To the Honor of Mandelbrot

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This fractal image a gave him as a small frame when he visited Lund (a university town in the south of Sweden) in the autumn 2002. No he is died, see my journal [link] The motive is 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 = 0.3
*a_imag = 0
*b_real = #pixel (horizontal)
*b_imag = #pixel (vertical)

M+ and M- are plotted in separate layers. The color map in both layers is one of the standard maps incuded in UF.

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 [link]

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

Below the parameter file. Play and have fun

ForMandelbrot {
fractal:
title="For Mandelbrot" width=480 height=640 layers=2
credits="Ingvar Kullberg;10/19/2010"
layer:
caption="M-" opacity=46 method=multipass
mapping:
center=-0.410894096536518734/0.641319444444444444 magn=88.6154
formula:
maxiter=10000 filename="sp3.ufm" entry="CubicParameterspace3"
p_PlottedPlane="6.(b-real,b-imag)" p_M=M- p_SetBorders=no p_hide=yes
p_areal=0.3 p_aimag=0.0 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=0 color=9043968 index=69 color=3158085 index=150
color=14736366 index=302 color=675176
opacity:
smooth=no index=0 opacity=255
layer:
caption="M+" opacity=100 method=multipass
mapping:
center=-0.410894096536518734/0.641319444444444444 magn=88.6154
formula:
maxiter=10000 filename="sp3.ufm" entry="CubicParameterspace3"
p_PlottedPlane="6.(b-real,b-imag)" p_M=M+ p_SetBorders=no p_hide=yes
p_areal=0.3 p_aimag=0.0 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=0 color=9043968 index=69 color=3158085 index=150
color=14736366 index=302 color=675176
opacity:
smooth=no index=0 opacity=255
}