Download for 1280x960 resolution

This motive one comes from an alternative setup of cubic parameter space parameterized as z -> z^3 + az^2 + b, critical points z = 0 and z = -2a/3. This setup is made by myself, the history behind it is narrated on [link] . The a-plane is plotted, the b-plane fixed to zero. That is,

*a_real = #pixel (vertical)
*a_imag = #pixel (horizontal)
*b_real = 0
*b_imag = 0

If z = 0 had been used we would have a completely black “infinity-plane” (the orbit being 0 -> 0 -> 0 ->0 -> 0), so we draw the other subset using the other critical point z = -2a/3 the set turning out to have the shape of CCAP, see my deviation PrototypeCCAP as well as the linked journal When z = a is a superattractive fixpoint [link] . It’s very fascinating to see how the same shape occurs in different parameterizations of cubics as well as in yet higher parameter spaces (it’s also being found in pentics, see [link] ) That’s one of the things that makes exploring fractal formulas so interesting

Unlike most of my images, this image is not drawn in a purist way, as both inside and outside filters are used

Other non purist top magnifications of CCAP shapes are,


[link]
[link]


Below the UF parameter file. Play and have fun

Pedesta4 {
fractal:
title="Pedesta4" width=640 height=480 layers=1
credits="Ingvar Kullberg;6/26/2009"
layer:
caption="Background" opacity=100 method=multipass
mapping:
center=0/2.115 magn=2.5
formula:
maxiter=10000 filename="ik3.ufm" entry="KullbergCubic3"
p_PlottedPlane="1.(a-real,a-imag)" p_M=M- p_SetBorders=no p_hide=yes
p_areal=0.0 p_aimag=0.0 p_breal=0.0 p_bimag=0.0 p_xrot=0.0
p_yrot=0.0 p_xrott=0.0 p_yrott=0.0 p_zrot=0.0 p_LocalRot=no
p_diff=no p_bailout=100.0 p_dbailout=1E-6
inside:
density=2 transfer=linear filename="sp.ucl" entry="Inside"
p_absz=1.0 p_realz=0.0 p_imagz=0.0
outside:
density=2 transfer=linear filename="sp.ucl" entry="Bubbles"
f_func1=ident f_func2=ident p_itrap=0.0/1.0 p_solid=yes
p_colindex=0.0 p_radie=1.0 p_col=1.0 p_numiter=0.0 p_loo=1.0
gradient:
smooth=yes index=9 color=327680 index=40 color=15794175 index=91
color=0 index=161 color=16441594 index=202 color=2445567
opacity:
smooth=no index=0 opacity=255
}