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Description

Updated to 1960x1470 resolution when downloaded

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 here.

More info about Cubics can be found at my
Cubic Tutorial
and the "cubic" articles in my
Chaotic series of fractal articles.
Below the parameter file. Play and have fun

ChantingDragon {
fractal:
title="Chanting Dragon" width=800 height=600 layers=2
credits="Ingvar Kullberg;7/1/2017"
layer:
caption="M-" opacity=38 mergemode=multiply method=multipass
mapping:
center=-0.250136917319121598/0.378761032844732315
magn=74.7496368432685675
formula:
maxiter=25000 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:
caption="M+" opacity=100 method=multipass
mapping:
center=-0.250136917319121598/0.378761032844732315
magn=74.7496368432685675
formula:
maxiter=25000 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
}

Description

Updated to 1960x1470 resolution when downloaded

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 here.

More info about Cubics can be found at my
Cubic Tutorial
and the "cubic" articles in my
Chaotic series of fractal articles.
Below the parameter file. Play and have fun

ChantingDragon {
fractal:
title="Chanting Dragon" width=800 height=600 layers=2
credits="Ingvar Kullberg;7/1/2017"
layer:
caption="M-" opacity=38 mergemode=multiply method=multipass
mapping:
center=-0.250136917319121598/0.378761032844732315
magn=74.7496368432685675
formula:
maxiter=25000 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:
caption="M+" opacity=100 method=multipass
mapping:
center=-0.250136917319121598/0.378761032844732315
magn=74.7496368432685675
formula:
maxiter=25000 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
}