Fractal 094 C – Star Gateway

Part of OUTER SPACE series – 09 2022

cosmos . frontier . galaxy . gate . outerspace . pass . spacetime . transition . universe
Fractal 094 C | Star gateway
Fractal 094 C zoom1

Fractal 094 C – zoom level 1

Fractal 094 C zoom2

Fractal 094 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 In each case, the numerical characters have been replaced by ■ to prevent unauthorized reproduction.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 094 C - Star Gateway - Part of OUTER SPACE series - 09.2022

Fractal 094 C | Star gateway

Fractal_■■■_C {
fractal:
  title="Fractal_■■■_C" width=■■■■ height=■■■■ layers=■
  credits="Philoxerax;■/■■/■■■■"
layer:
  caption="Layer ■" opacity=■■■ mergemode=subtraction
mapping:
  center=-■.■■■■■■■■■■■■/-■.■■■■■■■■■■■■■ magn=■■■.■■■■■
  angle=-■■■■.■■■■
formula:
  maxiter=■■■ filename="mt.ufm" entry="mt-■■■■■■a-m" p_e■=■.■ p_e■=■.■
  p_bailout=■■■■.■ f_fn■=flip f_fn■=ident
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  smooth=yes rotation=-■■ 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-PhoenixDNovaMandel" p_start=■/■ p_power■=■/■ p_power■=■/■
  p_coeff■=■/■ p_coeff■=-■/■ p_induct=-■.■/■ p_bailout=■.■■■■■
  p_usecritical=no p_relax=■/■
inside:
  transfer=sqr solid=■■■■■■■■■■
outside:
  transfer=linear solid=■■■■■■■■■■
gradient:
  smooth=yes rotation=-■■■ index=■ color=■■■■■■■■ index=-■■■
  color=■■■■■■■ index=-■■■ color=■■■■■■■ index=-■■■ color=■■■■■■■
  index=■■■ color=■■■■■■■■ index=-■■■ color=■■■■■■■■ index=-■■■
  color=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■ index=■■ opacity=■■■ index=■■■
  opacity=■■■ index=■■■ opacity=■
layer:
  caption="Layer ■" opacity=■■■ mergemode=blue
mapping:
  center=■.■■■■■■■■■■■■/■.■■■■■■■■■■■■■■■ magn=■■.■■■■■■ angle=■■■.■■■
formula:
  maxiter=■■■ filename="mt.ufm" entry="mt-■■■■■■b-m" p_e■=■.■ p_e■=■.■
  p_bailout=■■■.■ f_fn■=floor f_fn■=ident
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=overlay method=multipass
mapping:
  center=-■.■■■■■■■■■■■■■/■.■■■■■■■■■■■■ magn=■■.■■■■■■ angle=■■■.■■■■
  stretch=■.■■■■ skew=■.■■■■
formula:
  maxiter=■■■ percheck=off filename="lkm.ufm" entry="gap-mandelbrot"
  p_manparam=■/■ p_n=■.■ p_type="between ■ lines" p_c■=-■.■ p_c■=■.■
  p_theta=■■.■ p_center=■/■ p_radius■=■.■ p_radius■=■.■
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=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■■ mergemode=lighten
mapping:
  center=■.■■■■■■■■■■■■■/■.■■■■■■■■■■■■■■ magn=■■.■■■■■■ angle=■■■.■■■
formula:
  maxiter=■■■ filename="mt.ufm" entry="mt-■■■■■■b-m" p_e■=■.■ p_e■=■.■
  p_bailout=■■■.■ f_fn■=floor f_fn■=ident
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  smooth=yes rotation=-■■ index=■■ color=■■■■■■■ index=■■
  color=■■■■■■■■ index=■■■ color=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■ visible=no mergemode=multiply
mapping:
  center=■.■■■■■■■■■■■■/■.■■■■■■■■■■■■■■ magn=■■.■■■■■■ angle=■■■.■■■
formula:
  maxiter=■■■ filename="mt.ufm" entry="mt-■■■■■■b-m" p_e■=■.■ p_e■=■.■
  p_bailout=■■■.■ f_fn■=floor f_fn■=ident
inside:
  transfer=none solid=■■■■■■■■■■
outside:
  transfer=linear
gradient:
  smooth=yes rotation=■■ index=■■ color=■■■■■■ index=■■■ color=■■■■■■■
  index=■■■ color=■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Background" opacity=■■■ visible=no
mapping:
  center=■.■■■■■■■■■■■■/■.■■■■■■■■■■■■■■ magn=■■.■■■■■■ angle=■■■.■■■
formula:
  maxiter=■■■ filename="mt.ufm" entry="mt-■■■■■■b-m" p_e■=■.■ p_e■=■.■
  p_bailout=■■■.■ f_fn■=floor f_fn■=ident
inside:
  transfer=none solid=■■■■■■■■■■
outside:
  transfer=linear
gradient:
  smooth=yes rotation=-■■■ index=■■ color=■■■■■■■■ index=■■■
  color=■■■■■■■ index=-■■■ color=■■■■■■ index=■■■ color=■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
}

mt-■■■■■■a-m { ; Mark Townsend, Aug ■ ■■■■
init:
  z = ■
  c = #pixel
loop:
  z = @fn■(c■z^@e■) + @fn■(z^@e■) + c
bailout:
  |z| < @bailout
default:
  title = "■■■■■■a Mset"
  param e■
    caption = "First exponent"
    default = ■.■
  endparam  
  param e■
    caption = "Second exponent"
    default = ■.■
  endparam  
  func fn■
    default = ident()
  endfunc  
  func fn■
    default = ident()
  endfunc  
  param bailout
    caption = "Bailout value"
    default = ■■■■.■
  endparam  
  func fn■
    caption = "First Function"
    default = ident()
  endfunc  
  func fn■
    caption = "Second Function"
    default = ident()
  endfunc  
switch:
  type = "mt-■■■■■■a-j"
  e■ = e■
  e■ = e■  
  fn■ = fn■
  fn■ = fn■
  bailout = bailout
  c = #pixel
}

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-■■■■■■b-m { ; Mark Townsend, Aug ■ ■■■■
init:
  z = ■
  c = #pixel
loop:
  z = @fn■(c■z^@e■) + @fn■(-c■z^@e■) + c
bailout:
  |z| < @bailout
default:
  title = "■■■■■■b Mset"
  param e■
    caption = "First exponent"
    default = ■.■
  endparam  
  param e■
    caption = "Second exponent"
    default = ■.■
  endparam  
  func fn■
    default = ident()
  endfunc  
  func fn■
    default = ident()
  endfunc  
  param bailout
    caption = "Bailout value"
    default = ■■■■.■
  endparam  
  func fn■
    caption = "First Function"
    default = ident()
  endfunc  
  func fn■
    caption = "Second Function"
    default = ident()
  endfunc  
switch:
  type = "mt-■■■■■■b-j"
  e■ = e■
  e■ = e■  
  fn■ = fn■
  fn■ = fn■
  bailout = bailout
  c = #pixel
}

gap-mandelbrot { ; Kerry Mitchell ■■dec■■
;
; z^n+c Mandelbrot
; bails out when orbit falls into gap
; either between ■ circles or ■ lines
;
; updates:
;   ■■dec■■ to add general starting point
;   ■■feb■■ to add complex exponent
;   ■■feb■■ to add switching to gap-julia
;   ■■mar■■ removed complex exponent for backwards compatibility
;
init:
  z=@manparam
  c=#pixel
  float a=■.■
  float b=■.■
  float gap=■.■
  float radsqr■=sqr(@radius■)
  float radsqr■=sqr(@radius■)
  float x=■.■
  float y=■.■
  float rmax=■e■■
  float tempr=■.■
  int done=■
;
; set up line/circle parameters
;
  if(@type==■)                       ; lines
    tempr=@theta/■■■■pi
    a=sin(tempr)
    b=-cos(tempr)
    gap=@c■-@c■
  else                               ; circles
    gap=radsqr■-radsqr■
  endif
loop:
  z=z^@n+c
  x=real(z)
  y=imag(z)
;
; check for falling into gap
;
  if(@type==■)                       ; lines
    tempr=a■x+b■y
    if((tempr>@c■)&&(tempr<@c■))
      done=■
      tempr=(tempr-@c■)/gap
      z=tempr■z/cabs(z)
    endif
  else                               ; circles
    tempr=|z-@center|
    if((tempr>radsqr■)&&(temprrmax))
    done=■
    z=(■.■,■.■)
  endif
bailout:
  done==■
default:
  title="Gap Mandelbrot"
  maxiter=■■■
  periodicity=■
  center=(■,■)
  method=multipass
  magn=■
  angle=■
  param manparam
    caption="Mandelbrot start"
    default=(■,■)
    hint="use (■,■) for basic Mandelbrot set"
  endparam
  param n
    caption="z exponent"
    default=■.■
    hint="Real--use Gap Mandelbrot C for complex exponents."
  endparam
  param type
    caption="gap type"
    default=■
    enum="between ■ lines" "between ■ circles"
  endparam
  param c■
    caption="line ■ c value"
    default=-■.■
    hint="must be less than line ■ c value"
  endparam
  param c■
    caption="line ■ c value"
    default=■.■
    hint="must be more than line ■ c value"
  endparam
  param theta
    caption="line angle"
    default=■■.■
    hint="angle to horizontal, degrees"
  endparam
  param center
    caption="circle center"
    default=(■,■)
  endparam
  param radius■
    caption="circle ■ radius"
    default=■.■
    hint="must be less than circle ■ radius"
  endparam
  param radius■
    caption="circle ■ radius"
    default=■.■
    hint="must be more than circle ■ radius"
  endparam
switch:
  type="gap-julia"
  n=n
  julparam=#pixel
  type=type
  c■=c■
  c■=c■
  theta=theta
  center=center
  radius■=radius■
  radius■=radius■
}
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