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 In each case, the numerical characters have been replaced by ■ to prevent unauthorized reproduction.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.

Fractal_■■■_D {
fractal:
title="Fractal_■■■_D" width=■■■■ height=■■■■ layers=■
credits="Philoxerax;■■/■■/■■■■"
layer:
caption="Layer ■" opacity=■■■ mergemode=overlay
mapping:
center=-■.■■■■■■■■■■■■■/-■.■■■■■■■■■■■■ magn=■■.■■■■■■
angle=■■■.■■■■
formula:
maxiter=■■■■ percheck=off filename="dmj.ufm"
entry="dmj-PhoenixDNovaMandel" p_start=■/■ p_power■=■/■ p_power■=■/■
p_coeff■=■/■ p_coeff■=-■/■ p_induct=-■.■/■ p_bailout=■.■■■■■
p_usecritical=no p_relax=■/■
inside:
transfer=linear
outside:
transfer=linear
gradient:
comments="Use with Lighting coloring algorithm." smooth=yes
rotation=■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■
opacity:
smooth=no index=■ opacity=■■■
layer:
caption="Layer ■" opacity=■■■ mergemode=overlay
mapping:
center=-■.■■■■■■■■■■■■/-■.■■■■■■■■■■■■ magn=■■.■■■■■■ angle=■■■.■■■■
formula:
maxiter=■■■■ percheck=off filename="dmj.ufm"
entry="dmj-PhoenixDNovaMandel" p_start=■/■ p_power■=■/■ p_power■=■/■
p_coeff■=■/■ p_coeff■=-■/■ p_induct=-■.■/■ p_bailout=■.■■■■■
p_usecritical=no p_relax=■/■
inside:
transfer=linear
outside:
transfer=linear
gradient:
comments="Use with Lighting coloring algorithm." smooth=yes
rotation=■■■ index=■■■ color=■■■■■■■■ index=■■■ color=■
opacity:
smooth=no index=■ opacity=■■■
layer:
caption="Layer ■" opacity=■■■ mergemode=difference
mapping:
center=■.■■■■■■■■■/-■.■■■■■■■■■ magn=■.■■■■■■■■
formula:
maxiter=■■■ percheck=off filename="mt.ufm" entry="mt-zeepop-m"
p_h=■.■/■ p_bailout=■■■ p_epsilon=■E-■ f_fn■=atan f_fn■=abs
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=■ 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=■■■■■ 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="Layer ■" opacity=■■■ mergemode=overlay
mapping:
center=■.■■■■■■■■■■■/-■.■■■■■■■■■■■■ magn=■■.■■■■■■
formula:
maxiter=■■■ percheck=off filename="mt.ufm" entry="mt-zeepop-j"
p_c=■/■ p_h=■.■■■/■ p_bailout=■■ p_epsilon=■E-■ f_fn■=cabs f_fn■=tan
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=■■■■■■■ index=-■■ color=■■■■■■■■ index=-■■
color=■■■■■■■■ index=-■■ color=■■■■■
opacity:
smooth=no index=■ opacity=■■■
layer:
caption="Background" opacity=■■■
mapping:
center=■.■■■■■■■■■■■/-■.■■■■■■■■■■■■ magn=■■.■■
formula:
maxiter=■■■ percheck=off filename="mt.ufm" entry="mt-zeepop-j"
p_c=■/■ p_h=■.■/■ p_bailout=■■ p_epsilon=■E-■ f_fn■=cabs f_fn■=tan
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=■■■■■■■ index=■■■ color=■■■■■■■ index=-■■ color=■■■■■■■■
index=-■■ color=■■■■■■■■ index=-■■ color=■■■■■■■
opacity:
smooth=no index=■ opacity=■■■
}

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 = (■,■)
complex y = (■,■)

z = @start
IF (@usecritical)
z = ( -((@power■-■)■@power■■@coeff■) / \
((@power■-■)■@power■■@coeff■) ) ^ (■/(@power■-@power■))
ENDIF

loop:
y = zold
zold = z
z = z - (@coeff■■z^@power■ + @coeff■■z^@power■ - ■) ■ @relax / \
(@coeff■■@power■■z^(@power■-■) + @coeff■■@power■■z^(@power■-■)) + #pixel + @induct■y

bailout:
|z - zold| > @bailout

default:
title = "PhoenixDoubleNova (Mandelbrot)"
helpfile = "dmj-pub\dmj-pub-uf-pdn.htm"
maxiter = ■■■■
periodicity = ■
center = (-■.■,■)
magn = ■.■

param start
caption = "Start Value"
default = (■,■)
hint = "Starting value for each point. You can use this to \
'perturb' the fractal."
endparam
param power■
caption = "Primary Exponent"
default = (■,■)
hint = "Defines the primary exponent for the equation."
endparam
param power■
caption = "Secondary Exponent"
default = (■,■)
hint = "Defines the secondary exponent for the equation."
endparam
param coeff■
caption = "Primary Scale"
default = (■,■)
hint = "Defines the coefficient (multiplier) for the \
primary exponent term."
endparam
param coeff■
caption = "Secondary Scale"
default = (-■,■)
hint = "Defines the coefficient (multiplier) for the \
secondary exponent term."
endparam
param induct
caption = "Phoenix Distortion"
default = (-■.■,■)
hint = "Sets how 'strong' the previous iteration's effect should be \
on the fractal."
endparam
param bailout
caption = "Bailout"
default = ■.■■■■■
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 = (■,■)
hint = "This can be used to slow down the convergence of \
the formula."
endparam

switch:
type = "dmj-PhoenixDNovaJulia"
seed = #pixel
power■ = @power■
power■ = @power■
coeff■ = @coeff■
coeff■ = @coeff■
bailout = @bailout
relax = @relax
}

mt-zeepop-m { ; Mark Townsend, ■ May ■■■■
init:
c = #pixel
z = sqr(■ - #pixel)
oldz = ■
loop:
oldz = z
z = z - @h ■ @fn■(z + @fn■(c ■ z))
bailout:
|z - oldz| > @epsilon
default:
title = "Zeepop Mset"
periodicity = ■
param h
caption = "Step Size"
default = (■.■,■)
endparam 
param bailout
caption = "Bailout Value"
default = ■■■
endparam 
param epsilon
caption = "Epsilon"
default = ■e-■
endparam 
func fn■
caption = "Function #■"
default = sin()
endfunc 
func fn■
caption = "Function #■"
default = tan()
endfunc 
switch:
type = "mt-zeepop-j"
c = #pixel
h = h
fn■ = fn■
fn■ = fn■
bailout = bailout
epsilon = epsilon
}

mt-zeepop-m { ; Mark Townsend, ■ May ■■■■
init:
c = #pixel
z = sqr(■ - #pixel)
oldz = ■
loop:
oldz = z
z = z - @h ■ @fn■(z + @fn■(c ■ z))
bailout:
|z - oldz| > @epsilon
default:
title = "Zeepop Mset"
periodicity = ■
param h
caption = "Step Size"
default = (■.■,■)
endparam 
param bailout
caption = "Bailout Value"
default = ■■■
endparam 
param epsilon
caption = "Epsilon"
default = ■e-■
endparam 
func fn■
caption = "Function #■"
default = sin()
endfunc 
func fn■
caption = "Function #■"
default = tan()
endfunc 
switch:
type = "mt-zeepop-j"
c = #pixel
h = h
fn■ = fn■
fn■ = fn■
bailout = bailout
epsilon = epsilon
}