Ultra Fractal, formula Pentic Parameterspace3, can be downloaded from [link] .

This motive from the eight dimensional pentic parameter space is the same as my scrap [link] . However here “SetBorders” is enabled. This means that the contours of the other sets are visible. And in this 2D slice all of the sets are distinct, that is no set coalesces entirely with another set. Thus if we go from the left to the right we first past a Mandelbrot like border, it’s the border of the set M3, the next border is the border of the set M2, the next border is the border of the set M4. Finally the next border is the border of the set M1. When we past the last border we are inside all the four subsets, that is we are inside Pentic Connectedness Locus. More about the use of SetBorders can be red in article 19b in the chaotic series [link] .

Now the diligent reader who are lucky to have UF and, running the parameter file, may perform the following experiment. Select Switch Mode, move the cursor from left to right, and observe what happens with the Julia fractal in the little window down to the right when you pass the borders. Of cause you can also move the cursor in the opposite direction.

Below the parameter file, play and have fun

PCL+SetBorders {
fractal:
title="PCL+SetBorders" width=640 height=480 layers=1
credits="Ingvar Kullberg;6/19/2007"
layer:
method=multipass caption="PCL+SetBorders" opacity=100
mapping:
center=-1.1518741678/0.745547584065 magn=2.2447926
formula:
maxiter=1000 filename="SP3.ufm" entry="PenticParameterspace3"
p_PlottedPlane="2.(a-real,b-real)" p_MCL p_SetBorders=yes
p_hide=yes p_areal=0.0 p_aimag=0.2 p_breal=0.0 p_bimag=0.2
p_creal=0.2 p_cimag=0.2 p_dreal=0.2 p_dimag=0.2 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:
density=4 transfer=linear
gradient:
smooth=yes index=0 color=8716288 index=100 color=16121855 index=200
color=46591 index=300 color=156
opacity:
smooth=no index=0 opacity=255
}