Fractal 099 A – Ego

Part of ENCOUNTER series – 11 2022

ego . fascination . illusion . mirror . mistake . reflection . shape
Fractal 099A | Ego
Fractal 099 A zoom1

Fractal 099 A – zoom level 1

Fractal 099 A zoom2

Fractal 099 A – 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 In each case, the numerical characters have been replaced by ■ to prevent unauthorized reproduction.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 099 A - Ego - Part of ENCOUNTER series - 11.2022

Fractal 099A | Ego

Fractal_■■■_A {
fractal:
  title="Fractal_■■■_A" width=■■■■ height=■■■■ layers=■
  credits="Philoxerax;■■/■/■■■■" antialiasing=yes
layer:
  caption="Background" opacity=■■■ mergemode=screen
mapping:
  center=-■.■■■■■■■■■■■/-■.■■■■■■■■■■■ magn=■■.■■■■■■ angle=-■■.■■■■
formula:
  maxiter=■■■ percheck=off filename="lkm.ufm"
  entry="general-tent-mandelbrot" p_manparam=■/■ p_bailout=■■■■.
  p_rtype=magnitude p_rottype=none p_rotamount=■■.■ p_rotunit=degrees
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  comments="Default Ultra Fractal gradient." smooth=yes index=■■
  color=■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Background" opacity=■■ mergemode=screen
mapping:
  center=-■.■■■■■■■■■■/-■■.■■■■■■■■■ magn=■.■■■■■■■ angle=-■■.■■■■
formula:
  maxiter=■■■ percheck=off filename="lkm.ufm"
  entry="embossed-explog-newton" p_bailout=■■■■.■ p_parttype=iteration
  p_numsect=■ p_lightangle=■.■ p_sizefac=■.■
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  comments="Default Ultra Fractal gradient." smooth=yes rotation=■■
  index=■■ color=■ index=■■■ color=■■■■■■■ index=■■■ color=■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■■ mergemode=hardlight transparent=yes
mapping:
  center=■.■■■■■■■■■■■■■■■■■■/■.■■■■■■■■■■■■■■■■■■ magn=■■■■■■■■
  angle=-■■■.■■■■
formula:
  maxiter=■■■■ percheck=off filename="dmj.ufm" entry="dmj-DNovaMandel"
  p_start=■/■ p_power■=■/■ p_power■=■/■ p_coeff■=■/■ p_coeff■=-■/■
  p_bailout=■.■■■■■ p_usecritical=no p_relax=■/■
inside:
  transfer=none solid=■■■■■■■■■■
outside:
  transfer=sqr
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=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Background" opacity=■■■ transparent=yes
mapping:
  center=■.■■■■■■■■■■■■■■■■■/■.■■■■■■■■■■■■■■■■■■ magn=■■■■■■■■
  angle=-■■■.■■■■
formula:
  maxiter=■■■■ percheck=off filename="dmj.ufm" entry="dmj-DNovaMandel"
  p_start=■/■ p_power■=■/■ p_power■=■/■ p_coeff■=■/■ p_coeff■=-■/■
  p_bailout=■.■■■■■ p_usecritical=no p_relax=■/■
inside:
  transfer=none solid=■■■■■■■■■■
outside:
  transfer=sqr
gradient:
  smooth=yes rotation=■■ 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=■■■
}

general-tent-mandelbrot { ; Kerry Mitchell ■■oct■■■■
;
; Variation on the standard tent map
;
init:
  z=@manparam
  c=pixel
  float r=■.■
  if(@rotunit==■)            ; radians
    r=@rotamount
  else                       ; degrees
    r=@rotamount■#pi/■■■
  endif 
  rot■=cos(r)+flip(sin(r))
  rot=rot■
  temp=(■,■)
loop:
;
; rotate the map
;
  if(@rottype==■)            ; constant rotation
    temp=rot■■z
  elseif(@rottype==■)        ; progressive rotation
    rot=rot■rot■
    temp=rot■z
  elseif(@rottype==■)        ; oscillating rotation
    rot=rot■/rot
    temp=rot■z
  else                       ; no rotation
    temp=z
  endif
;
; choose the map variable
;
  if(@rtype==■)              ; real part
    r=real(temp)
  elseif(@rtype==■)          ; imag part
    r=imag(temp)
  elseif(@rtype==■)          ; real■imag
    r=imag(temp)■real(temp)
  elseif(@rtype==■)          ; imag/real
    r=imag(temp)/real(temp)
  else                       ; magnitude
    r=cabs(temp)
  endif
;
; execute tent map
;
  if(r<=■.■)
    z=c■temp
  else
    z=c■(■-temp)
  endif
bailout:
  |z|<@bailout
default:
  title="General Tent Mandelbrot"
  helpfile="lkm-help\lkm-tent.html"
  maxiter=■■■
  periodicity=■
  center=(■,■)
  magn=■.■
  angle=■
  param manparam
    caption="initial z"
    default=(■,■)
    hint="Use (■,■) for the standard map."
  endparam
  param bailout
    caption="bailout"
    default=■■■■.
  endparam
  param rtype
    caption="r type"
    default=■
    enum="magnitude" "real part" "imag part" "real■imag" "imag/real"
    hint="Determines the r value used in the tent map."
  endparam
  param rottype
    caption="rotation type"
    default=■
    enum="none" "constant" "progressive" "oscillating"
    hint="In 'constant' mode, the same angle is used every iteration. \
      In 'progressive' mode, the angle is increased by the amount every \
      iteration. In 'oscillating' mode, the map is rotated forward, then \
      back, then forward, etc."
  endparam
  param rotamount
    caption="rotation amount"
    default=■■.■
    hint="How much the map is rotated."
  endparam
  param rotunit
    caption="rotation units"
    default=■
    enum="degrees" "radians"
    hint="Units in which the rotation is expressed."
  endparam
switch:
  type="general-tent-julia"
  julparam=#pixel
  bailout=bailout
  rtype=rtype
  rottype=rottype
  rotamount=rotamount
  rotunit=rotunit
}

embossed-explog-newton { ; Kerry Mitchell ■■sep■■
;
; Newton's method for exp(z)=log(z).
; See comment block for more information
; about embossing effect.
;
; updates:
;   ■■nov■■ to add more embossing types
;   ■■dec■■ to add "angle" embossing type
;
init:
  float theta=@lightangle■pi/■■■.■
  float size=@sizefac■■.■■■■/#magn
  dr=size■(cos(theta)+flip(sin(theta)))
  z■=#pixel-dr
  z■=#pixel+dr
  int iter■=■
  int iter■=■
  int iter=■
  float r=■.■
  float t=■.■
  float rmin=■e■■
  float part■=■.■
  float part■=■.■
loop:
  iter=iter+■
  if(iter■==■)
    fp=exp(z■)
    f=fp-log(z■)
    fp=fp-■/z■
    dz=f/fp
    z■=z■-dz
    dz=■.■/dz
    if(|dz|>@bailout)
      iter■=iter
    endif
    if(@parttype==■)
      if(real(dz)>■.■)
        part■=part■+■.■
      endif
    elseif(@parttype==■)
      if(imag(dz)>■.■)
        part■=part■+■.■
      endif
    elseif(@parttype==■)
      r=|dz|
      if(r@bailout)
      iter■=iter
    endif
    if(@parttype==■)
      if(real(dz)>■.■)
        part■=part■+■.■
      endif
    elseif(@parttype==■)
      if(imag(dz)>■.■)
        part■=part■+■.■
      endif
    elseif(@parttype==■)
      r=|dz|
      if(r■" "imag(z)>■" "smallest mag"\
      "magnitude" "angle"
  endparam
  param numsect
    caption="# of sections"
    default=■
    min=■
    hint="for 'angle' embossing method"
  endparam
  param lightangle
    caption="light angle"
    default=■.■
    hint="Angle of apparant light source, in degrees"
  endparam
  param sizefac
    caption="contour size"
    default=■.■
    hint="relative size of contours bands"
  endparam
}

dmj-DNovaMandel {
;
; This is the DoubleNova fractal (Mandelbrot form),
; a modified Newtonian-style fractal. DoubleNova is
; like Nova, but with two terms instead of one.
;
init:
  complex zold = (■,■)
  
  z = @start
  IF (@usecritical)
    z = ( -((@power■-■)■@power■■@coeff■) / \
           ((@power■-■)■@power■■@coeff■) ) ^ (■/(@power■-@power■))
  ENDIF
  
loop:
  zold = z
  z = z - (@coeff■■z^@power■ + @coeff■■z^@power■ - ■) ■ @relax / \
          (@coeff■■@power■■z^(@power■-■) + @coeff■■@power■■z^(@power■-■)) + #pixel
  
bailout:
  |z - zold| > @bailout
  
default:
  title = "DoubleNova (Mandelbrot)"
  helpfile = "dmj-pub\dmj-pub-uf-dn.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 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-DNovaJulia"
  seed = #pixel
  power■ = @power■
  power■ = @power■
  coeff■ = @coeff■
  coeff■ = @coeff■
  bailout = @bailout
  relax = @relax
}
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