Magnification in a 2D-slice of the four dimensional cubic parameter space using the standard parameterizing z -> z^3 - 3a^2 z + b, critical points z = +a (making the set M+) and z = -a (making the set M-).

*a_real = 0.4
*a_imag = #pixel (horizontal))
*b_real = 0.4
*b_imag = #pixel (vertical)

Both M+ and M- plotted in separate layers.

No filters or post processing except resizing (from 6400 x 4800). Especially note that NO tranformations formulas is used in order to obtain the tied structures. They are quite natural in this 2D-slice of cubic parameter space!

Ultra Fractal, formula Cubic 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]

More info about Cubics can be foud at my Cubic Tutorial [link] and the "cubic" articles in my Chaotic series [link]

Below the parameter file. Play and have fun

ChantingDragon {
fractal:
title="Chanting Dragon" width=640 height=480 layers=2
credits="Ingvar Kullberg;2/24/2007"
layer:
method=multipass caption="M-" opacity=38 mergemode=multiply
mapping:
center=-0.250136917319121598/0.378761032844732315
magn=74.7496368432685675
formula:
maxiter=10000 filename="sp3.ufm" entry="CubicParameterspace3"
p_PlottedPlane="5.(a-imag,b-imag)" p_M=M- p_SetBorders=no p_hide=yes
p_areal=0.4 p_aimag=0.0 p_breal=0.4 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:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes index=9 color=327680 index=40 color=15794175 index=52
color=655360 index=107 color=16769274 index=187 color=2445567
opacity:
smooth=no index=0 opacity=255
layer:
method=multipass caption="M+" opacity=100
mapping:
center=-0.250136917319121598/0.378761032844732315
magn=74.7496368432685675
formula:
maxiter=10000 filename="sp3.ufm" entry="CubicParameterspace3"
p_PlottedPlane="5.(a-imag,b-imag)" p_M=M+ p_SetBorders=no p_hide=yes
p_areal=-0.4 p_aimag=0.0 p_breal=-0.4 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:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes index=9 color=327680 index=40 color=15794175 index=52
color=655360 index=107 color=16769274 index=187 color=2445567
opacity:
smooth=no index=0 opacity=255
}