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 In each case, the numerical characters have been replaced by ■ to prevent unauthorized reproduction. If you are interested in using the full data set to train an AI, please contact Philippe.

Layers {
layer:
caption="Layer ■" opacity=■■■ mergemode=overlay transparent=yes
mapping:
center=■.■■■■■■■■■■/-■.■■■■■■■■ magn=■.■■■■■■■ angle=■■■.■■■■
formula:
maxiter=■■■ filename="reb.ufm" entry="JuliaCrossOrbitLambda"
p_version=■.■ p_test=and p_bailout=■ p_p■=■.■/■ p_p■=■■■/■
p_p■=-■.■■/■.■ p_thresh=■.■ p_cross="Func Divide" f_fn■=sqrt
inside:
transfer=none solid=■
outside:
transfer=linear
gradient:
smooth=yes rotation=■■■ index=■■■ color=■■■■■■■ index=■■■
color=■■■■■■■ index=■■■ color=■■■■■■■ index=■■■ color=■■■■■■■■
index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■ index=■■■
color=■■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■
index=■■■ color=■■■■■■■ index=■■■ color=■■■■■■■■
opacity:
smooth=no index=■ opacity=■■■
layer:
caption="Layer ■" opacity=■■■ mergemode=color transparent=yes
mapping:
center=■.■■■■■■■■■■/-■.■■■■■■■■ magn=■.■■■■■■■ angle=■■■.■■■■
formula:
maxiter=■■■ filename="reb.ufm" entry="JuliaCrossOrbitLambda"
p_version=■.■ p_test=and p_bailout=■ p_p■=■.■/■ p_p■=■■■/■
p_p■=-■.■■/■.■ p_thresh=■.■ p_cross="Func Divide" f_fn■=sqrt
inside:
transfer=none solid=■
outside:
transfer=linear
gradient:
smooth=yes rotation=-■■■ index=■ color=■■■■■■■■ index=■■
color=■■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■■
index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■
color=■■■■■■■■ index=■■■ color=■■■■■■■ index=-■■■ color=■■■■■■■■
index=-■■■ color=■■■■■■■ index=-■■■ color=■■■■■■■■ index=-■■■
color=■■■■■■■■ index=-■■■ color=■■■■■■■■ index=-■■■ color=■■■■■■■
index=-■■■ color=■■■■■■■ index=-■■■ color=■■■■■■■ index=-■■
color=■■■■■■■ index=-■■ color=■■■■■■■■ index=■■■ color=■■■■■■■■
opacity:
smooth=no index=■ opacity=■■■
layer:
caption="Background" opacity=■■■ mergemode=luminance transparent=yes
mapping:
center=■.■■■■■■■■■/-■.■■■■■■■■■ magn=■.■■■■■■■
formula:
maxiter=■■■ filename="reb.ufm" entry="JuliaCrossOrbitLambda"
p_version=■.■ p_test=and p_bailout=■ p_p■=■.■/■ p_p■=■■■/■
p_p■=-■.■■/■.■ p_thresh=■.■ p_cross="Func Divide" f_fn■=sqrt
inside:
transfer=none solid=■
outside:
transfer=linear
gradient:
smooth=yes rotation=-■ index=■ color=■■■■■■■ index=■ color=■■■■■■■■
index=■■ color=■■■■■■■■ index=■■ color=■■■■■■■■ index=■■
color=■■■■■■■ index=■■ color=■■■■■■■ index=■■ color=■■■■■■■ index=■■
color=■■■■■■■ index=■■ color=■■■■■■■■ index=■■■ color=■■■■■■■■
index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■
color=■■■■■■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■■■■■■■■
index=■■■ color=■■■■■■■ index=-■ color=■■■■■■■■
opacity:
smooth=no index=■ opacity=■■■
layer:
caption="Background" opacity=■■■ mergemode=lighten
mapping:
center=■.■■■■■■■■■■■■e-■/-■.■■■■■■■■■■■■e-■ magn=■■■■■■.■■
angle=■■.■■■■
formula:
maxiter=■■■ percheck=off filename="reb.ufm" entry="GopalsamyFn"
p_version=■.■ p_test=mod p_bailout=■■■■■ p_p■=■/■.■■ f_fn■=recip
f_fn■=sin f_fn■=recip f_fn■=cabs
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes rotation=-■■■ index=■ color=■■■■■ index=■■■ color=■■■
index=-■■■ color=■■■■■■■ index=-■■■ color=■■■■■■■■
opacity:
smooth=no index=■ opacity=■■■
layer:
caption="Background" opacity=■■■
mapping:
center=■.■■■■■■■■■■/■.■■■■■■■■■■■ magn=■.■■■■■■■ angle=■■.■■■■
formula:
maxiter=■■■ percheck=off filename="reb.ufm" entry="GopalsamyFn"
p_version=■.■ p_test=mod p_bailout=■■■■■ p_p■=-■.■■/■.■■ f_fn■=sqr
f_fn■=recip f_fn■=cos f_fn■=cabs
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes rotation=-■■ index=■ color=■■■■■■■ index=■■
color=■■■■■■■■ index=■■ color=■■■■■ index=■■■ color=■■■■■■■
index=■■■ color=■■■■■■■ index=■■■ color=■■■■■■■ index=-■■
color=■■■■■■■ index=-■ color=■■■■■■■■
opacity:
smooth=no index=■ opacity=■■■
}

JuliaCrossOrbitLambda {; Ron Barnett, Movember ■■■■
; Cross orbit boost when crossing Lambda
init:
#z = #pixel
w = #z
float d = ■
loop:
#z = #z^@p■ + @p■
w = @p■*w*(■ - w^@p■) 
d = cabs(#z-w)
r = d/@thresh
if d < @thresh
if @cross == ■
#z = #z + w*r
elseif @cross == ■
#z = #z - w*r
elseif @cross == ■
#z = #z*w*r
elseif @cross == ■
#z = #z/w/r
elseif @cross == ■
#z = #z + @fn■(w)*r
elseif @cross == ■
#z = #z - @fn■(w)*r
elseif @cross == ■
#z = #z*@fn■(w)*r
elseif @cross == ■
#z = #z/@fn■(w)*r
elseif @cross == ■
#z = #z^w*r
endif 
endif
bailout:
(@test == ■ && |#z| <= @bailout) || \
(@test == ■ && sqr(real(#z)) <= @bailout) || \
(@test == ■ && sqr(imag(#z)) <= @bailout) || \
(@test == ■ && (sqr(real(#z)) <= @bailout && sqr(imag(#z)) < @bailout)) || \
(@test == ■ && (sqr(real(#z)) <= @bailout || sqr(imag(#z)) < @bailout)) || \
(@test == ■ && (sqr(abs(real(#z)) + abs(imag(#z))) <= @bailout)) || \
(@test == ■ && (sqr(real(#z) + imag(#z)) <= @bailout))
default:
title = "Julia Cross Orbit Lambda"
maxiter = ■■■
center = (■, ■)
param version
caption = "Formula Version"
default = ■.■
hint = "You should never see this parameter; it's used internally to track \
which version of the formula was used to create your image, so that \
if a bug is found which breaks backwards-compatibility, the formula \
can adapt transparently."
visible = false
endparam
param test
caption = "Bailout Test"
default = ■
enum = "mod" "real" "imag" "or" "and" "manh" "manr"
endparam
param bailout
caption = "Bailout value"
default = ■.■
min = ■
endparam
param p■
caption = "Power"
default = (■.■, ■)
endparam
param p■
caption = "Lambda Power"
default = (■.■,■)
endparam
param p■
caption = "Seed"
default = (-■.■■, ■.■)
endparam 
param thresh
caption = "Threshold"
default = ■.■
endparam
param cross
caption = "Cross Type"
enum = "Add" "Subtract" "Multiply" "Divide" "Func Add" "Func Subtract" \
"Func Multiply" "Func Divide" "Exponential" 
default = ■
endparam 
func fn■
caption = "Function"
default = cabs()
endfunc 
switch:
type = "MandelbrotCrossOrbitLambda"
bailout = bailout
p■ = p■
p■ = p■
thresh = thresh
cross = cross
test = test
fn■ = fn■
}
GopalsamyFn { ; Ron Barnett, ■■■■
; Modified and tweaked March ■■■■
; modified October ■■■■
init:
#z = #pixel
loop:
x = real(#z)
y = imag(#z)
x■ = @fn■(x)*@fn■(y)
y■ = @fn■(x)*@fn■(y)
x■ = -■*x■*y■ + @p■
y = y■*y■ - x■*x■
#z = x■ + flip(y)
bailout:
(@test == ■ && |#z| <= @bailout) || \
(@test == ■ && sqr(real(#z)) <= @bailout) || \
(@test == ■ && sqr(imag(#z)) <= @bailout) || \
(@test == ■ && (sqr(real(#z)) <= @bailout && sqr(imag(#z)) < @bailout)) || \
(@test == ■ && (sqr(real(#z)) <= @bailout || sqr(imag(#z)) < @bailout)) || \
(@test == ■ && (sqr(abs(real(#z)) + abs(imag(#z))) <= @bailout)) || \
(@test == ■ && (sqr(real(#z) + imag(#z)) <= @bailout))
default:
title = "GopalsamyFn"
center = (■.■, ■.■)
maxiter = ■■■
periodicity = ■
param version
caption = "Formula Version"
default = ■.■
hint = "You should never see this parameter; it's used internally to track \
which version of the formula was used to create your image, so that \
if a bug is found which breaks backwards-compatibility, the formula \
can adapt transparently."
visible = false
endparam
param test
caption = "Bailout Test"
default = ■
enum = "mod" "real" "imag" "or" "and" "manh" "manr"
endparam
float param bailout
caption = "Bailout value"
default = ■■■■■
min = ■
endparam
param p■
caption = "Parameter ■"
default = (-■.■■, -■.■)
endparam
func fn■
caption = "First Function"
default = asin()
endfunc
func fn■
caption = "Second Function"
default = cos()
endfunc
func fn■
caption = "Third Function"
default = cosh()
endfunc
func fn■
caption = "Fourth Function"
default = atan()
endfunc
switch:
type = "MandelGopalsamyFn"
bailout = @bailout
fn■ = @fn■
fn■ = @fn■
fn■ = @fn■
fn■ = @fn■
}