p_power=■■.■/■ p_bailout=■.■■■■■ p_relax=■/■
inside:
  transfer=none solid=■■■■■■■■■■
outside:
  transfer=linear
gradient:
  smooth=yes rotation=■■ index=■■■ color=■■■■■■■■ index=■■
  color=■■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■■
  index=■■■ color=■■■■■■ index=■■■ color=■■■■■■■■ index=■■■
  color=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Background" opacity=■■ mergemode=overlay method=multipass
  transparent=yes
mapping:
  center=-■.■■■■■■■■■■■■■■/-■.■■■■■■■■■■■■■■ magn=■■■.■■■■■
  angle=-■■■.■■■■
formula:
  maxiter=■■■ percheck=off filename="lkm.ufm"
  entry="compounding-tweaked-mandelbrot" p_manparam=■.■/■.■
  p_bailout=■■■■.■ p_nexp=■/■ p_tweaktype="c; fn(c)"
  p_tweakage=■.■■/■.■ f_tweakfunction=recip
inside:
  transfer=none solid=■
outside:
  transfer=sqr
gradient:
  comments="Default Ultra Fractal gradient." smooth=yes rotation=-■■■
  index=■■ color=■■■■■■■■ index=■■■ color=■■■ index=-■■■ color=■■■■■■■
  index=-■■ color=■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■■ mergemode=multiply
mapping:
  center=-■.■■■■■■■■■■■■/■.■■■■■■■■■■ magn=■■.■■■■■■ angle=■.■■■■
formula:
  maxiter=■■■■ percheck=off filename="dmj.ufm" entry="dmj-NovaMandel"
  p_start=■/■ p_power=■■.■/■ p_bailout=■.■■■■■ p_relax=■/■
inside:
  transfer=none solid=■■■■■■■■■■
outside:
  transfer=linear
gradient:
  smooth=yes rotation=-■■ index=■■ color=■■■■■■■■ index=■■■
  color=■■■■■ index=-■■ color=■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■■ mergemode=multiply
mapping:
  center=-■.■■■■■■■■■■■■/■.■■■■■■■■■■ magn=■■.■■■■■■ angle=■.■■■■
formula:
  maxiter=■■■■ percheck=off filename="dmj.ufm" entry="dmj-NovaMandel"
  p_start=■/■ p_power=■■.■/■ p_bailout=■.■■■■■ p_relax=■/■
inside:
  transfer=none solid=■■■■■■■■■■
outside:
  transfer=linear
gradient:
  smooth=yes index=■■ color=■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■
  color=■■■■■■■ index=■■■ color=■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■■
mapping:
  center=-■.■■■■■■■■■■■■/■.■■■■■■■■■■ magn=■■.■■■■■■ angle=■.■■■■
formula:
  maxiter=■■■■ percheck=off filename="dmj.ufm" entry="dmj-NovaMandel"
  p_start=■/■ p_power=■■.■/■ p_bailout=■.■■■■■ p_relax=■/■
inside:
  transfer=none solid=■■■■■■■■■■
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=■■■■■■■
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
}

dmj-NovaMandel {
;
; This is the Nova fractal (Mandelbrot form), a
; modified Newtonian-style fractal.  The formula
; was first shown to me by Paul Derbyshire (who
; named it Nova).  It has also appeared elsewhere
; under other names.  Use this formula and the
; Switch feature to select a NovaJulia.
;
init:
  complex zsquared = (■,■)
  complex zcubed = (■,■)
  complex zold = (■,■)
  
  z = @start
  
loop:
  IF (@power == (■,■)); special optimized routine for power ■
    zsquared = sqr(z)
    zcubed = zsquared ■ z
    zold = z
    z = z - @relax ■ (zcubed-■) / (■■zsquared) + #pixel
  ELSE
    zold = z
    z = z - @relax ■ (z^@power-■) / (@power ■ z^(@power-■)) + #pixel
  ENDIF
  
bailout:
  |z - zold| > @bailout
  
default:
  title = "Nova (Mandelbrot)"
  helpfile = "dmj-pub\dmj-pub-uf-nova.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 = "Exponent"
    default = (■,■)
    hint = "Overall exponent for the equation.  (■,■) gives \
            the classic NovaM type."
  endparam
  param bailout
    caption = "Bailout"
    default = ■.■■■■■
    hint = "Bailout value; smaller values will cause more \
            iterations to be done for each point."
  endparam
  param relax
    caption = "Relaxation"
    default = (■,■)
    hint = "This can be used to slow down the convergence of \
            the formula."
  endparam

switch:
  type = "dmj-NovaJulia"
  seed = #pixel
  power = @power
  bailout = @bailout
  relax = @relax
}

compounding-tweaked-mandelbrot { ; Kerry Mitchell ■■oct■■
;
; Tweaks either c or z each iteration, so that the tweaking compounds
;
init:
  z=@manparam
  c=#pixel
loop:
  z=z^@nexp+c
  if(@tweaktype==■)
    c=c+@tweakage■@tweakfunction(z)
  elseif(@tweaktype==■)
    c=c+@tweakage■@tweakfunction(c■z)
  elseif(@tweaktype==■)
    c=c+@tweakage■@tweakfunction(z/c)
  elseif(@tweaktype==■)
    z=z+@tweakage■@tweakfunction(c)
  elseif(@tweaktype==■)
    z=z+@tweakage■@tweakfunction(z)
  elseif(@tweaktype==■)
    z=z+@tweakage■@tweakfunction(c■z)
  elseif(@tweaktype==■)
    z=z+@tweakage■@tweakfunction(z/c)
  else
    c=c+@tweakage■@tweakfunction(c)
  endif
bailout:
  |z|<@bailout
default:
  title="Compounding Tweaked Mandelbrot"
  helpfile="lkm-help\lkm-compounding.html"
  maxiter=■■■
  periodicity=■
  center=(-■.■,■.■)
  magn=■.■
  angle=■
  method=multipass
  param manparam
    caption="initial z"
    default=(■.■,■.■)
    hint="Use (■,■) for something resembling the \
      standard Mandelbrot set."
  endparam
  param bailout
    caption="bailout value"
    default=■■■■.■
  endparam
  param nexp
    caption="exponent"
    default=(■,■)
    hint="Use ■.■ for something resembling the \
      standard Mandelbrot set."
  endparam
  param tweaktype
    caption="tweaking type"
    default=■
    enum="c; fn(c)" "c; fn(z)" "c; fn(c■z)" "c; fn(z/c)" \
      "z; fn(c)" "z; fn(z)" "z; fn(c■z)" "z; fn(z/c)"
    hint="Sets what gets tweaked, and how."
  endparam
  param tweakage
    caption="tweaking amount"
    default=(■.■■,■.■)
    hint="Make small for something resembling the \
      standard Mandelbrot set."
  endparam
  func tweakfunction
    caption="tweaking function"
    default=recip()
    hint="Function of the tweaking variable."
  endfunc
switch:
  type="compounding-tweaked-julia"
  julparam=#pixel
  nexp=nexp
  bailout=bailout
  tweaktype=tweaktype
  tweakage=tweakage
}
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