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/usr/share/xscreensaver/config/kaleidescope.xml is in xscreensaver-data-extra 5.15-2ubuntu1.

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The actual contents of the file can be viewed below.

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<?xml version="1.0" encoding="ISO-8859-1"?>

<screensaver name="kaleidescope" _label="Kaleidescope">

  <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="nsegments" type="slider" arg="-nsegments %"
          _label="Segments" _low-label="Few" _high-label="Many"
          low="1" high="100" default="7"/>

  <number id="symmetry" type="slider" arg="-symmetry %"
          _label="Symmetry" _low-label="3" _high-label="32"
          low="3" high="32" default="11"/>

  <number id="ntrails" type="slider" arg="-ntrails %"
          _label="Trails" _low-label="Few" _high-label="Many"
          low="1" high="1000" default="100"/>

  <!-- #### -local_rotation [-59] -->
  <!-- #### -global_rotation [1] -->
  <!-- #### -spring_constant [5] -->

  <boolean id="showfps" _label="Show frame rate" arg-set="-fps"/>

  <_description>
A simple kaleidoscope.  See also "GLeidescope".

http://en.wikipedia.org/wiki/Kaleidoscope

Written by Ron Tapia; 1997.
  </_description>
</screensaver>