Fractal 053 B – Secret Foliage
Part of LIFE series – 12 2021
dark blue . ecosystem . foliage . forest . gold . life . maze . night . secret
Fractal 053 B – zoom level 1
Fractal 053 B – 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 In each case, the numerical characters have been replaced by â– to prevent unauthorized reproduction.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 053 B - Secret Foliage - Part of LIFE series - 12.2021
Fractal_â– â– â– _B {
fractal:
title="Fractal_â– â– â– _B" width=â– â– â– â– height=â– â– â– â– layers=â–
credits="Philoxerax;â– /â– /â– 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– 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– index=â– color=â– index=â– â– â– color=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– 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–
layer:
caption="Layer â– " opacity=â– â– mergemode=hardlight 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– 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– percheck=off filename="lkm.ufm" entry="gap-mandelbrot"
p_manparam=â– /â– p_n=â– .â– p_type="between â– lines" p_câ– =-â– .â– p_câ– =â– .â–
p_theta=â– â– .â– p_center=â– /â– p_radiusâ– =â– .â– p_radiusâ– =â– .â–
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes rotation=-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– 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=darken 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– 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– percheck=off filename="lkm.ufm" entry="gap-mandelbrot"
p_manparam=â– /â– p_n=â– .â– p_type="between â– lines" p_câ– =-â– .â– p_câ– =â– .â–
p_theta=â– â– .â– p_center=â– /â– p_radiusâ– =â– .â– p_radiusâ– =â– .â–
inside:
transfer=none
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– 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–
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=darken 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– 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– percheck=off filename="lkm.ufm" entry="gap-mandelbrot"
p_manparam=â– /â– p_n=â– .â– p_type="between â– lines" p_câ– =-â– .â– p_câ– =â– .â–
p_theta=â– â– .â– p_center=â– /â– p_radiusâ– =â– .â– p_radiusâ– =â– .â–
inside:
transfer=none solid=â– â– â– â– â– â– â– â– â– â–
outside:
transfer=linear solid=â– â– â– â– â– â– â– â– â– â–
gradient:
smooth=yes rotation=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– 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–
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– 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="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 solid=â– â– â– â– â– â– â– â– â– â–
gradient:
smooth=yes rotation=-â– â– index=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– color=â– 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
}
gap-mandelbrot { ; Kerry Mitchell â– â– decâ– â–
;
; z^n+c Mandelbrot
; bails out when orbit falls into gap
; either between â– circles or â– lines
;
; updates:
; â– â– decâ– â– to add general starting point
; â– â– febâ– â– to add complex exponent
; â– â– febâ– â– to add switching to gap-julia
; â– â– marâ– â– removed complex exponent for backwards compatibility
;
init:
z=@manparam
c=#pixel
float a=â– .â–
float b=â– .â–
float gap=â– .â–
float radsqrâ– =sqr(@radiusâ– )
float radsqrâ– =sqr(@radiusâ– )
float x=â– .â–
float y=â– .â–
float rmax=â– eâ– â–
float tempr=â– .â–
int done=â–
;
; set up line/circle parameters
;
if(@type==â– ) ; lines
tempr=@theta/â– â– â– â– pi
a=sin(tempr)
b=-cos(tempr)
gap=@câ– -@câ–
else ; circles
gap=radsqrâ– -radsqrâ–
endif
loop:
z=z^@n+c
x=real(z)
y=imag(z)
;
; check for falling into gap
;
if(@type==â– ) ; lines
tempr=aâ– x+bâ– y
if((tempr>@câ– )&&(tempr<@câ– ))
done=â–
tempr=(tempr-@câ– )/gap
z=temprâ– z/cabs(z)
endif
else ; circles
tempr=|z-@center|
if((tempr>radsqrâ– )&&(temprrmax))
done=â–
z=(â– .â– ,â– .â– )
endif
bailout:
done==â–
default:
title="Gap Mandelbrot"
maxiter=â– â– â–
periodicity=â–
center=(â– ,â– )
method=multipass
magn=â–
angle=â–
param manparam
caption="Mandelbrot start"
default=(â– ,â– )
hint="use (â– ,â– ) for basic Mandelbrot set"
endparam
param n
caption="z exponent"
default=â– .â–
hint="Real--use Gap Mandelbrot C for complex exponents."
endparam
param type
caption="gap type"
default=â–
enum="between â– lines" "between â– circles"
endparam
param câ–
caption="line â– c value"
default=-â– .â–
hint="must be less than line â– c value"
endparam
param câ–
caption="line â– c value"
default=â– .â–
hint="must be more than line â– c value"
endparam
param theta
caption="line angle"
default=â– â– .â–
hint="angle to horizontal, degrees"
endparam
param center
caption="circle center"
default=(â– ,â– )
endparam
param radiusâ–
caption="circle â– radius"
default=â– .â–
hint="must be less than circle â– radius"
endparam
param radiusâ–
caption="circle â– radius"
default=â– .â–
hint="must be more than circle â– radius"
endparam
switch:
type="gap-julia"
n=n
julparam=#pixel
type=type
câ– =câ–
câ– =câ–
theta=theta
center=center
radiusâ– =radiusâ–
radiusâ– =radiusâ–
}
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
}
