Fractal 049 D – Unicellular
Part of LIFE series – 11 2021
cell . circle . liquid . organic . ripples . wave . white
Fractal 049 D – zoom level 1
Fractal 049 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 In each case, the numerical characters have been replaced by â– to prevent unauthorized reproduction.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 to train an AI, please contact Philippe.
Fractal 049 D - Unicellular - Part of LIFE series - 11.2021
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– " antialiasing=yes
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– magn=â– .â– â– â– â– â– â– â– â– â– angle=â– â– â– .â– â– â– â–
formula:
maxiter=â– â– â– filename="dmj.ufm" entry="dmj-DoubleJulia" p_seed=â– /â–
p_powerâ– =â– /â– p_powerâ– =-â– /â– p_coeffâ– =â– /â– p_coeffâ– =â– /â– p_bailout=â– Eâ– â–
inside:
transfer=none
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– 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="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– magn=â– .â– â– â– â– â– â– â– â– angle=â– â– .â– â– â– â–
formula:
maxiter=â– â– â– filename="dmj.ufm" entry="dmj-DoubleJulia" p_seed=â– /â–
p_powerâ– =â– /â– p_powerâ– =-â– /â– p_coeffâ– =â– /â– p_coeffâ– =â– /â– p_bailout=â– Eâ– â–
inside:
transfer=none
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– index=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="Layer â– " opacity=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– â– â– magn=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=none
outside:
transfer=linear
gradient:
comments="Use with Emboss coloring algorithm." smooth=no 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–
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=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– â– â– magn=â– â– â– â– .â– â– â– â–
angle=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=none
outside:
transfer=linear
gradient:
comments="Use with Emboss coloring algorithm." smooth=no index=â–
color=â– â– â– â– â– 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– 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="Layer â– " opacity=â– â– visible=no 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– 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– 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– 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– 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– 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="Background" opacity=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– 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="lkm.ufm" entry="mitch-mandelbrot"
p_manparam=â– /â– p_bailout=â– â– â– â– .â– p_bailtype="|z|"
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–
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–
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– index=-â– â– color=â– â– â– â– â– â– â–
opacity:
smooth=no index=â– opacity=â– â– â–
}
dmj-DoubleJulia {
;
; This is based on an idea by Jim Muth. It is the
; classical Julia equation, but with two terms of
; user-specified power and weight.
;
init:
z = #pixel
loop:
z = @coeffâ– â– z^@powerâ– + @coeffâ– â– z^@powerâ– + @seed
bailout:
|z| < @bailout
default:
title = "DoubleJulia"
helpfile = "dmj-pub\dmj-pub-uf-dmj.htm"
param seed
caption = "Julia Seed"
default = (â– ,â– )
hint = "This is the Julia seed, a constant parameter which \
defines the shape of 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 bailout
caption = "Bailout"
default = â– eâ– â–
hint = "Bailout value; larger values will cause more \
iterations to be done for each point."
endparam
switch:
type = "dmj-DoubleMandel"
powerâ– = @powerâ–
powerâ– = @powerâ–
coeffâ– = @coeffâ–
coeffâ– = @coeffâ–
}
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
}
mitch-mandelbrot { ; Kerry Mitchell â– â– marâ– â–
;
; câ– (z^â– +â– /z^â– ) Mandelbrot
;
; updated â– â– febâ– â– to change bailout variable
;
init:
bool done=false
z=@manparam
c=#pixel
loop:
zâ– =sqr(z)
z=câ– (zâ– +â– /zâ– )
if((@bailtype==â– )&&(|z|>@bailout))
done=true
elseif((@bailtype==â– )&&(|zâ– c|>@bailout))
done=true
endif
bailout:
done==false
default:
title="Mitch's Mandelbrot"
periodicity=â–
magn=â–
param manparam
caption="Mandelbrot start"
default=(â– ,â– )
hint="use (â– ,â– ) for standard set"
endparam
param bailout
caption="bailout value"
default=â– â– â– â– .â–
endparam
param bailtype
caption="bailout type"
default=â–
enum="|z|" "|zâ– c|"
endparam
switch:
type="mitch-julia"
julparam=#pixel
bailout=bailout
bailtype=bailtype
}
