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 In each case, the numerical characters have been replaced by ■ to prevent unauthorized reproduction.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_■■■_C {
fractal:
  title="Fractal_■■■_C" width=■■■■ height=■■■■ layers=■
  credits="Philoxerax;■/■/■■■■"
layer:
  caption="Layer ■" opacity=■■■ mergemode=lighten
mapping:
  center=-■.■■■■■■■■■■■■■/■.■■■■■■■■■■■■ magn=■■■.■■■■■
  angle=-■■■.■■■■
formula:
  maxiter=■■■ filename="mt.ufm" entry="mt-■■■■■■a-m" p_e■=■.■ p_e■=■.■
  p_bailout=■■■■.■ f_fn■=flip f_fn■=ident
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=■■■
layer:
  caption="Background" opacity=■■■ mergemode=overlay
mapping:
  center=-■.■■■■■■■■■■■■■/■.■■■■■■■■■■■■■ magn=■■■.■■■■■
  angle=-■■.■■■■
formula:
  maxiter=■■■ filename="lkm■.ufm"
  entry="mixed-up-multiplication-mandelbrot" p_power=■ p_bailout=■■■■
  p_shape_type=square p_q■_type=out p_q■_type=out p_q■_type=out
  p_q■_type=out p_freq=■ p_amp=■.■ p_nteeth=■ p_rsmall=■.■
  p_inrad=■.■■
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="Layer ■" opacity=■■ mergemode=red
mapping:
  center=-■.■■■■■■■■■■■■■/■.■■■■■■■■■■■■■ magn=■■■.■■■■■
  angle=-■■■.■■■■
formula:
  maxiter=■■■ filename="mt.ufm" entry="mt-■■■■■■a-m" p_e■=■.■ p_e■=■.■
  p_bailout=■■■■.■ f_fn■=flip f_fn■=ident
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="Background" opacity=■■■
mapping:
  center=-■.■■■■■■■■■■■■■/■.■■■■■■■■■■■■■ magn=■■■.■■■■■
  angle=-■■■.■■■■
formula:
  maxiter=■■■ filename="mt.ufm" entry="mt-■■■■■■a-m" p_e■=■.■ p_e■=■.■
  p_bailout=■■■■.■ f_fn■=flip f_fn■=ident
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=■■■
}

mt-■■■■■■a-m { ; Mark Townsend, Aug ■ ■■■■
init:
  z = ■
  c = #pixel
loop:
  z = @fn■(c■z^@e■) + @fn■(z^@e■) + c
bailout:
  |z| < @bailout
default:
  title = "■■■■■■a Mset"
  param e■
    caption = "First exponent"
    default = ■.■
  endparam  
  param e■
    caption = "Second exponent"
    default = ■.■
  endparam  
  func fn■
    default = ident()
  endfunc  
  func fn■
    default = ident()
  endfunc  
  param bailout
    caption = "Bailout value"
    default = ■■■■.■
  endparam  
  func fn■
    caption = "First Function"
    default = ident()
  endfunc  
  func fn■
    caption = "Second Function"
    default = ident()
  endfunc  
switch:
  type = "mt-■■■■■■a-j"
  e■ = e■
  e■ = e■  
  fn■ = fn■
  fn■ = fn■
  bailout = bailout
  c = #pixel
}

mixed-up-multiplication-mandelbrot { ; Kerry Mitchell ■■Nov■■■■
;
; Instead of using regular complex multiplication, this method uses a base
; shape (= unit circle normally). Use the polar angle of z to reach back
; to the base shape and find its coordinates. Then, use the actual and base
; magnitudes to determine a scale factor, and the arc length to determine
; the angle (angle = arc length / base magnitude). From there, the magnitude
; of z^power = scale factor ^ power, and angle of z^power = power ■ angle.
;
$define debug
global:
  complex corner[■■]
  float pitch_s=■
  float pitch_trad=■
  float smax=■
  float tdegmax[■■]
  float twopi=■■#pi
  int gi=■
;
; cruciform settings: central square side & four other squares, one
; on each side of central square
;
  if(@shape_type=="cruciform")
    corner[■]=(■,■)
    corner[■]=(■,■)
    corner[■]=(■,■)
    corner[■]=(■,■)
    corner[■]=(-■,■)
    corner[■]=(-■,■)
    corner[■]=(-■,■)
    corner[■]=(-■,-■)
    corner[■]=(-■,-■)
    corner[■]=(-■,-■)
    corner[■■]=(■,-■)
    corner[■■]=(■,-■)
    corner[■■]=(■,-■)
    corner[■■]=(■,■)
;
;   rescale so that corner[■] = (■,■)
;   find degree measures of corners
;
    gi=-■
    while(gi<■■)
      gi=gi+■
      corner[gi]=corner[gi]/■
      tdegmax[gi]=(atan■(corner[gi])/#pi■■■■+■■■)%■■■
    endwhile
  elseif(@shape_type=="triangle")
    corner[■]=(■,■)
    corner[■]=(-■+flip(sqrt(■)))/■
    corner[■]=(-■-flip(sqrt(■)))/■
    tdegmax[■]=■
    tdegmax[■]=■■■
    tdegmax[■]=■■■
    tdegmax[■]=■■■
  elseif(@shape_type=="star")
    corner[■]=(■,■)
    corner[■]=@inrad■(■,■)/sqrt(■)
    corner[■]=(■,■)
    corner[■]=@inrad■(-■,■)/sqrt(■)
    corner[■]=(-■,■)
    corner[■]=@inrad■(-■,-■)/sqrt(■)
    corner[■]=(■,-■)
    corner[■]=@inrad■(■,-■)/sqrt(■)
    corner[■]=(■,■)
    tdegmax[■]=■
    tdegmax[■]=■■
    tdegmax[■]=■■
    tdegmax[■]=■■■
    tdegmax[■]=■■■
    tdegmax[■]=■■■
    tdegmax[■]=■■■
    tdegmax[■]=■■■
    tdegmax[■]=■■■
  endif
;
; gear settings
;
  if(@shape_type=="gear")
    pitch_trad=twopi/@nteeth
    smax=#pi■(■+@rsmall)
    pitch_s=smax/@nteeth
  endif
init:
  complex arccenter=(■,■)
  complex c=#pixel
  complex compk=(■,■)
  complex w=(■,■)
  complex z=#pixel
  float afac=■
  float bfac=■
  float cfac=■
  float dcrit=■/(■+@rsmall)
  float dtooth=■
  float h■=■
  float k■=■
  float k=■
  float phi=■
  float phimax=■
  float r=■
  float s=■
  float slope=■
  float tdeg=■
  float third=■/■
  float trad=■
  float x=■
  float xb=■
  float x■=■
  float y=■
  float yb=■
  float y■=■
  int itooth=■
loop:
;
; decompose z
;
  x=real(z), y=imag(z)
;
; square
;
  if(@shape_type=="square")
;
;   determine arc length from basis shape
;
    phimax=■
;
;   find scale factor k
;
    k=abs(x)
    if(abs(y)>k)
      k=abs(y)
    endif
;
;   find standard polar angle
;
    trad=atan■(z)
    if(trad<■)
      trad=trad+■■#pi
    endif
    tdeg=trad/#pi■■■■
;
;   use polar angle to find coordinates of point on base shape
;   and base shape arc length
;
    if(tdeg<■■) ; upper right side
      xb=■, yb=y/k, s=yb
    elseif(tdeg<■■■) ; top
      xb=x/k, yb=■, s=■-xb
    elseif(tdeg<■■■) ; left side
      xb=-■, yb=y/k, s=■-yb
    elseif(tdeg<■■■) ; bottom
      xb=x/k, yb=-■, s=■+xb
    else ; lower right side
      xb=■, yb=y/k, s=■+yb
    endif
    phi=s
;
;   raise z to power
;
    k=k^@power, phi=(@power■phi)%phimax
;
;   use phi and k to return new x & y and add c
;
    if(phi<■) ; upper right side
      xb=■, yb=phi
    elseif(phi<■) ; top
      xb=■-phi, yb=■
    elseif(phi<■) ; left side
      xb=-■, yb=■-phi
    elseif(phi<■) ; bottom
      xb=phi-■, yb=-■
    else ; lower right side
      xb=■, yb=phi-■
    endif
    x=xb■k, y=yb■k
    z=x+flip(y)+c
;
; triangle
;
  elseif(@shape_type=="triangle")
;
;   determine arc length from basis shape
;
    third=sqrt(■)
    phimax=■■third
;
;   find standard magnitude and polar angle
;
    r=cabs(z)
    trad=atan■(z)
    tdeg=(trad/#pi■■■■+■■■)%■■■
    trad=tdeg/■■■■#pi
;
;   use polar angle to find coordinates of point on base shape
;   and base shape arc length
;
    if(tdeg