Fractal 025 D – Microbe
Part of LIFE series – 09 2021
blue . cell . deep . microbe . virus
Fractal 025 D – zoom level 1
Fractal 025 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 In each case, the numerical characters have been replaced by â– to prevent unauthorized reproduction.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 025 D - Microbe - Part of LIFE series - 09.2021
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="Background" opacity=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– 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="Standard.ufm" entry="Mandelbrot" p_start=â– /â–
p_power=â– /â– p_bailout=â– â– â–
inside:
transfer=none offset=â– â– â– repeat=no solid=â– â– â– â– â– â– â– â– â– â–
outside:
transfer=cube solid=â– â– â– â– â– â– â– â– â– â– filename="Standard.ucl"
entry="Smooth" p_power=â– /â– p_bailout=â– â– â– .â–
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– â– index=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– 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– 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– 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– 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="Background" opacity=â– 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– â– â– â– â– â– â– â– â– â– â– â– magn=â– .â– â– â– â– â– â– â– Eâ–
angle=â– â– .â– â– â–
formula:
maxiter=â– â– â– â– percheck=off filename="dmj.ufm"
entry="dmj-PhoenixDNovaJulia" p_seed=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_relax=â– /â–
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes index=â– color=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–
opacity:
smooth=no index=â– opacity=â– â– â–
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– magn=â– .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-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 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–
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– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– index=â– â– â– color=â–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Layer â– " opacity=â– â– mergemode=color
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– â– angle=â– â– .â– â– â– â–
formula:
maxiter=â– â– â– â– percheck=off 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– 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– 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– â– index=â– â– â– color=â– index=â– â– â– color=â–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Layer â– " opacity=â– â– â– mergemode=softlight
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– 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-ManyNova"
p_power=â– /â– p_bailout=â– .â– â– â– â– â– p_relax=â– /â– p_scale=â– .â– p_jscale=â– .â–
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes index=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– 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–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Layer â– " opacity=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– magn=â– â– .â– â– â– â– â– â–
formula:
maxiter=â– â– â– â– percheck=off filename="dmj.ufm" entry="dmj-ManyNova"
p_power=â– /â– p_bailout=â– .â– â– â– â– â– p_relax=â– /â– p_scale=â– .â– p_jscale=â– .â–
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes rotation=-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– 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– 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–
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–
formula:
maxiter=â– â– â– â– percheck=off filename="dmj.ufm" entry="dmj-ManyNova"
p_power=â– /â– p_bailout=â– .â– â– â– â– â– p_relax=â– /â– p_scale=â– .â– p_jscale=â– .â–
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes index=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– 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–
opacity:
smooth=no index=â– opacity=â– â– â–
}
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
}
dmj-PhoenixDNovaJulia {
;
; This is the DoubleNova fractal (Julia 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 = #pixel
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– )) + @seed + @inductâ– y
bailout:
|z - zold| > @bailout
default:
title = "PhoenixDoubleNova (Julia)"
helpfile = "dmj-pub\dmj-pub-uf-pdn.htm"
maxiter = â– â– â– â–
periodicity = â–
center = (â– ,â– )
magn = â– .â–
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 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 relax
caption = "Relaxation"
default = (â– ,â– )
hint = "This can be used to slow down the convergence of \
the formula."
endparam
switch:
type = "dmj-PhoenixDNovaMandel"
powerâ– = @powerâ–
powerâ– = @powerâ–
coeffâ– = @coeffâ–
coeffâ– = @coeffâ–
bailout = @bailout
relax = @relax
}
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-ManyNova {
;
; This formula breaks the image up into a grid of
; squares, each square containing a small Nova Julia set
; using the c value from the center of the square.
;
init:
float iscale = â– / @scale
c = round(#pixel â– @scale) â– iscale
z = (#pixel - c) â– @scale â– @jscale
complex zsquared = (â– ,â– )
complex zcubed = (â– ,â– )
complex zold = (â– ,â– )
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) + c
ELSE
zold = z
z = z - @relax â– (z^@power-â– ) / (@power â– z^(@power-â– )) + c
ENDIF
bailout:
|z-zold| > @bailout
default:
title = "ManyNova"
helpfile = "dmj-pub\dmj-pub-uf-manynova.htm"
maxiter = â– â– â– â–
periodicity = â–
center = (â– ,â– )
magn = â– .â–
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
param scale
caption = "Julia Density"
default = â– .â–
hint = "Specifies the density of separate Julia sets; higher \
numbers will produce more divisions."
endparam
param jscale
caption = "Julia Zoom"
default = â– .â–
hint = "Specifies the zoom level of Julia sets within each division."
endparam
}
