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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
*a_imag = 0.907
*b_real = #pixel (horizontal)
*b_imag = #pixel (vertical)

Both M+ and M- plotted, each one in separate layers. The lower Mandy belongs to M+ and the upper Mandy belongs to M-.

No filters or post processing.

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

CollisionsOfMandys {
fractal:
title="Collisions of Mandys" width=800 height=600 layers=2
credits="Ingvar Kullberg;6/15/2018"
layer:
caption="M-" opacity=100 mergemode=difference method=multipass
mapping:
center=0/0 magn=72
formula:
maxiter=10000 percheck=off filename="sp3.ufm"
entry="CubicParameterspace3" p_PlottedPlane="6.(b-real,b-imag)"
p_M=M- p_SetBorders=no p_hide=yes p_areal=0.0 p_aimag=0.907
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:
transfer=none
outside:
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
layer:
caption="M+" opacity=100 method=multipass
mapping:
center=0/0 magn=72
formula:
maxiter=10000 percheck=off filename="sp3.ufm"
entry="CubicParameterspace3" p_PlottedPlane="6.(b-real,b-imag)"
p_M=M+ p_SetBorders=no p_hide=yes p_areal=0.0 p_aimag=0.907
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:
transfer=none
outside:
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
}

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
*a_imag = 0.907
*b_real = #pixel (horizontal)
*b_imag = #pixel (vertical)

Both M+ and M- plotted, each one in separate layers. The lower Mandy belongs to M+ and the upper Mandy belongs to M-.

No filters or post processing.

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

CollisionsOfMandys {
fractal:
title="Collisions of Mandys" width=800 height=600 layers=2
credits="Ingvar Kullberg;6/15/2018"
layer:
caption="M-" opacity=100 mergemode=difference method=multipass
mapping:
center=0/0 magn=72
formula:
maxiter=10000 percheck=off filename="sp3.ufm"
entry="CubicParameterspace3" p_PlottedPlane="6.(b-real,b-imag)"
p_M=M- p_SetBorders=no p_hide=yes p_areal=0.0 p_aimag=0.907
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:
transfer=none
outside:
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
layer:
caption="M+" opacity=100 method=multipass
mapping:
center=0/0 magn=72
formula:
maxiter=10000 percheck=off filename="sp3.ufm"
entry="CubicParameterspace3" p_PlottedPlane="6.(b-real,b-imag)"
p_M=M+ p_SetBorders=no p_hide=yes p_areal=0.0 p_aimag=0.907
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:
transfer=none
outside:
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
}