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Description
Download for 1280x960 resolution

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 = #pixel (vertical)
*a_imag = 0.01
*b_real = 0
*b_imag = #pixel (horizontal)

The motive is drawn using the technique of “CCL+Setborders”. This displays the contours of both M+ and M-, the black part being a part of Cubic Connectedness Locus (CCL), the set which is common to M+ and M-, the full analogue to the Mandelbrot set for quadratic polynomials. More about this can be read on point 9 page 4 in my article 19b [link] in my Chaotic series [link] .

The motive is rotated 90 degrees to the left (under the Location tab) before zooming. For that reason the axis a_real is the vertical axis, dividing the motive in two symmetric halves.

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

TheDarkSecretOfTheCave {
fractal:
title="The Dark Secret of the Cave" width=640 height=480 layers=1
credits="Ingvar Kullberg;3/24/2009"
layer:
caption="CCL+SetBorders" opacity=100 method=multipass
mapping:
center=0.8151900944615/0 magn=184.29051 angle=270
formula:
maxiter=5000 filename="sp3.ufm" entry="CubicParameterspace3"
p_PlottedPlane="3.(a-real,b-imag)" p_M=CCL p_SetBorders=yes
p_hide=yes p_areal=0.0 p_aimag=0.01 p_breal=0.0 p_bimag=0 p_xrot=0
p_yrot=0 p_xrott=0 p_yrott=0 p_zrot=0 p_LocalRot=no p_diff=no
p_bailout=100 p_dbailout=1E-6
inside:
transfer=none
outside:
density=2 transfer=linear
gradient:
smooth=yes index=2 color=17749 index=42 color=62720 index=74
color=2235420 index=115 color=65530 index=153 color=329215 index=211
color=15335546 index=308 color=22816
opacity:
smooth=no index=0 opacity=255
}

Description
Download for 1280x960 resolution

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 = #pixel (vertical)
*a_imag = 0.01
*b_real = 0
*b_imag = #pixel (horizontal)

The motive is drawn using the technique of “CCL+Setborders”. This displays the contours of both M+ and M-, the black part being a part of Cubic Connectedness Locus (CCL), the set which is common to M+ and M-, the full analogue to the Mandelbrot set for quadratic polynomials. More about this can be read on point 9 page 4 in my article 19b [link] in my Chaotic series [link] .

The motive is rotated 90 degrees to the left (under the Location tab) before zooming. For that reason the axis a_real is the vertical axis, dividing the motive in two symmetric halves.

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

TheDarkSecretOfTheCave {
fractal:
title="The Dark Secret of the Cave" width=640 height=480 layers=1
credits="Ingvar Kullberg;3/24/2009"
layer:
caption="CCL+SetBorders" opacity=100 method=multipass
mapping:
center=0.8151900944615/0 magn=184.29051 angle=270
formula:
maxiter=5000 filename="sp3.ufm" entry="CubicParameterspace3"
p_PlottedPlane="3.(a-real,b-imag)" p_M=CCL p_SetBorders=yes
p_hide=yes p_areal=0.0 p_aimag=0.01 p_breal=0.0 p_bimag=0 p_xrot=0
p_yrot=0 p_xrott=0 p_yrott=0 p_zrot=0 p_LocalRot=no p_diff=no
p_bailout=100 p_dbailout=1E-6
inside:
transfer=none
outside:
density=2 transfer=linear
gradient:
smooth=yes index=2 color=17749 index=42 color=62720 index=74
color=2235420 index=115 color=65530 index=153 color=329215 index=211
color=15335546 index=308 color=22816
opacity:
smooth=no index=0 opacity=255
}