Burning ship version of Pauldebrot formula is quite an intriguing. Actualy not all of them, but a version what is generated when z seed is small fractional number but a W seed aproaches zero with w= 0 representing singularity a normal mandelbrot set.
Navalis_Ignis_Pauldebroti {
fractal:
title="Navalis_Ignis_Pauldebroti" width=640 height=480 layers=1
credits="Asdam;1/27/2013;Edgar;1/24/2013"
layer:
caption="Background" opacity=100
mapping:
center=-0.525/-0.3625 magn=1.0169492
formula:
maxiter=500 percheck=off filename="em.ufm" entry="Pauldebrot"
p_seed=0.0001/0 p_seed2=0.00000000001/0 p_wfactor=0.6
p_bailout=1000000.0 p_settype=Mandelbrot p_switchsettype=Julia
p_julia=0.3/0.6 f_func_post=ident p_zfunction="Burning Ship"
p_inverted=no
inside:
transfer=none
outside:
transfer=linear filename="em.ucl" entry="Pauldebrots_Smooth"
p_convergent=no p_esm=no p_alt=no p_perfix=1.0 p_zmax=100 p_power=2
p_fit=yes p_fittimes=1.0 p_fitminit=1 p_fitmaxit=500 p_transfer=Log
p_transpower=3.0 p_bailout=1000000.0
gradient:
comments="my original creation." smooth=yes index=30 color=24800
index=130 color=9164785 index=262 color=10176512 index=363
color=5998
opacity:
smooth=no index=0 opacity=255
}
(http://www.ljplus.ru/img4/a/s/asdam/Navalis_Ignis_Pauldebroti.jpg)
It have interesting quadratic symmetric julia set, maybe with parameter tweaking one can get julia set of perfect circular figures.
Lepus_Navalis_Pauldebroti {
fractal:
title="Lepus_Navalis_Pauldebroti" width=640 height=480 layers=1
credits="Edgar;1/28/2013"
layer:
caption="Background" opacity=100 transparent=yes
mapping:
center=0.0125/0.0125 magn=1.2903226
formula:
maxiter=10000 percheck=off filename="em.ufm" entry="Pauldebrot"
p_seed=0.396874957/-0.6943749845 p_seed2=0.00000000001/0
p_wfactor=0.6 p_bailout=1000000.0 p_settype=Julia
p_switchsettype=Mandelbrot p_julia=0.4025/-0.71 f_func_post=ident
p_zfunction="Burning Ship" p_inverted=no
inside:
transfer=linear filename="em.ucl" entry="WaveTrichrome"
p_palette="Fractal Explorer like" p_seed=-0.3913 p_orbits=None
p_switchRB=yes p_colmethod="With counter" p_naturalise=yes
p_postfn="11- SineCosineMix" p_lightR=0.7 p_scalarR=0.7 p_lightG=1.2
p_scalarG=1.2 p_lightB=0.25 p_scalarB=0.25
outside:
transfer=linear filename="em.ucl" entry="Pauldebrots_Smooth"
p_convergent=no p_esm=no p_alt=no p_perfix=1.0 p_zmax=100 p_power=2
p_fit=yes p_fittimes=1 p_fitminit=3 p_fitmaxit=7642
p_transfer=Sigmoid p_transpower=3.0 p_bailout=1000000.0
gradient:
smooth=yes rotation=68 index=52 color=2039583 index=126
color=16121855 index=263 color=3289650 index=389 color=33023
opacity:
smooth=yes index=50 opacity=255 index=100 opacity=255 index=200
opacity=255 index=302 opacity=255 index=376 opacity=255
}
(http://www.ljplus.ru/img4/a/s/asdam/Lepus_Navalis_Pauldebroti.jpg)
Zoom in somewhere in middle of m-set. In smooth colouring, when min and max iter parameters are what statistics say, sigmoid transfer function gives the most accurate results (but only then).
Folia_arborum_Pauldebroti {
fractal:
title="Folia_arborum_Pauldebroti" width=640 height=480 layers=1
credits="Edgar;1/27/2013;Edgar;1/24/2013"
layer:
caption="Background" opacity=100 transparent=yes
mapping:
center=-0.99866059029278/-0.012796875 magn=10164.706
formula:
maxiter=500 percheck=off filename="em.ufm" entry="Pauldebrot"
p_seed=0.0001/0 p_seed2=0.00000000001/0 p_wfactor=0.6
p_bailout=100000000.0 p_settype=Mandelbrot p_switchsettype=Julia
p_julia=0.3/0.6 f_func_post=ident p_zfunction="Burning Ship"
p_inverted=no
inside:
transfer=linear filename="em.ucl" entry="WaveTrichrome"
p_palette="Fractal Explorer like" p_seed=5 p_orbits=None
p_switchRB=no p_colmethod="With counter" p_naturalise=no
p_postfn="7- Haversine" p_lightR=0.7 p_scalarR=0.7 p_lightG=1.2
p_scalarG=1.2 p_lightB=0.25 p_scalarB=0.25
outside:
transfer=linear filename="em.ucl" entry="Pauldebrots_Smooth"
p_convergent=no p_esm=no p_alt=no p_perfix=1.0 p_zmax=100 p_power=2
p_fit=yes p_fittimes=1.0 p_fitminit=15 p_fitmaxit=206
p_transfer=Sigmoid p_transpower=3.0 p_bailout=100000000.0
gradient:
comments="my original creation." smooth=yes index=30 color=21727
index=130 color=9163505 index=262 color=28416 index=363 color=4975
opacity:
smooth=no index=0 opacity=255
}
(http://www.ljplus.ru/img4/a/s/asdam/Folia_arborum_Pauldebroti.jpg)
Looks like a variant of the Burning Ship to me.