Fractal 087 D – Lust
Part of ENCOUNTER series – 07 2022
attraction . desire . diamonds . lust . red . satin . sex . silk
Fractal 087 D – zoom level 1
Fractal 087 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 In each case, the numerical characters have been replaced by â– to prevent unauthorized reproduction.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 087 D - Lust - Part of ENCOUNTER series - 07.2022
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="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– â– â–
formula:
maxiter=â– â– â– â– percheck=off filename="dmj.ufm"
entry="dmj-PhoenixDNovaMandel" p_start=â– /â– p_powerâ– =â– /â– p_powerâ– =â– /â–
p_coeffâ– =â– /â– p_coeffâ– =-â– /â– p_induct=-â– .â– /â– p_bailout=â– .â– â– â– â– â–
p_usecritical=no p_relax=â– /â–
inside:
transfer=sqr
outside:
transfer=linear
gradient:
smooth=yes rotation=-â– â– â– index=â– color=â– index=â– â– â– color=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–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Red" opacity=â– â– mergemode=red
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– magn=â– â– .â– â– â– â– â– â– angle=â– .â– â– â– â–
formula:
maxiter=â– â– â– â– percheck=off filename="dmj.ufm" entry="dmj-NovaMandel"
p_start=â– /â– p_power=â– â– .â– /â– p_bailout=â– .â– â– â– â– â– p_relax=â– /â–
inside:
transfer=none solid=â– â– â– â– â– â– â– â– â– â–
outside:
transfer=linear
gradient:
smooth=yes rotation=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– 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– 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– mergemode=overlay method=multipass
transparent=yes
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– magn=â– â– â– .â– â– â– â– â–
angle=-â– â– â– .â– â– â– â–
formula:
maxiter=â– â– â– percheck=off filename="lkm.ufm"
entry="compounding-tweaked-mandelbrot" p_manparam=â– .â– /â– .â–
p_bailout=â– â– â– â– .â– p_nexp=â– /â– p_tweaktype="c; fn(c)"
p_tweakage=â– .â– â– /â– .â– f_tweakfunction=recip
inside:
transfer=none solid=â–
outside:
transfer=sqr
gradient:
comments="Default Ultra Fractal gradient." smooth=yes rotation=-â– â– â–
index=â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– index=-â– â– â– color=â– â– â– â– â– â– â–
index=-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– â– mergemode=multiply
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– magn=â– â– .â– â– â– â– â– â– angle=â– .â– â– â– â–
formula:
maxiter=â– â– â– â– percheck=off filename="dmj.ufm" entry="dmj-NovaMandel"
p_start=â– /â– p_power=â– â– .â– /â– p_bailout=â– .â– â– â– â– â– p_relax=â– /â–
inside:
transfer=none solid=â– â– â– â– â– â– â– â– â– â–
outside:
transfer=linear
gradient:
smooth=yes rotation=-â– â– index=â– â– color=â– â– â– â– â– â– â– â– index=â– â– â–
color=â– â– â– â– â– index=-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– â– mergemode=multiply
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– magn=â– â– .â– â– â– â– â– â– angle=â– .â– â– â– â–
formula:
maxiter=â– â– â– â– percheck=off filename="dmj.ufm" entry="dmj-NovaMandel"
p_start=â– /â– p_power=â– â– .â– /â– p_bailout=â– .â– â– â– â– â– p_relax=â– /â–
inside:
transfer=none solid=â– â– â– â– â– â– â– â– â– â–
outside:
transfer=linear
gradient:
smooth=yes index=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– 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– â–
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– magn=â– â– .â– â– â– â– â– â– angle=â– .â– â– â– â–
formula:
maxiter=â– â– â– â– percheck=off filename="dmj.ufm" entry="dmj-NovaMandel"
p_start=â– /â– p_power=â– â– .â– /â– p_bailout=â– .â– â– â– â– â– p_relax=â– /â–
inside:
transfer=none solid=â– â– â– â– â– â– â– â– â– â–
outside:
transfer=linear
gradient:
smooth=yes rotation=-â– index=â– color=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– index=â– â– â– color=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– 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– index=â– â– â– color=â– â– â– â– â– â– â–
opacity:
smooth=no index=â– opacity=â– â– â–
}
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 = (â– ,â– )
complex y = (â– ,â– )
z = @start
IF (@usecritical)
z = ( -((@powerâ– -â– )â– @powerâ– â– @coeffâ– ) / \
((@powerâ– -â– )â– @powerâ– â– @coeffâ– ) ) ^ (â– /(@powerâ– -@powerâ– ))
ENDIF
loop:
y = zold
zold = z
z = z - (@coeffâ– â– z^@powerâ– + @coeffâ– â– z^@powerâ– - â– ) â– @relax / \
(@coeffâ– â– @powerâ– â– z^(@powerâ– -â– ) + @coeffâ– â– @powerâ– â– z^(@powerâ– -â– )) + #pixel + @inductâ– y
bailout:
|z - zold| > @bailout
default:
title = "PhoenixDoubleNova (Mandelbrot)"
helpfile = "dmj-pub\dmj-pub-uf-pdn.htm"
maxiter = â– â– â– â–
periodicity = â–
center = (-â– .â– ,â– )
magn = â– .â–
param start
caption = "Start Value"
default = (â– ,â– )
hint = "Starting value for each point. You can use this to \
'perturb' the fractal."
endparam
param powerâ–
caption = "Primary Exponent"
default = (â– ,â– )
hint = "Defines the primary exponent for the equation."
endparam
param powerâ–
caption = "Secondary Exponent"
default = (â– ,â– )
hint = "Defines the secondary exponent for the equation."
endparam
param coeffâ–
caption = "Primary Scale"
default = (â– ,â– )
hint = "Defines the coefficient (multiplier) for the \
primary exponent term."
endparam
param coeffâ–
caption = "Secondary Scale"
default = (-â– ,â– )
hint = "Defines the coefficient (multiplier) for the \
secondary exponent term."
endparam
param induct
caption = "Phoenix Distortion"
default = (-â– .â– ,â– )
hint = "Sets how 'strong' the previous iteration's effect should be \
on the fractal."
endparam
param bailout
caption = "Bailout"
default = â– .â– â– â– â– â–
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 = (â– ,â– )
hint = "This can be used to slow down the convergence of \
the formula."
endparam
switch:
type = "dmj-PhoenixDNovaJulia"
seed = #pixel
powerâ– = @powerâ–
powerâ– = @powerâ–
coeffâ– = @coeffâ–
coeffâ– = @coeffâ–
bailout = @bailout
relax = @relax
}
dmj-NovaMandel {
;
; This is the Nova fractal (Mandelbrot form), a
; modified Newtonian-style fractal. The formula
; was first shown to me by Paul Derbyshire (who
; named it Nova). It has also appeared elsewhere
; under other names. Use this formula and the
; Switch feature to select a NovaJulia.
;
init:
complex zsquared = (â– ,â– )
complex zcubed = (â– ,â– )
complex zold = (â– ,â– )
z = @start
loop:
IF (@power == (â– ,â– )); special optimized routine for power â–
zsquared = sqr(z)
zcubed = zsquared â– z
zold = z
z = z - @relax â– (zcubed-â– ) / (â– â– zsquared) + #pixel
ELSE
zold = z
z = z - @relax â– (z^@power-â– ) / (@power â– z^(@power-â– )) + #pixel
ENDIF
bailout:
|z - zold| > @bailout
default:
title = "Nova (Mandelbrot)"
helpfile = "dmj-pub\dmj-pub-uf-nova.htm"
maxiter = â– â– â– â–
periodicity = â–
center = (-â– .â– ,â– )
magn = â– .â–
param start
caption = "Start Value"
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 NovaM type."
endparam
param bailout
caption = "Bailout"
default = â– .â– â– â– â– â–
hint = "Bailout value; smaller values will cause more \
iterations to be done for each point."
endparam
param relax
caption = "Relaxation"
default = (â– ,â– )
hint = "This can be used to slow down the convergence of \
the formula."
endparam
switch:
type = "dmj-NovaJulia"
seed = #pixel
power = @power
bailout = @bailout
relax = @relax
}
compounding-tweaked-mandelbrot { ; Kerry Mitchell â– â– octâ– â–
;
; Tweaks either c or z each iteration, so that the tweaking compounds
;
init:
z=@manparam
c=#pixel
loop:
z=z^@nexp+c
if(@tweaktype==â– )
c=c+@tweakageâ– @tweakfunction(z)
elseif(@tweaktype==â– )
c=c+@tweakageâ– @tweakfunction(câ– z)
elseif(@tweaktype==â– )
c=c+@tweakageâ– @tweakfunction(z/c)
elseif(@tweaktype==â– )
z=z+@tweakageâ– @tweakfunction(c)
elseif(@tweaktype==â– )
z=z+@tweakageâ– @tweakfunction(z)
elseif(@tweaktype==â– )
z=z+@tweakageâ– @tweakfunction(câ– z)
elseif(@tweaktype==â– )
z=z+@tweakageâ– @tweakfunction(z/c)
else
c=c+@tweakageâ– @tweakfunction(c)
endif
bailout:
|z|<@bailout
default:
title="Compounding Tweaked Mandelbrot"
helpfile="lkm-help\lkm-compounding.html"
maxiter=â– â– â–
periodicity=â–
center=(-â– .â– ,â– .â– )
magn=â– .â–
angle=â–
method=multipass
param manparam
caption="initial z"
default=(â– .â– ,â– .â– )
hint="Use (â– ,â– ) for something resembling the \
standard Mandelbrot set."
endparam
param bailout
caption="bailout value"
default=â– â– â– â– .â–
endparam
param nexp
caption="exponent"
default=(â– ,â– )
hint="Use â– .â– for something resembling the \
standard Mandelbrot set."
endparam
param tweaktype
caption="tweaking type"
default=â–
enum="c; fn(c)" "c; fn(z)" "c; fn(câ– z)" "c; fn(z/c)" \
"z; fn(c)" "z; fn(z)" "z; fn(câ– z)" "z; fn(z/c)"
hint="Sets what gets tweaked, and how."
endparam
param tweakage
caption="tweaking amount"
default=(â– .â– â– ,â– .â– )
hint="Make small for something resembling the \
standard Mandelbrot set."
endparam
func tweakfunction
caption="tweaking function"
default=recip()
hint="Function of the tweaking variable."
endfunc
switch:
type="compounding-tweaked-julia"
julparam=#pixel
nexp=nexp
bailout=bailout
tweaktype=tweaktype
tweakage=tweakage
}
