/usr/share/xscreensaver/config/epicycle.xml is in xscreensaver-data-extra 5.15-2ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | <?xml version="1.0" encoding="ISO-8859-1"?>
<screensaver name="epicycle" _label="Epicycle">
<command arg="-root"/>
<number id="delay" type="slider" arg="-delay %"
_label="Frame rate" _low-label="Low" _high-label="High"
low="0" high="100000" default="20000"
convert="invert"/>
<number id="ncolors" type="slider" arg="-colors %"
_label="Number of colors" _low-label="Two" _high-label="Many"
low="1" high="255" default="100"/>
<number id="holdtime" type="slider" arg="-holdtime %"
_label="Linger" _low-label="1 second" _high-label="30 seconds"
low="1" high="30" default="2"/>
<hgroup>
<number id="linewidth" type="spinbutton" arg="-linewidth %"
_label="Line thickness" low="1" high="50" default="4"/>
<number id="harmonics" type="spinbutton" arg="-harmonics %"
_label="Harmonics" low="1" high="20" default="8"/>
</hgroup>
<!-- #### -color0 [red] -->
<!-- #### -colours [100] -->
<!-- #### -foreground [white] -->
<!-- #### -min_circles [2] -->
<!-- #### -max_circles [10] -->
<!-- #### -min_speed [0.003] -->
<!-- #### -max_speed [0.005] -->
<!-- #### -timestep [1.0] -->
<!-- #### -divisor_poisson [0.4] -->
<!-- #### -size_factor_min [1.05] -->
<!-- #### -size_factor_max [2.05] -->
<boolean id="showfps" _label="Show frame rate" arg-set="-fps"/>
<_description>
This draws the path traced out by a point on the edge of a
circle. That circle rotates around a point on the rim of another
circle, and so on, several times. These were the basis for the
pre-heliocentric model of planetary motion.
http://en.wikipedia.org/wiki/Deferent_and_epicycle
Written by James Youngman; 1998.
</_description>
</screensaver>
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