Fractal 043 A – Heart
Part of LIFE series – 10 2021
blood . body . engine . heart . life . nature . organ . red . vein
Fractal 043 A – zoom level 1
Fractal 043 A – 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 In each case, the numerical characters have been replaced by â– to prevent unauthorized reproduction.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 043 A - Heart - Part of LIFE series - 10.2021
Layers {
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– 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="explog-newton"
p_bailout=â– â– â– .â–
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes rotation=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–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Layer â– " opacity=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– 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-DNovaMandel"
p_start=â– /â– p_powerâ– =â– /â– p_powerâ– =â– /â– p_coeffâ– =â– /â– p_coeffâ– =-â– /â–
p_bailout=â– .â– â– â– â– â– p_usecritical=no p_relax=â– /â–
inside:
transfer=none
outside:
transfer=sqr
gradient:
smooth=yes rotation=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– 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=hsladd
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–
formula:
maxiter=â– â– â– â– percheck=off filename="dmj.ufm" entry="dmj-DNovaMandel"
p_start=â– /â– p_powerâ– =â– /â– p_powerâ– =â– /â– p_coeffâ– =â– /â– p_coeffâ– =-â– /â–
p_bailout=â– .â– â– â– â– â– p_usecritical=no p_relax=â– /â–
inside:
transfer=none
outside:
transfer=sqr
gradient:
smooth=yes rotation=â– â– â– index=â– color=â– â– â– â– index=â– â– color=â– â– 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– index=â– â– â– color=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– â– â– â– â– â– â– â– â– magn=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="general-tent-mandelbrot" p_manparam=â– /â– p_bailout=â– â– â– â– .
p_rtype="real part" p_rottype=none p_rotamount=â– â– .â–
p_rotunit=degrees
inside:
transfer=none solid=â– â– â– â– â– â– â– â– â– â–
outside:
transfer=linear
gradient:
comments="Default Ultra Fractal 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– â– index=â– â– â–
color=â– â– â– â– â– index=â– â– â– color=â– â– â–
opacity:
smooth=no index=â– opacity=â– â– â–
}
explog-newton { ; Kerry Mitchell â– â– octâ– â–
;
; Uses Newton's method to find the roots
; of exp(zc)=log(zc). The variable zc is
; used for the orbit computation, and z
; is the reciprocal of the adjustment to
; zc each iteration. That is, when z
; approaches infinity, the orbit has settled
; down into a root. Consequently, set the
; bailout value to some large number. This
; was done for compatibility with coloring
; schemes that expect z to be large on bailout.
;
init:
zc=#pixel
loop:
f=exp(zc)
fp=f-â– /zc
f=f-log(zc)
dz=f/fp
zc=zc-dz
z=â– /dz
bailout:
|z|<@bailout
default:
title="Newton's Method for exp(z) = log(z)"
maxiter=â– â– â–
periodicity=â–
center=(â– .â– ,â– .â– )
magn=â– .â–
angle=â–
param bailout
caption="bailout value"
default=â– â– â– .â–
min=â– .â–
hint="make large"
endparam
}
dmj-DNovaMandel {
;
; This is the DoubleNova fractal (Mandelbrot form),
; a modified Newtonian-style fractal. DoubleNova is
; like Nova, but with two terms instead of one.
;
init:
complex zold = (â– ,â– )
z = @start
IF (@usecritical)
z = ( -((@powerâ– -â– )â– @powerâ– â– @coeffâ– ) / \
((@powerâ– -â– )â– @powerâ– â– @coeffâ– ) ) ^ (â– /(@powerâ– -@powerâ– ))
ENDIF
loop:
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
bailout:
|z - zold| > @bailout
default:
title = "DoubleNova (Mandelbrot)"
helpfile = "dmj-pub\dmj-pub-uf-dn.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 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-DNovaJulia"
seed = #pixel
powerâ– = @powerâ–
powerâ– = @powerâ–
coeffâ– = @coeffâ–
coeffâ– = @coeffâ–
bailout = @bailout
relax = @relax
}
general-tent-mandelbrot { ; Kerry Mitchell â– â– octâ– â– â– â–
;
; Variation on the standard tent map
;
init:
z=@manparam
c=pixel
float r=â– .â–
if(@rotunit==â– ) ; radians
r=@rotamount
else ; degrees
r=@rotamountâ– #pi/â– â– â–
endif
rotâ– =cos(r)+flip(sin(r))
rot=rotâ–
temp=(â– ,â– )
loop:
;
; rotate the map
;
if(@rottype==â– ) ; constant rotation
temp=rotâ– â– z
elseif(@rottype==â– ) ; progressive rotation
rot=rotâ– rotâ–
temp=rotâ– z
elseif(@rottype==â– ) ; oscillating rotation
rot=rotâ– /rot
temp=rotâ– z
else ; no rotation
temp=z
endif
;
; choose the map variable
;
if(@rtype==â– ) ; real part
r=real(temp)
elseif(@rtype==â– ) ; imag part
r=imag(temp)
elseif(@rtype==â– ) ; realâ– imag
r=imag(temp)â– real(temp)
elseif(@rtype==â– ) ; imag/real
r=imag(temp)/real(temp)
else ; magnitude
r=cabs(temp)
endif
;
; execute tent map
;
if(r<=â– .â– )
z=câ– temp
else
z=câ– (â– -temp)
endif
bailout:
|z|<@bailout
default:
title="General Tent Mandelbrot"
helpfile="lkm-help\lkm-tent.html"
maxiter=â– â– â–
periodicity=â–
center=(â– ,â– )
magn=â– .â–
angle=â–
param manparam
caption="initial z"
default=(â– ,â– )
hint="Use (â– ,â– ) for the standard map."
endparam
param bailout
caption="bailout"
default=â– â– â– â– .
endparam
param rtype
caption="r type"
default=â–
enum="magnitude" "real part" "imag part" "realâ– imag" "imag/real"
hint="Determines the r value used in the tent map."
endparam
param rottype
caption="rotation type"
default=â–
enum="none" "constant" "progressive" "oscillating"
hint="In 'constant' mode, the same angle is used every iteration. \
In 'progressive' mode, the angle is increased by the amount every \
iteration. In 'oscillating' mode, the map is rotated forward, then \
back, then forward, etc."
endparam
param rotamount
caption="rotation amount"
default=â– â– .â–
hint="How much the map is rotated."
endparam
param rotunit
caption="rotation units"
default=â–
enum="degrees" "radians"
hint="Units in which the rotation is expressed."
endparam
switch:
type="general-tent-julia"
julparam=#pixel
bailout=bailout
rtype=rtype
rottype=rottype
rotamount=rotamount
rotunit=rotunit
}
