Fractal 033 D – Buddhist Heaven

Part of BEYOND series – 10 2021

beyond . buddhism . contact . heaven . light . meditation . paradise . spirit . spirituality . white
Fractal 033 D | Buddhist Heaven
Fracta 033 D zoom1

Fracta 033 D – zoom level 1

Fractal 033 D zoom2

Fracta 033 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 In each case, the numerical characters have been replaced by ■ to prevent unauthorized reproduction.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 033 D - Buddhist Heaven - Part of BEYOND series - 10.2021

Fractal 033 D | Buddhist Paradise

Fractal_■■■_D {
fractal:
  title="Fractal_■■■_D" width=■■■■ height=■■■■ layers=■
  credits="Philoxerax;■■/■/■■■■" antialiasing=yes
layer:
  caption="Layer ■" opacity=■■ mergemode=overlay
mapping:
  center=-■.■■■■■■■■■■■■■■/-■.■■■■■■■■■■■■■ magn=■■.■■■■■■
  angle=-■■.■■
formula:
  maxiter=■■■ filename="lkm■.ufm" entry="unit-vector-tweak-mandelbrot"
  p_initial_z=■/■ p_power=■/■ p_bailout=■■■■ p_tweak_type=after
  p_fac_pre=-■.■/■.■ f_func_pre=cos p_fac_post=■.■■/■
  f_func_post=ident
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=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Background" opacity=■■■ mergemode=lighten
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=none
outside:
  transfer=linear
gradient:
  smooth=yes index=■■ color=■ index=■■■ color=■■■■■■■■ index=■■■
  color=■■■■■■■■ index=■■■ color=■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■ mergemode=difference
mapping:
  center=-■.■■■■■■■■■■■■■■■■/■.■■■■■■■■■■■■■■■■ magn=■■■■■■.■■
  angle=■■■.■■■■
formula:
  maxiter=■■■ filename="Standard.ufm" entry="Mandelbrot" p_start=■/■
  p_power=■/■ p_bailout=■■■
inside:
  transfer=none
outside:
  transfer=sqr filename="Standard.ucl" entry="Smooth" p_power=■/■
  p_bailout=■■■.■
gradient:
  smooth=yes index=■■ color=■■■■■■■■ index=■■■ color=■■■■■■■ index=■■■
  color=■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Background" opacity=■■ mergemode=addition
mapping:
  center=-■.■■■■■■■■■■■■■■■■/■.■■■■■■■■■■■■■■■■ magn=■■■■■■.■■
  angle=■■■.■■■■
formula:
  maxiter=■■■ filename="Standard.ufm" entry="Mandelbrot" p_start=■/■
  p_power=■/■ p_bailout=■■■
inside:
  transfer=none
outside:
  transfer=sqr filename="Standard.ucl" entry="Smooth" p_power=■/■
  p_bailout=■■■.■
gradient:
  smooth=yes index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■■
  index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Layer ■" opacity=■■ mergemode=multiply method=multipass
mapping:
  center=-■.■■■■■■■■■■■/-■.■■■■■■■■■ magn=■.■■■■■■■ angle=-■■.■■■■
formula:
  maxiter=■■■ percheck=off filename="ldm.ufm" entry="dm■■a"
  p_p■=-■.■/■ f_fn■=exp f_fn■=cosh
inside:
  transfer=none solid=■■■■■■■■■■
outside:
  transfer=cuberoot
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=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
layer:
  caption="Background" opacity=■■■ method=multipass
mapping:
  center=-■.■■■■■■■■■■■/-■.■■■■■■■■■ magn=■.■■■■■■■ angle=-■■.■■■■
formula:
  maxiter=■■■ percheck=off filename="ldm.ufm" entry="dm■■a"
  p_p■=-■.■/■ f_fn■=exp f_fn■=cosh
inside:
  transfer=none solid=■■■■■■■■■■
outside:
  transfer=cuberoot
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=■■■■■■■■
opacity:
  smooth=no index=■ opacity=■■■
}

unit-vector-tweak-mandelbrot { ; Kerry Mitchell ■■dec■■■■
;
; Add a tweak of the unit vector for z at each iteation.
; Either add before the z^power+c step, after, or both.
;
; Based on Asdam's Mandelbrot variation, posted to Fractal Forums ■■/■■/■■■■
; http://www.fractalforums.com/new-theories-and-research/
; is-there-anything-novel-left-to-do-in-m-like-escape-time-fractals-in-■d/
; msg■■■■■/#newinit:
;
  complex c=#pixel
  complex unit_vector=(■,■)
  complex z=@initial_z
loop:
  if((@tweak_type=="before")||(@tweak_type=="both"))
    if(cabs(z)==■)
      unit_vector=■
    else
      unit_vector=z/cabs(z)
    endif
    z=z+@fac_pre■@func_pre(unit_vector)
  endif
  z=z^@power+c
  if((@tweak_type=="after")||(@tweak_type=="both"))
    if(cabs(z)==■)
      unit_vector=■
    else
      unit_vector=z/cabs(z)
    endif
    z=z+@fac_post■@func_post(unit_vector)
  endif
bailout:
  |z|<@bailout
default:
  title="Unit Vector Tweak Mandelbrot"
  complex param initial_z
    caption="initial z"
    default=(■,■)
  endparam
  complex param power
    caption="power"
    default=■
  endparam
  float param bailout
    caption="bailout"
    default=■■■■
  endparam
  param tweak_type
    caption="tweak type"
    default=■
    enum="before" "after" "both"
  endparam
  complex param fac_pre
    caption="before factor"
    default=(-■.■,■.■)
    visible=((@tweak_type=="before")||(@tweak_type=="both"))
  endparam
  func func_pre
    caption="before function"
    default=cos()
    visible=((@tweak_type=="before")||(@tweak_type=="both"))
  endfunc
  complex param fac_post
    caption="after factor"
    default=■.■■
    visible=((@tweak_type=="after")||(@tweak_type=="both"))
  endparam
  func func_post
    caption="after function"
    default=ident()
    visible=((@tweak_type=="after")||(@tweak_type=="both"))
  endfunc
switch:
  type="unit-vector-tweak-julia"
  julparam=#pixel
  power=power
  bailout=bailout
  tweak_type=tweak_type
  fac_pre=fac_pre
  func_pre=func_pre
  fac_post=fac_post
  func_post=func_post
}

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
}

Mandelbrot {
;
; Generic Mandelbrot set.
;
init:
  z = @start
loop:
  z = z^@power + #pixel
bailout:
  |z| <= @bailout

$IFDEF VER■■
perturbinit:
  #dz = ■
perturbloop:
  if @power == (■, ■)
    #dz = ■ ■ #z ■ #dz + sqr(#dz) + #dpixel
  elseif @power == (■, ■)
    complex z■ = sqr(#z)
    complex dz■ = sqr(#dz)
    #dz = ■ ■ z■ ■ #dz + ■ ■ #z ■ dz■ + #dz ■ dz■ + #dpixel
  else ; power ■
    complex z■ = sqr(#z)
    complex dz■ = sqr(#dz)
    complex zdz■ = ■■#z■#dz
    #dz = #dpixel + zdz■■z■ + ■■z■■dz■ + zdz■■dz■ + sqr(dz■)
  endif
$ENDIF

default:
  title = "Mandelbrot"
  center = (-■.■, ■)
  helpfile = "Uf■.chm"
  helptopic = "Html\formulas\standard\mandelbrot.html"
$IFDEF VER■■
  rating = recommended
$ENDIF
$IFDEF VER■■
  perturb = @power == (■, ■) || @power == (■, ■) || @power == (■, ■)
$ENDIF
  param start
    caption = "Starting point"
    default = (■,■)
    hint = "The starting point parameter can be used to distort the Mandelbrot \
            set. Use (■, ■) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (■,■)
    hint = "This parameter sets the exponent for the Mandelbrot formula. \
            Increasing the real part to ■, ■, and so on, will add discs to \
            the Mandelbrot figure. Non-integer real values and non-zero \
            imaginary values will create distorted Mandelbrot sets. Use (■, ■) \
            for the standard Mandelbrot set."
  endparam
  float param bailout
    caption = "Bailout value"
    default = ■.■
    min = ■.■
$IFDEF VER■■
    exponential = true
$ENDIF
    hint = "This parameter defines how soon an orbit bails out while \
            iterating. Larger values give smoother outlines; values around ■ \
            give more interesting shapes around the set. Values less than ■ \
            will distort the fractal."
  endparam
switch:
  type = "Julia"
  seed = #pixel
  power = power
  bailout = bailout
}

dm■■a{
init:
  z= pixel 
loop:
  z=fn■(p■)■fn■(z+p■)
bailout:
  |z|<=■
default:
  method = multipass
  periodicity = ■
  param p■
  default=(-■.■,■)
  endparam
  
  func fn■
  default=exp()
  endfunc

  func fn■
  default=cosh()
  endfunc
}
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