Fractal 092 C – Falling in Love

Part of ENCOUNTER series – 09 2022

attraction . couple . desire . heart . love . red . share . symbiosis
Fractal 092 C | Falling in Love
Fractal 092 C zoom1

Fractal 092 C – zoom level 1

Fractal 092 C zoom2

Fractal 092 C – 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 In each case, the numerical characters have been replaced by ■ to prevent unauthorized reproduction.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 092 C - Falling in Love - Part of ENCOUNTER series - 09.2022

Fractal 092 C | Falling in Love

Fractal_■■■_C {
fractal:
  title="Fractal_■■■_C" width=■■■■ height=■■■■ layers=■
  credits="Philoxerax;■■/■/■■■■" antialiasing=yes
layer:
  caption="Background" opacity=■■ mergemode=addition method=multipass
mapping:
  center=■■■■.■■■■■■/■.■■■■■■■■■■ magn=■.■■■■■■■■ angle=■■■.■■■
  skew=-■.■■■■
formula:
  maxiter=■■■ percheck=off filename="ldm.ufm" entry="DM■■" f_fn■=sqrt
  f_fn■=cos f_fn■=sin p_p■=■.■/■■
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="Background" opacity=■■ visible=no mergemode=overlay
mapping:
  center=-■.■■■■■■■■■■■■■/■.■■■■■■■■■■■■■■ magn=■■■■.■■■■
  angle=■■.■■■■
formula:
  maxiter=■■■■ filename="dmj.ufm" entry="dmj-BoostMandel" p_start=■/■
  p_power=■/■ p_bailout=■.■E■■ p_boostcenter=■/■ p_boostradius=■.■
  p_boostmode=displace p_boostamount=■/■
inside:
  transfer=cube
outside:
  transfer=sqr
gradient:
  smooth=yes index=■ color=■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■
  color=■■■■■■■■ index=■■■ color=■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■ mergemode=darken
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=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■ mergemode=softlight
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=■■■■■■■
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=sqr
outside:
  transfer=linear
gradient:
  smooth=yes 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=■■■ percheck=off filename="lkm.ufm"
  entry="general-tent-mandelbrot" p_manparam=■/■ p_bailout=■■■■.
  p_rtype="real part" p_rottype=none p_rotamount=■■.■
  p_rotunit=degrees
inside:
  transfer=none solid=■■■■■■■■■■
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="Background" opacity=■■■ mergemode=lighten
mapping:
  center=■.■■■■■■■■■■■■■■■■/-■.■■■■■■■■■■■■■■ magn=■■■■■.■
  angle=■■.■■■■
formula:
  maxiter=■■■ percheck=off filename="lkm.ufm"
  entry="general-tent-mandelbrot" p_manparam=■/■ p_bailout=■■■■.
  p_rtype="real part" p_rottype=none p_rotamount=■■.■
  p_rotunit=degrees
inside:
  transfer=none solid=■■■■■■■■■■
outside:
  transfer=linear
gradient:
  comments="Default Ultra Fractal gradient." smooth=yes rotation=■■
  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=■■ 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=■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■■
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=■■■ index=-■■ color=■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
}

DM■■ {
init:
  z = pixel
loop:
  a=fn■(z)
  b=a+p■
  c=fn■((a-p■)/b)
  d=c^■/p■
  w=a/b/c■(d+p■)
  z=fn■(w/z^p■)
bailout:
  |z| <= ■
default:
  method = multipass
  periodicity = ■
  param p■
  default=(.■■,■)
  endparam
  
  func fn■
  default=cos()
  endfunc
}

dmj-BoostMandel {
;
; This formula is an implementation of Orbit Boosting,
; an idea by Earl Hinrichs.
;
; The basic idea is that we perform a normal Mandelbrot
; iteration, but if the orbit enters a specified region
; of the complex plane (much like an orbit trap) we
; "boost" it in some fashion. A variety of boosting modes
; are included. Boost regions are ALWAYS circular in this
; implementation.
;
init:
  float d = ■; distance to boost area
  float radius■ = sqr(@boostradius); pre-calc this
  float iradius = ■/@boostradius; pre-calc this
;  complex c = ■

  z = @start
  
loop:
  z = z^@power + #pixel; calculate the M-set

  d = |z - @boostcenter|; distance to boost area
  IF (d < radius■); within threshold
    IF (@boostmode == ■); displace (addition)
      z = z + @boostamount
    ELSEIF (@boostmode == ■); orbit origin (multiply)
      z = z ■ @boostamount
    ELSEIF (@boostmode == ■); orbit boost (multiply)
      z = (z-@boostcenter) ■ @boostamount + @boostcenter
    ELSEIF (@boostmode == ■); flip out (reverse distance)
      d = ■■@boostradius/sqrt(d)-■
      z = @boostcenter + (z-@boostcenter)■d■@boostamount
    ELSEIF (@boostmode == ■); repel (reverse distance squared)
      d = ■-sqr(■-@boostradius/sqrt(d))
      z = @boostcenter + (z-@boostcenter)■d■@boostamount
    ELSEIF (@boostmode == ■); exponentiate origin (exponent)
      z = z ^ @boostamount
    ELSEIF (@boostmode == ■); exponentiate boost (exponent)
      z = (z-@boostcenter) ^ @boostamount + @boostcenter
    ELSEIF (@boostmode == ■); invert
      z = conj(iradius/(z-@boostcenter)) + @boostcenter
    ELSEIF (@boostmode == ■); pass through
      z = z + ■■(z-@boostcenter)■@boostamount
    ELSEIF (@boostmode == ■); pass through ■
      z = z + ■■(@boostcenter-z)/cabs(@boostcenter-z)■@boostradius■@boostamount
    ENDIF
  ENDIF

bailout:
  |z| < @bailout
  
default:
  title = "Orbit Boost (Mandelbrot)"
  helpfile = "dmj-pub\dmj-pub-uf-ob.htm"
  center = (-■.■, ■.■)
  maxiter = ■■■■
  
  param start
    caption = "Starting Point"
    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 Julia type."
  endparam
  param bailout
    caption = "Bail-out Value"
    default = ■.■e■■
    min = ■.■
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Julia set anymore."
  endparam

  param boostcenter
    caption = "Boost Center"
    default = (■,■)
    hint = "This is the location of the boost area in the complex plane."
  endparam
  param boostradius
    caption = "Boost Radius"
    default = ■.■
    hint = "This is the size of the boost area."
  endparam
  param boostmode
    caption = "Boost Mode"
    default = ■
    enum = "displace" "orbit origin" "orbit boost" "flip out" "repel" \
           "exponentiate origin" "exponentiate boost" "invert" "pass through" \
           "pass through ■"
    hint = "Sets the type of effect when the orbit enters the boost area."
  endparam
  param boostamount
    caption = "Boost Amount"
    default = (■,■)
    hint = "This is the amount to boost."
  endparam

switch:
  type = "dmj-BoostJulia"
  seed = #pixel
  power = @power
  bailout = @bailout
  
  boostcenter = @boostcenter
  boostradius = @boostradius
  boostmode = @boostmode
  boostamount = @boostamount
}

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
}

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
}
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