Fractal 118 C – Opposite Multiverse Dimensions
Part of OUTER SPACE series – 05 2023
antagonist . blackhole . dimensions . frontier . multiverse . spacetime . universe
Fractal 118 C – zoom level 1
Fractal 118 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 In each case, the numerical characters have been replaced by â– to prevent unauthorized reproduction.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 to train an AI, please contact Philippe.
Fractal 118 C - Opposite Multiverse Dimensions - Part of OUTER SPACE series - 05.2023
Fractal_â– â– â– _C {
fractal:
title="Fractal_â– â– â– _C" width=â– â– â– â– height=â– â– â– â– layers=â– â–
credits="Philoxerax;â– /â– â– /â– 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– 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– 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– 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="Layer â– " opacity=â– â– â– transparent=yes
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–
formula:
maxiter=â– â– â– filename="mt.ufm" entry="mt-gen-celtic-m" p_n=â–
p_bailout=â– â– â– â– .â– f_fnâ– =floor f_fnâ– =abs
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes rotation=â– â– â– index=â– â– â– color=â–
opacity:
smooth=no index=â– opacity=â–
layer:
caption="Layer â– " opacity=â– â– â– transparent=yes
mapping:
center=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– angle=â– â– â–
formula:
maxiter=â– â– â– filename="mt.ufm" entry="mt-gen-celtic-m" p_n=â–
p_bailout=â– â– â– â– .â– f_fnâ– =floor f_fnâ– =abs
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes rotation=â– â– â– index=â– â– â– color=â–
opacity:
smooth=no index=â– opacity=â–
layer:
caption="Layer â– " opacity=â– â– mergemode=addition
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– magn=â– â– â– .â– â– â– â– â–
angle=-â– â– â– â– .â– â– â– â–
formula:
maxiter=â– â– â– filename="mt.ufm" entry="mt-â– â– â– â– â– â– a-m" p_eâ– =â– .â– p_eâ– =â– .â–
p_bailout=â– â– â– â– .â– f_fnâ– =flip f_fnâ– =ident
inside:
transfer=none solid=â– â– â– â– â– â– â– â– â– â–
outside:
transfer=linear
gradient:
smooth=yes rotation=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–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Background" opacity=â– 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– 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– 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– color=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=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–
formula:
maxiter=â– â– â– filename="mt.ufm" entry="mt-gen-celtic-m" p_n=â–
p_bailout=â– â– â– â– .â– f_fnâ– =floor f_fnâ– =abs
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes rotation=â– â– â– index=â– â– â– color=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– â–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Background" opacity=â– 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– magn=â– .â– â– â– angle=â– â– â–
formula:
maxiter=â– â– â– filename="mt.ufm" entry="mt-gen-celtic-m" p_n=â–
p_bailout=â– â– â– â– .â– f_fnâ– =floor f_fnâ– =abs
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes rotation=â– â– â– index=â– â– â– color=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– â–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Background" opacity=â– 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– 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– filename="mt.ufm" entry="mt-gen-celtic-m" p_n=â–
p_bailout=â– â– â– â– .â– f_fnâ– =sqr f_fnâ– =trunc
inside:
transfer=none
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– 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–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Layer â– " opacity=â– â– â– mergemode=addition
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– â– â–
formula:
maxiter=â– â– â– filename="mt.ufm" entry="mt-gen-celtic-m" p_n=â– .â–
p_bailout=â– â– â– â– .â– f_fnâ– =ident f_fnâ– =abs
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–
opacity:
smooth=no index=â– opacity=â– â– â–
layer:
caption="Layer â– " opacity=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– magn=â– â– â– â– â– .â– â– â–
angle=â– â– .â– â– â– â–
formula:
maxiter=â– â– â– filename="mt.ufm" entry="mt-gen-celtic-m" p_n=â– .â–
p_bailout=â– â– â– â– .â– f_fnâ– =ident f_fnâ– =abs
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes rotation=â– â– index=â– â– color=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–
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– filename="mt.ufm" entry="mt-gen-celtic-m" p_n=â– .â–
p_bailout=â– â– â– â– .â– f_fnâ– =ident f_fnâ– =abs
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– 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–
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
}
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
}
mt-â– â– â– â– â– â– a-m { ; Mark Townsend, Aug â– â– â– â– â–
init:
z = â–
c = #pixel
loop:
z = @fnâ– (câ– z^@eâ– ) + @fnâ– (z^@eâ– ) + c
bailout:
|z| < @bailout
default:
title = "â– â– â– â– â– â– a Mset"
param eâ–
caption = "First exponent"
default = â– .â–
endparam
param eâ–
caption = "Second exponent"
default = â– .â–
endparam
func fnâ–
default = ident()
endfunc
func fnâ–
default = ident()
endfunc
param bailout
caption = "Bailout value"
default = â– â– â– â– .â–
endparam
func fnâ–
caption = "First Function"
default = ident()
endfunc
func fnâ–
caption = "Second Function"
default = ident()
endfunc
switch:
type = "mt-â– â– â– â– â– â– a-j"
eâ– = eâ–
eâ– = eâ–
fnâ– = fnâ–
fnâ– = fnâ–
bailout = bailout
c = #pixel
}
