Fractal 092 C – Falling in Love
Part of ENCOUNTER series – 09 2022
attraction . couple . desire . heart . love . red . share . symbiosis
Fractal 092 C – zoom level 1
Fractal 092 C – 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 In each case, the numerical characters have been replaced by â– to prevent unauthorized reproduction.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 092 C - Falling in Love - Part of ENCOUNTER series - 09.2022
Fractal_â– â– â– _C {
fractal:
title="Fractal_â– â– â– _C" 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– mergemode=addition 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– magn=â– .â– â– â– â– â– â– â– â– angle=â– â– â– .â– â– â–
skew=-â– .â– â– â– â–
formula:
maxiter=â– â– â– percheck=off filename="ldm.ufm" entry="DMâ– â– " f_fnâ– =sqrt
f_fnâ– =cos f_fnâ– =sin p_pâ– =â– .â– /â– â–
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes rotation=-â– â– â– index=â– â– color=â– â– â– index=-â– â– â– color=â–
index=-â– â– color=â– index=-â– color=â–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Background" 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– â– magn=â– â– â– â– .â– â– â– â–
angle=â– â– .â– â– â– â–
formula:
maxiter=â– â– â– â– filename="dmj.ufm" entry="dmj-BoostMandel" p_start=â– /â–
p_power=â– /â– p_bailout=â– .â– Eâ– â– p_boostcenter=â– /â– p_boostradius=â– .â–
p_boostmode=displace p_boostamount=â– /â–
inside:
transfer=cube
outside:
transfer=sqr
gradient:
smooth=yes index=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=darken
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– angle=-â– â– .â– â– â– â–
formula:
maxiter=â– â– percheck=off filename="dmj.ufm"
entry="dmj-PhoenixDNovaMandel" p_start=â– 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– â– p_usecritical=no p_relax=â– /â– .â– â–
inside:
transfer=sqr
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–
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=softlight
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– percheck=off filename="dmj.ufm"
entry="dmj-PhoenixDNovaMandel" p_start=â– 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– â– p_usecritical=no p_relax=â– /â– .â– â–
inside:
transfer=sqr
outside:
transfer=linear
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– 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– 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=overlay
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– percheck=off filename="dmj.ufm"
entry="dmj-PhoenixDNovaMandel" p_start=â– 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– â– p_usecritical=no p_relax=â– /â– .â– â–
inside:
transfer=sqr
outside:
transfer=linear
gradient:
smooth=yes 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–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Layer â– " 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– 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="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– â– color=â– index=â– â– â– color=â– â– â– index=â– â– â– color=â–
opacity:
smooth=no index=â– opacity=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– magn=â– â– â– â– â– .â–
angle=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– â– color=â– index=â– â– â– color=â– â– â– index=â– â– â– color=â– â– â– index=â– â– â–
color=â–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Background" opacity=â– â– mergemode=screen
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– percheck=off filename="dmj.ufm"
entry="dmj-PhoenixDNovaMandel" p_start=â– 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– â– p_usecritical=no p_relax=â– /â– .â– â–
inside:
transfer=sqr
outside:
transfer=linear
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–
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– magn=â– .â– â– â– â– â– â– â– angle=-â– â– .â– â– â– â–
formula:
maxiter=â– â– percheck=off filename="dmj.ufm"
entry="dmj-PhoenixDNovaMandel" p_start=â– 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– â– p_usecritical=no p_relax=â– /â– .â– â–
inside:
transfer=sqr
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– 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– index=-â– â– color=â– â– â– â– â– â– â–
opacity:
smooth=no index=â– opacity=â– â– â–
}
DMâ– â– {
init:
z = pixel
loop:
a=fnâ– (z)
b=a+pâ–
c=fnâ– ((a-pâ– )/b)
d=c^â– /pâ–
w=a/b/câ– (d+pâ– )
z=fnâ– (w/z^pâ– )
bailout:
|z| <= â–
default:
method = multipass
periodicity = â–
param pâ–
default=(.â– â– ,â– )
endparam
func fnâ–
default=cos()
endfunc
}
dmj-BoostMandel {
;
; This formula is an implementation of Orbit Boosting,
; an idea by Earl Hinrichs.
;
; The basic idea is that we perform a normal Mandelbrot
; iteration, but if the orbit enters a specified region
; of the complex plane (much like an orbit trap) we
; "boost" it in some fashion. A variety of boosting modes
; are included. Boost regions are ALWAYS circular in this
; implementation.
;
init:
float d = â– ; distance to boost area
float radiusâ– = sqr(@boostradius); pre-calc this
float iradius = â– /@boostradius; pre-calc this
; complex c = â–
z = @start
loop:
z = z^@power + #pixel; calculate the M-set
d = |z - @boostcenter|; distance to boost area
IF (d < radiusâ– ); within threshold
IF (@boostmode == â– ); displace (addition)
z = z + @boostamount
ELSEIF (@boostmode == â– ); orbit origin (multiply)
z = z â– @boostamount
ELSEIF (@boostmode == â– ); orbit boost (multiply)
z = (z-@boostcenter) â– @boostamount + @boostcenter
ELSEIF (@boostmode == â– ); flip out (reverse distance)
d = â– â– @boostradius/sqrt(d)-â–
z = @boostcenter + (z-@boostcenter)â– dâ– @boostamount
ELSEIF (@boostmode == â– ); repel (reverse distance squared)
d = â– -sqr(â– -@boostradius/sqrt(d))
z = @boostcenter + (z-@boostcenter)â– dâ– @boostamount
ELSEIF (@boostmode == â– ); exponentiate origin (exponent)
z = z ^ @boostamount
ELSEIF (@boostmode == â– ); exponentiate boost (exponent)
z = (z-@boostcenter) ^ @boostamount + @boostcenter
ELSEIF (@boostmode == â– ); invert
z = conj(iradius/(z-@boostcenter)) + @boostcenter
ELSEIF (@boostmode == â– ); pass through
z = z + â– â– (z-@boostcenter)â– @boostamount
ELSEIF (@boostmode == â– ); pass through â–
z = z + â– â– (@boostcenter-z)/cabs(@boostcenter-z)â– @boostradiusâ– @boostamount
ENDIF
ENDIF
bailout:
|z| < @bailout
default:
title = "Orbit Boost (Mandelbrot)"
helpfile = "dmj-pub\dmj-pub-uf-ob.htm"
center = (-â– .â– , â– .â– )
maxiter = â– â– â– â–
param start
caption = "Starting Point"
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 Julia type."
endparam
param bailout
caption = "Bail-out Value"
default = â– .â– eâ– â–
min = â– .â–
hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
to the Julia set anymore."
endparam
param boostcenter
caption = "Boost Center"
default = (â– ,â– )
hint = "This is the location of the boost area in the complex plane."
endparam
param boostradius
caption = "Boost Radius"
default = â– .â–
hint = "This is the size of the boost area."
endparam
param boostmode
caption = "Boost Mode"
default = â–
enum = "displace" "orbit origin" "orbit boost" "flip out" "repel" \
"exponentiate origin" "exponentiate boost" "invert" "pass through" \
"pass through â– "
hint = "Sets the type of effect when the orbit enters the boost area."
endparam
param boostamount
caption = "Boost Amount"
default = (â– ,â– )
hint = "This is the amount to boost."
endparam
switch:
type = "dmj-BoostJulia"
seed = #pixel
power = @power
bailout = @bailout
boostcenter = @boostcenter
boostradius = @boostradius
boostmode = @boostmode
boostamount = @boostamount
}
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
}
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
}
