Fractal 033 D – Buddhist Heaven
Part of BEYOND series – 10 2021
beyond . buddhism . contact . heaven . light . meditation . paradise . spirit . spirituality . white
Fracta 033 D – zoom level 1
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 In each case, the numerical characters have been replaced by â– to prevent unauthorized reproduction.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_â– â– â– _D {
fractal:
title="Fractal_â– â– â– _D" width=â– â– â– â– height=â– â– â– â– layers=â–
credits="Philoxerax;â– â– /â– /â– â– â– â– " antialiasing=yes
layer:
caption="Layer â– " opacity=â– â– mergemode=overlay
mapping:
center=-â– .â– â– â– â– â– â– â– â– â– â– â– â– â– â– /-â– .â– â– â– â– â– â– â– â– â– â– â– â– â– magn=â– â– .â– â– â– â– â– â–
angle=-â– â– .â– â–
formula:
maxiter=â– â– â– filename="lkmâ– .ufm" entry="unit-vector-tweak-mandelbrot"
p_initial_z=â– /â– p_power=â– /â– p_bailout=â– â– â– â– p_tweak_type=after
p_fac_pre=-â– .â– /â– .â– f_func_pre=cos p_fac_post=â– .â– â– /â–
f_func_post=ident
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes rotation=â– â– index=â– â– color=â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â–
index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Background" opacity=â– â– â– mergemode=lighten
mapping:
center=-â– .â– â– â– â– â– â– â– â– â– â– â– â– /â– .â– â– â– â– â– â– â– â– â– â– â– â– magn=â– .â– â– â– â– â– â– â– angle=-â– â– .â– â– â–
formula:
maxiter=â– â– â– â– filename="dmj.ufm" entry="dmj-BoostMandel" p_start=â– /â–
p_power=â– /â– p_bailout=â– .â– Eâ– â– p_boostcenter=â– /â– p_boostradius=â– .â–
p_boostmode=displace p_boostamount=â– /â–
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes index=â– â– color=â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– â– â– â– index=â– â– â– color=â–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Layer â– " opacity=â– â– mergemode=difference
mapping:
center=-â– .â– â– â– â– â– â– â– â– â– â– â– â– â– â– â– â– /â– .â– â– â– â– â– â– â– â– â– â– â– â– â– â– â– â– magn=â– â– â– â– â– â– .â– â–
angle=â– â– â– .â– â– â– â–
formula:
maxiter=â– â– â– filename="Standard.ufm" entry="Mandelbrot" p_start=â– /â–
p_power=â– /â– p_bailout=â– â– â–
inside:
transfer=none
outside:
transfer=sqr filename="Standard.ucl" entry="Smooth" p_power=â– /â–
p_bailout=â– â– â– .â–
gradient:
smooth=yes index=â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– â–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Background" opacity=â– â– mergemode=addition
mapping:
center=-â– .â– â– â– â– â– â– â– â– â– â– â– â– â– â– â– â– /â– .â– â– â– â– â– â– â– â– â– â– â– â– â– â– â– â– magn=â– â– â– â– â– â– .â– â–
angle=â– â– â– .â– â– â– â–
formula:
maxiter=â– â– â– filename="Standard.ufm" entry="Mandelbrot" p_start=â– /â–
p_power=â– /â– p_bailout=â– â– â–
inside:
transfer=none
outside:
transfer=sqr filename="Standard.ucl" entry="Smooth" p_power=â– /â–
p_bailout=â– â– â– .â–
gradient:
smooth=yes index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â–
index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Layer â– " opacity=â– â– mergemode=multiply method=multipass
mapping:
center=-â– .â– â– â– â– â– â– â– â– â– â– â– /-â– .â– â– â– â– â– â– â– â– â– magn=â– .â– â– â– â– â– â– â– angle=-â– â– .â– â– â– â–
formula:
maxiter=â– â– â– percheck=off filename="ldm.ufm" entry="dmâ– â– a"
p_pâ– =-â– .â– /â– f_fnâ– =exp f_fnâ– =cosh
inside:
transfer=none solid=â– â– â– â– â– â– â– â– â– â–
outside:
transfer=cuberoot
gradient:
smooth=yes rotation=â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â–
index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– color=â– â– â– â– â– â– â– â– index=â– â–
color=â– â– â– â– â– â– â– â– index=â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â–
index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â–
index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â–
index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â–
index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– â– â– â–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Background" opacity=â– â– â– method=multipass
mapping:
center=-â– .â– â– â– â– â– â– â– â– â– â– â– /-â– .â– â– â– â– â– â– â– â– â– magn=â– .â– â– â– â– â– â– â– angle=-â– â– .â– â– â– â–
formula:
maxiter=â– â– â– percheck=off filename="ldm.ufm" entry="dmâ– â– a"
p_pâ– =-â– .â– /â– f_fnâ– =exp f_fnâ– =cosh
inside:
transfer=none solid=â– â– â– â– â– â– â– â– â– â–
outside:
transfer=cuberoot
gradient:
smooth=yes rotation=â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â–
index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– color=â– â– â– â– â– â– â– â– index=â– â–
color=â– â– â– â– â– â– â– â– index=â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â–
index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â–
index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â–
index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â–
index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– â– â– â–
opacity:
smooth=no index=â– opacity=â– â– â–
}
unit-vector-tweak-mandelbrot { ; Kerry Mitchell â– â– decâ– â– â– â–
;
; 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 â– â– /â– â– /â– â– â– â–
; http://www.fractalforums.com/new-theories-and-research/
; is-there-anything-novel-left-to-do-in-m-like-escape-time-fractals-in-â– d/
; msgâ– â– â– â– â– /#newinit:
;
complex c=#pixel
complex unit_vector=(â– ,â– )
complex z=@initial_z
loop:
if((@tweak_type=="before")||(@tweak_type=="both"))
if(cabs(z)==â– )
unit_vector=â–
else
unit_vector=z/cabs(z)
endif
z=z+@fac_preâ– @func_pre(unit_vector)
endif
z=z^@power+c
if((@tweak_type=="after")||(@tweak_type=="both"))
if(cabs(z)==â– )
unit_vector=â–
else
unit_vector=z/cabs(z)
endif
z=z+@fac_postâ– @func_post(unit_vector)
endif
bailout:
|z|<@bailout
default:
title="Unit Vector Tweak Mandelbrot"
complex param initial_z
caption="initial z"
default=(â– ,â– )
endparam
complex param power
caption="power"
default=â–
endparam
float param bailout
caption="bailout"
default=â– â– â– â–
endparam
param tweak_type
caption="tweak type"
default=â–
enum="before" "after" "both"
endparam
complex param fac_pre
caption="before factor"
default=(-â– .â– ,â– .â– )
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=â– .â– â–
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 = â– ; distance to boost area
float radiusâ– = sqr(@boostradius); pre-calc this
float iradius = â– /@boostradius; pre-calc this
; complex c = â–
z = @start
loop:
z = z^@power + #pixel; calculate the M-set
d = |z - @boostcenter|; distance to boost area
IF (d < radiusâ– ); within threshold
IF (@boostmode == â– ); displace (addition)
z = z + @boostamount
ELSEIF (@boostmode == â– ); orbit origin (multiply)
z = z â– @boostamount
ELSEIF (@boostmode == â– ); orbit boost (multiply)
z = (z-@boostcenter) â– @boostamount + @boostcenter
ELSEIF (@boostmode == â– ); flip out (reverse distance)
d = â– â– @boostradius/sqrt(d)-â–
z = @boostcenter + (z-@boostcenter)â– dâ– @boostamount
ELSEIF (@boostmode == â– ); repel (reverse distance squared)
d = â– -sqr(â– -@boostradius/sqrt(d))
z = @boostcenter + (z-@boostcenter)â– dâ– @boostamount
ELSEIF (@boostmode == â– ); exponentiate origin (exponent)
z = z ^ @boostamount
ELSEIF (@boostmode == â– ); exponentiate boost (exponent)
z = (z-@boostcenter) ^ @boostamount + @boostcenter
ELSEIF (@boostmode == â– ); invert
z = conj(iradius/(z-@boostcenter)) + @boostcenter
ELSEIF (@boostmode == â– ); pass through
z = z + â– â– (z-@boostcenter)â– @boostamount
ELSEIF (@boostmode == â– ); pass through â–
z = z + â– â– (@boostcenter-z)/cabs(@boostcenter-z)â– @boostradiusâ– @boostamount
ENDIF
ENDIF
bailout:
|z| < @bailout
default:
title = "Orbit Boost (Mandelbrot)"
helpfile = "dmj-pub\dmj-pub-uf-ob.htm"
center = (-â– .â– , â– .â– )
maxiter = â– â– â– â–
param start
caption = "Starting Point"
default = (â– ,â– )
hint = "Starting value for each point. You can use this to \
'perturb' the fractal."
endparam
param power
caption = "Exponent"
default = (â– ,â– )
hint = "Overall exponent for the equation. (â– ,â– ) gives \
the classic Julia type."
endparam
param bailout
caption = "Bail-out Value"
default = â– .â– eâ– â–
min = â– .â–
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 = (â– ,â– )
hint = "This is the location of the boost area in the complex plane."
endparam
param boostradius
caption = "Boost Radius"
default = â– .â–
hint = "This is the size of the boost area."
endparam
param boostmode
caption = "Boost Mode"
default = â–
enum = "displace" "orbit origin" "orbit boost" "flip out" "repel" \
"exponentiate origin" "exponentiate boost" "invert" "pass through" \
"pass through â– "
hint = "Sets the type of effect when the orbit enters the boost area."
endparam
param boostamount
caption = "Boost Amount"
default = (â– ,â– )
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 VERâ– â–
perturbinit:
#dz = â–
perturbloop:
if @power == (â– , â– )
#dz = â– â– #z â– #dz + sqr(#dz) + #dpixel
elseif @power == (â– , â– )
complex zâ– = sqr(#z)
complex dzâ– = sqr(#dz)
#dz = â– â– zâ– â– #dz + â– â– #z â– dzâ– + #dz â– dzâ– + #dpixel
else ; power â–
complex zâ– = sqr(#z)
complex dzâ– = sqr(#dz)
complex zdzâ– = â– â– #zâ– #dz
#dz = #dpixel + zdzâ– â– zâ– + â– â– zâ– â– dzâ– + zdzâ– â– dzâ– + sqr(dzâ– )
endif
$ENDIF
default:
title = "Mandelbrot"
center = (-â– .â– , â– )
helpfile = "Ufâ– .chm"
helptopic = "Html\formulas\standard\mandelbrot.html"
$IFDEF VERâ– â–
rating = recommended
$ENDIF
$IFDEF VERâ– â–
perturb = @power == (â– , â– ) || @power == (â– , â– ) || @power == (â– , â– )
$ENDIF
param start
caption = "Starting point"
default = (â– ,â– )
hint = "The starting point parameter can be used to distort the Mandelbrot \
set. Use (â– , â– ) for the standard Mandelbrot set."
endparam
param power
caption = "Power"
default = (â– ,â– )
hint = "This parameter sets the exponent for the Mandelbrot formula. \
Increasing the real part to â– , â– , 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 (â– , â– ) \
for the standard Mandelbrot set."
endparam
float param bailout
caption = "Bailout value"
default = â– .â–
min = â– .â–
$IFDEF VERâ– â–
exponential = true
$ENDIF
hint = "This parameter defines how soon an orbit bails out while \
iterating. Larger values give smoother outlines; values around â– \
give more interesting shapes around the set. Values less than â– \
will distort the fractal."
endparam
switch:
type = "Julia"
seed = #pixel
power = power
bailout = bailout
}
dmâ– â– a{
init:
z= pixel
loop:
z=fnâ– (pâ– )â– fnâ– (z+pâ– )
bailout:
|z|<=â–
default:
method = multipass
periodicity = â–
param pâ–
default=(-â– .â– ,â– )
endparam
func fnâ–
default=exp()
endfunc
func fnâ–
default=cosh()
endfunc
}
