FourthInsideSecond

Magnification in a 2D-slice of the eight dimensional pentic parameter space using the standard form of setup z -> z^5 + 5/3[ab + ac + bc - (a + b + c)^2]z^3 - 5/2[abc - (ab + ac +bc)(a + b + c)]z^2 - 5abc(a + b + c)z + d, critical points z = a making the set M1, z = b making the set M2, z = c making the set M3, and z = -(a + b + c) making the set M4.

*a_real = 0.2
*a_imag = 0
*b_real = 0.2
*b_imag = 0
*c_real = 0.2
*c_imag = 0
*d_real = #pixel (horizontal)
*d_imag = #pixel (vertical)

M1 plotted in one layer and M4 in the other layer. Further more M1, M2, and M3, coalesces giving rice to the phenomena with quartic Mandelbrot structures. In this part of the slice this quartic Mandelbrot stuctures are inside the structures of the Quadratic Mandelbrot structures, the same phenomena as is figure 4 page 4 in article 32 in my chaotic series [link] .

For those of you who don’t know how the prototype Quartic Mandelbrot set looks like, see my scrap [link] .

No filters or post processing except resizing (from 6400 x 4800).

Ultra Fractal, formula Pentic 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]

Below the parameter file, play and have fun

FourthInsideSecond {
fractal:
title="FourthInsideSecond" width=640 height=480 layers=2
credits="Ingvar Kullberg;6/4/2007"
layer:
method=multipass caption="M4" opacity=100 mergemode=difference
mapping:
center=-0.82166666652/0.35083333333 magn=40.909091
formula:
maxiter=10000 filename="sp3.ufm" entry="PenticParameterspace3"
p_PlottedPlane="28.(d-real,d-imag)" p_M=M4 p_SetBorders=no
p_hide=yes p_areal=0.2 p_aimag=0.0 p_breal=0.2 p_bimag=0.0
p_creal=0.2 p_cimag=0.0 p_dreal=0.0 p_dimag=0.0 p_xrot=0.0
p_yrot=0.0 p_xrott=0.0 p_yrott=0.0 p_xrotu=0.0 p_yrotu=0.0
p_xrotv=0.0 p_yrotv=0.0 p_xrotr=0.0 p_yrotr=0.0 p_xrots=0.0
p_yrots=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:
method=multipass caption="M1=M2=M3" opacity=100
mapping:
center=-0.82166666652/0.35083333333 magn=40.909091
formula:
maxiter=10000 filename="sp3.ufm" entry="PenticParameterspace3"
p_PlottedPlane="28.(d-real,d-imag)" p_M=M1 p_SetBorders=no
p_hide=yes p_areal=0.2 p_aimag=0.0 p_breal=0.2 p_bimag=0.0
p_creal=0.2 p_cimag=0.0 p_dreal=0.0 p_dimag=0.0 p_xrot=0.0
p_yrot=0.0 p_xrott=0.0 p_yrott=0.0 p_xrotu=0.0 p_yrotu=0.0
p_xrotv=0.0 p_yrotv=0.0 p_xrotr=0.0 p_yrotr=0.0 p_xrots=0.0
p_yrots=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
}