Icons

From Ultrafractal Wiki

Icons is a really nice formula that is implemented as a coloring method (in UF4). This means that to see the results you needed to use it with the 'pixel' formula.

The image that an icons fractal creates is a picture of a strange attractor, in a cumulative density plot made by iterating the fractal's orbit and "incrementing" each pixel that the orbit "lands on" throughout the iterations.

Under certain settings it takes on a delightful smokey-cloudyness or translucent-surface-like quality.

Escape-Time Icons Formula

Note, this fractal is also implemented in UF as an escape-time fractal formulae, but the full-frame 'density-count' version is what is predominantly shown here.

Symmetry

One of the main parameters decides the symmetry of the result. All upr's here so far show 5-way or 3-way symmetry.

Manual greyscale conversion

Most of these UPRs have been rendered and then the results converted to black-on-white manually in Irfanview, so the UPRs here may not create the same exact images shown! It's not hard to convert them though, just invert, adjust the levels/contrast, and de-saturate, this can even be done with a set of layers in UF, but the levels will need to be tuned individually in each case.

"Preview" mode - lower the "Sampling Factor"

These UPRs all have the the quality set high for final render, which means a high value (>100) for the parameter called "Sampling Factor". This will make them slow to preview unless you reduce the value.

To preview these fractals much more quickly in the GUI, try using a smaller value for "Sampling Factor" like 10 or even 4 can get a grainy result to look at a lot more quickly. Occasionally more samples than 20 may be needed to get an adequate preview.

Links

The precursor to Icons is the formula for the The 2d Bifurcation diagram for the Logistic Map.

icon five 03x yyyips 2partlymerged starg gibboiiipe

upr


icon_five_03x_yyyips_2partlymerged_starg_gibboiiipe {
fractal:
  title="icon_five_03x_yyyips_2partlymerged_starg_gibboiiipe"
  width=1024 height=1024 layers=1 credits="dan wills;10/4/2006"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=0.01128582245108/0.015 magn=3.11
formula:
  maxiter=1 percheck=off filename="mt.ufm" entry="mt-pixel"
  p_inside=yes
inside:
  density=0.1 transfer=linear repeat=no filename="jam2.ucl"
  entry="jam-symmicons3x" p_showcoeffs=yes p_n=5 p_lambda=-2.316191
  p_alpha=5.8411574 p_beta=-5.584757 p_gamma=1.241003
  p_omega=-0.386783 p_delta=-0.24292 p_p=0 p_showplot=yes
  p_hittype=pins p_samplefac=199 p_zinitial=0.001/0.002 p_ntrans=50
  p_showcolor=yes p_scalefactor=1 p_colorwarp="log(c)" p_cpower=0.25
  p_colorby=hits p_ranges=1 p_range1=4 p_range2=8 p_range3=11
  p_range4=14 p_range5=16 p_range6=18 p_range7=20 p_solidbg=yes
  p_BGindex=0.0 p_showmasks=yes p_maskA=no p_maskifA="falls above"
  p_maskAmin=8 p_maskAmax=16
outside:
  density=0.1 transfer=linear filename="Standard.ucl" entry="Default"
gradient:
  comments="Use with Lighting coloring algorithm." smooth=yes index=0
  color=0 index=5 color=921615 index=98 color=4007205 index=258
  color=6253201 index=354 color=10019832 index=387 color=15661823
  index=399 color=16777215
opacity:
  smooth=no index=0 opacity=255
}

icon five dotdotdot clovexah ovah

upr

icon_five_03x_yyyips_2partlymerged_starg_gibbo_toon_ganymede_freed_shmoogy_klumpz_clovexah_ovah {
fractal:
  title="icon_five_03x_yyyips_2partlymerged_starg_gibbo_toon_ganymede_\
  freed_shmoogy_klumpz_clovexah_ovah" width=1024 height=1024 layers=1
  credits="dan wills;10/7/2006"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=0/0 magn=3.15
formula:
  maxiter=1 percheck=off filename="mt.ufm" entry="mt-pixel"
  p_inside=yes
inside:
  density=0.1 transfer=linear repeat=no filename="jam2.ucl"
  entry="jam-symmicons3x" p_showcoeffs=yes p_n=5 p_lambda=-2.578764
  p_alpha=5.245254 p_beta=-8.768586 p_gamma=1.032758 p_omega=-0.290502
  p_delta=0.645348 p_p=0 p_showplot=yes p_hittype=pins p_samplefac=213
  p_zinitial=0.001/0.002 p_ntrans=50 p_showcolor=yes p_scalefactor=1
  p_colorwarp="log(c)" p_cpower=0.25 p_colorby=hits p_ranges=1
  p_range1=4 p_range2=8 p_range3=11 p_range4=14 p_range5=16
  p_range6=18 p_range7=20 p_solidbg=yes p_BGindex=0.0 p_showmasks=yes
  p_maskA=no p_maskifA="falls above" p_maskAmin=8 p_maskAmax=16
outside:
  density=0.1 transfer=linear filename="Standard.ucl" entry="Default"
gradient:
  comments="Use with Lighting coloring algorithm." smooth=yes index=0
  color=0 index=5 color=921615 index=98 color=4007205 index=258
  color=6253201 index=354 color=10019832 index=387 color=15661823
  index=399 color=16777215
opacity:
  smooth=no index=0 opacity=255
}

icon five dotdotdot flap gap

upr

icon_five_03x_yyyips_2partlymerged_starg_gibbo_toon_ganymede_freed_shmoogy_klumpz_clovexah_bap_flap_gap {
fractal:
  title="icon_five_03x_yyyips_2partlymerged_starg_gibbo_toon_ganymede_\
  freed_shmoogy_klumpz_clovexah_bap_flap_gap" width=1024 height=1024
  layers=1 credits="dan wills;1/28/2009"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=0.02/0 magn=3.4
formula:
  maxiter=1 percheck=off filename="mt.ufm" entry="mt-pixel"
  p_inside=yes
inside:
  density=0.1 transfer=linear repeat=no filename="jam2.ucl"
  entry="jam-symmicons3x" p_showcoeffs=yes p_n=5 p_lambda=-2.410571
  p_alpha=5.261802 p_beta=-8.102875 p_gamma=0.753004 p_omega=-0.290502
  p_delta=0.416298 p_p=0 p_showplot=yes p_hittype=pins p_samplefac=9
  p_zinitial=0.001/0.002 p_ntrans=50 p_showcolor=yes p_scalefactor=1
  p_colorwarp="log(c)" p_cpower=0.25 p_colorby=hits p_ranges=1
  p_range1=4 p_range2=8 p_range3=11 p_range4=14 p_range5=16
  p_range6=18 p_range7=20 p_solidbg=yes p_BGindex=0.0 p_showmasks=yes
  p_maskA=no p_maskifA="falls above" p_maskAmin=8 p_maskAmax=16
outside:
  density=0.1 transfer=linear filename="Standard.ucl" entry="Default"
gradient:
  comments="Use with Lighting coloring algorithm." smooth=yes index=0
  color=0 index=5 color=921615 index=98 color=4007205 index=258
  color=6253201 index=354 color=10019832 index=387 color=15661823
  index=399 color=16777215
opacity:
  smooth=no index=0 opacity=255
}

icon five 03x yyyips 2partlymerged starg

upr

icon_five_03x_yyyips_2partlymerged_starg {
fractal:
  title="icon_five_03x_yyyips_2partlymerged_starg" width=1024
  height=1024 layers=1 credits="dan wills;10/2/2006"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=0.00268582245108/0 magn=3.16
formula:
  maxiter=1 percheck=off filename="mt.ufm" entry="mt-pixel"
  p_inside=yes
inside:
  density=0.1 transfer=linear repeat=no filename="jam2.ucl"
  entry="jam-symmicons3x" p_showcoeffs=yes p_n=5 p_lambda=-2.257983
  p_alpha=5.90657 p_beta=-2.35455 p_gamma=0.249611 p_omega=0.2023674
  p_delta=-0.468425 p_p=0 p_showplot=yes p_hittype=pins p_samplefac=4
  p_zinitial=0.001/0.002 p_ntrans=50 p_showcolor=yes p_scalefactor=1
  p_colorwarp="log(c)" p_cpower=0.25 p_colorby=hits p_ranges=1
  p_range1=4 p_range2=8 p_range3=11 p_range4=14 p_range5=16
  p_range6=18 p_range7=20 p_solidbg=yes p_BGindex=0.0 p_showmasks=yes
  p_maskA=no p_maskifA="falls above" p_maskAmin=8 p_maskAmax=16
outside:
  density=0.1 transfer=linear filename="Standard.ucl" entry="Default"
gradient:
  comments="Use with Lighting coloring algorithm." smooth=yes index=0
  color=0 index=5 color=921615 index=98 color=4007205 index=258
  color=6253201 index=354 color=10019832 index=387 color=15661823
  index=399 color=16777215
opacity:
  smooth=no index=0 opacity=255
}

icon five 03x

upr

icon_five_03x {
fractal:
  title="icon_five_03x" width=1024 height=1024 layers=1
  credits="dan wills;10/2/2006"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=0.05268582245108/0 magn=1.94
formula:
  maxiter=1 percheck=off filename="mt.ufm" entry="mt-pixel"
  p_inside=yes
inside:
  density=0.1 transfer=linear repeat=no filename="jam2.ucl"
  entry="jam-symmicons3x" p_showcoeffs=yes p_n=5 p_lambda=-2.351173
  p_alpha=2.0 p_beta=0.2 p_gamma=0.258287 p_omega=0.0 p_delta=0.0
  p_p=0.0 p_showplot=yes p_hittype=pins p_samplefac=155
  p_zinitial=0.001/0.002 p_ntrans=50 p_showcolor=yes p_scalefactor=1
  p_colorwarp="log(c)" p_cpower=0.25 p_colorby=hits p_ranges=1
  p_range1=4 p_range2=8 p_range3=11 p_range4=14 p_range5=16
  p_range6=18 p_range7=20 p_solidbg=yes p_BGindex=0.0 p_showmasks=yes
  p_maskA=no p_maskifA="falls above" p_maskAmin=8 p_maskAmax=16
outside:
  density=0.1 transfer=linear filename="Standard.ucl" entry="Default"
gradient:
  comments="Use with Lighting coloring algorithm." smooth=yes index=0
  color=723723 index=5 color=791054 index=98 color=3357479 index=258
  color=6257041 index=354 color=10019832 index=387 color=16771557
  index=399 color=16777215
opacity:
  smooth=no index=0 opacity=255
}

Icon03 string2 6 5 55 bw

upr

icon03_string2_6__5_55 {
fractal:
  title="icon03_string2_6__5_55" width=1024 height=1024 layers=1
  credits="dan wills;10/3/2006"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=-0.033/-0.03 magn=1.7565201779
formula:
  maxiter=1 percheck=off filename="mt.ufm" entry="mt-pixel"
  p_inside=yes
inside:
  density=0.1 transfer=linear repeat=no filename="jam2.ucl"
  entry="jam-symmicons3x" p_showcoeffs=yes p_n=5 p_lambda=-2.151138
  p_alpha=1.567916 p_beta=0.17463 p_gamma=0.100357 p_omega=0.686362
  p_delta=0.0345788 p_p=0.0 p_showplot=yes p_hittype=pins
  p_samplefac=193 p_zinitial=0.001/0.002 p_ntrans=50 p_showcolor=yes
  p_scalefactor=1 p_colorwarp="log(c)" p_cpower=0.25 p_colorby=hits
  p_ranges=1 p_range1=4 p_range2=8 p_range3=11 p_range4=14 p_range5=16
  p_range6=18 p_range7=20 p_solidbg=yes p_BGindex=0.0 p_showmasks=yes
  p_maskA=no p_maskifA="falls above" p_maskAmin=8 p_maskAmax=16
outside:
  density=0.1 transfer=linear filename="Standard.ucl" entry="Default"
gradient:
  comments="Use with Lighting coloring algorithm." smooth=yes index=0
  color=723723 index=5 color=791054 index=98 color=3357479 index=258
  color=6257041 index=354 color=10019832 index=387 color=16771557
  index=399 color=16777215
opacity:
  smooth=no index=0 opacity=255
}

Icon03 la

upr

icon03_la {
fractal:
  title="icon03_la" width=1024 height=1024 layers=1
  credits="dan wills;1/28/2009"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=-0.0002441405/0 magn=1.9701779
formula:
  maxiter=1 percheck=off filename="mt.ufm" entry="mt-pixel"
  p_inside=yes
inside:
  density=0.1 transfer=linear repeat=no filename="jam2.ucl"
  entry="jam-symmicons3x" p_showcoeffs=yes p_n=5.0 p_lambda=-2.34
  p_alpha=1.930592 p_beta=0.2 p_gamma=0.05662 p_omega=0.0069408
  p_delta=0.017352 p_p=0.0 p_showplot=yes p_hittype=pins p_samplefac=9
  p_zinitial=0.001/0.002 p_ntrans=50 p_showcolor=yes p_scalefactor=1
  p_colorwarp="log(c)" p_cpower=0.25 p_colorby=hits p_ranges=1
  p_range1=4 p_range2=8 p_range3=11 p_range4=14 p_range5=16
  p_range6=18 p_range7=20 p_solidbg=yes p_BGindex=0.0 p_showmasks=yes
  p_maskA=no p_maskifA="falls above" p_maskAmin=8 p_maskAmax=16
outside:
  density=0.1 transfer=linear filename="Standard.ucl" entry="Default"
gradient:
  comments="Use with Lighting coloring algorithm." smooth=yes index=0
  color=723723 index=5 color=791054 index=98 color=3357479 index=258
  color=6257041 index=354 color=10019832 index=387 color=16771557
  index=399 color=16777215
opacity:
  smooth=no index=0 opacity=255
}

icon03 la xont shiv

upr

Copy2OfIcon03_la_xont_shiv {
fractal:
  title="Copy (2) of icon03_la_xont_shiv" width=1024 height=1024
  layers=1 credits="dan wills;10/3/2006"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=-0.0002441405/0 magn=1.9701779
formula:
  maxiter=1 percheck=off filename="mt.ufm" entry="mt-pixel"
  p_inside=yes
inside:
  density=0.1 transfer=linear repeat=no filename="jam2.ucl"
  entry="jam-symmicons3x" p_showcoeffs=yes p_n=5.0 p_lambda=-2.0962274
  p_alpha=1.930592 p_beta=-0.0861359 p_gamma=0.264843 p_omega=0.111053
  p_delta=-0.182195 p_p=0.0 p_showplot=yes p_hittype=pins
  p_samplefac=157 p_zinitial=0.001/0.002 p_ntrans=50 p_showcolor=yes
  p_scalefactor=1 p_colorwarp="log(c)" p_cpower=0.25 p_colorby=hits
  p_ranges=1 p_range1=4 p_range2=8 p_range3=11 p_range4=14 p_range5=16
  p_range6=18 p_range7=20 p_solidbg=yes p_BGindex=0.0 p_showmasks=yes
  p_maskA=no p_maskifA="falls above" p_maskAmin=8 p_maskAmax=16
outside:
  density=0.1 transfer=linear filename="Standard.ucl" entry="Default"
gradient:
  comments="Use with Lighting coloring algorithm." smooth=yes index=0
  color=723723 index=5 color=791054 index=98 color=3357479 index=258
  color=6257041 index=354 color=10019832 index=387 color=16771557
  index=399 color=16777215
opacity:
  smooth=no index=0 opacity=255
}