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A three dimensional slice of the six dimensional quartic parameter space parameterized as 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 = horizontal axis
*a_imag = vertical axis
*b_imag = depth axis
*b_real = 0.4
*c_real = 0
*c_imag = 0.2

That is we have performed the slice after having glided 0.4 units along the axis b_real and 0.2 units along the axis c_imag pointing into two of the three dimensions perpendicular to our space, at the same time as they are perpendicular to each other The motive have been rotated 10 degrees around the horizontal, vertical, as well as around the third axis coming out from the screen in order to get a better perspective.

The union set is drawn, the red part = M1, the green part = M2, and the blue part = M3 The black parts represents cut off at screen touch and shown up as more or less distorted versions of the ordinary Mandelbrot set [link] .

Ultra Fractal, one layer, Raytrace2 formula written by here on DA.

Below the parameter file. Play and have fun

EasternFeathers3 {
fractal:
title="Eastern Feathers3" width=640 height=480 layers=1
credits="Ingvar Kullberg;4/11/2009"
layer:
caption="Background" opacity=100 method=linear
mapping:
center=-0.161484254/0.09881462 magn=1
formula:
maxiter=100 percheck=off filename="spr.ufm" entry="Raytrace2"
p_maxiter=100 p_bailout=4.0 p_precision=10
p_Formula="Quartic Parameterspace" p_Fourth__Dimension=b_imag
p_Plotted_Space="a_real; a_imag; b_imag" p_Fourth_Dimension=Zk
p_Fourth_Dim=C_imag p_Fourth__Dim=Ck p_view=no p_MSet=Union
p_QMSet=Union p_init_zri=0/0 p_init__zri=0.5/0.0 p_init_zjk=0.0/0.0
p_init__zjk=0.0/0.0 p_cri1=-0.7/0.0 p_cjk1=0.0/0.0 p_cri2=-0.7/0.0
p_cjk2=0.0/0.0 p_cri3=-0.7/0.0 p_cjk3=0.0/0.0 p_bri=0.0/0.0
p_bjk=0.0/0.0 p_xrot=10 p_yrot=10 p_zrot=10 p_localrot=no
p_lightx=4.0 p_lighty=4.0 p_lightz=4.0 p_a_real=0.4 p_a_imag=0.0
p_b_real=0.4 p_b_imag=0.7 p_c_real=0.0 p_c_imag=0.2 p_fourthdim=0.0
p_zcenter=0 p_zlength=4 p_zpixels=640 p_touchscreen=yes
p_Coloring=Raytrace2.ucl p_Background=Floating
p_Gradient="One Gradient" p_Cubic_Gradient="One Gradient"
p_Quartic_Gradient="Four Gradients"
inside:
transfer=none
outside:
transfer=linear filename="spr.ucl" entry="Raytrace2"
gradient:
smooth=no index=0 color=0 index=100 color=10855845 index=100 color=0
index=185 color=655596 index=199 color=16117728 index=200 color=0
index=288 color=62976 index=300 color=12713942 index=301
color=7667712 index=357 color=13631488 index=399 color=16777215
opacity:
smooth=no index=0 opacity=255
}