This motive is another color setup figure 3 page 2 in the article 31) More about Quartics [link] in my Chaotic series [link] . It is a part of a 2d-slice of the six dimensional quartic parameter space in the form z -> z^4 + 2[ab - (a + b)^2]z^2 +4ab(a + b)z + c, the critical points being z = a, z = b, and z = -(a + b) forming the sets M1, M2 and M3 respectively.

*a_real = 0.3
*a_imag = 0
*b_real = 0.3
*b_imag = 0
*c_real = #pixel (horizontal)
*c_imag = #pixel (vertical)

The set M1, totally identical with M2, is drawn in one layer and M3 is drawn in the other layer. It’s the set M1 = M2 that forms the contour ot the cubic Mandelbrot set

Ultra Fractal, formula Quartic Parameterspace3 in the sp3-module written by my dear friend Stig Pettersson, Greenseng here at DeviantART. All his modules, as well as mine can be downloaded from [link]

No filters or postprocessing

Below the UF parameter file, play and have fun

CubeQuadraticConfussion2a {
fractal:
title="CubeQuadraticConfussion2a" width=640 height=480 layers=2
credits="Ingvar Kullberg;6/11/2008"
layer:
method=multipass caption="M3" opacity=100 mergemode=difference
mapping:
center=-0.5380029296875/0.293173828125 magn=25.3465346534653465
formula:
maxiter=5000 filename="sp3.ufm" entry="QuarticParameterspace3"
p_PlottedPlane="15.(c-real,c-imag)" p_M=M3 p_SetBorders=no
p_hide=yes p_areal=0.3 p_aimag=0.0 p_breal=0.3 p_bimag=0.0
p_creal=0.0 p_cimag=0.0 p_xrot=0.0 p_yrot=0.0 p_xrott=0.0
p_yrott=0.0 p_xrotu=0.0 p_yrotu=0.0 p_xrotv=0.0 p_yrotv=0.0
p_zrot=0.0 p_LocalRot=no p_diff=no p_bailout=100.0 p_dbailout=1E-6
inside:
transfer=none
outside:
density=2 transfer=linear
gradient:
smooth=yes index=2 color=8716288 index=84 color=16777205 index=128
color=46544 index=180 color=21760 index=235 color=53306 index=259
color=57413 index=323 color=170
opacity:
smooth=no index=0 opacity=255
layer:
method=multipass caption="M1=M2" opacity=100
mapping:
center=-0.5380029296875/0.293173828125 magn=25.3465346534653465
formula:
maxiter=5000 filename="sp3.ufm" entry="QuarticParameterspace3"
p_PlottedPlane="15.(c-real,c-imag)" p_M=M1 p_SetBorders=no
p_hide=yes p_areal=0.3 p_aimag=0.0 p_breal=0.3 p_bimag=0.0
p_creal=0.0 p_cimag=0.0 p_xrot=0.0 p_yrot=0.0 p_xrott=0.0
p_yrott=0.0 p_xrotu=0.0 p_yrotu=0.0 p_xrotv=0.0 p_yrotv=0.0
p_zrot=0.0 p_LocalRot=no p_diff=no p_bailout=100.0 p_dbailout=1E-6
inside:
transfer=none
outside:
density=2 transfer=linear
gradient:
smooth=no index=8 color=5899552 index=49 color=3185381 index=207
color=16777215 index=300 color=1716464
opacity:
smooth=no index=0 opacity=255
}