This is my implementation of a white board string-plotter.
The mechanical parts are designed to use inexpensive 28BYJ-48 5V stepper motors (search for them on Amazon - they sell for ~$6, including driver). More details under 'Instructions'.
UPDATE: I added links to the sources of some of the software I wrote for this project under 'Instructions'.

All parts are modules inside the provided .scad file - the code is not exactly pretty, but should be usable.
The pen guide on the carriage in the original design was to short, so I printed an extension (just cylindrical pipes, really) and super-glued them to the existing carriage (they don't have to take any real mechanical load). The guide is sized to hold an 'Expo' brand dry erase marker.
There is a small 9g servo on the bottom of the carriage that allows the pen to be retracted, so that the plotter can move without drawing a line.
After experimenting with various types of fishing line I settled on using dental floss as string and two pieces of knitting yarn to hold the carriage such that it can easily roatate.
For electronics I am using a Teensy 3.0 microcontroller board (ARM-based, but mostly Arduino compatible - a regular Arduino would work just fine, too) and a HC-05 (check Amazon) bluetooth module as a serial pipe (yes, the plotter is wireless).
On the software side, I have implemnted two solutions:

1. A Perl script that takes cartesian moves as inputs and generates spool-rotation steps as output that get sent to the plotter directly via bluetooth
2. An Android app that allows you to doodle on the touch screen of your phone and then send the results to the plotter directly (again via bluetooth)
   I also created auxiliary scripts to render photographs (any jpg, really) as line drawings by turning them into grayscale images and generating a square-wave path whose frequency is modulated by the 'darkness' of the image area (see the two images attached).
   The device is rather slow, its speed is limited by how fast the stepper motors can turn without missing steps. Realistically, plotting the more complex photo in this post (w/ two faces) took about 1.5 hours.
   EDIT: For completeness' sake, here is the script that controls the plotter:
   https://www.dropbox.com/s/ug2ghe095nh04gd/wb_plotter.pl
   And this is the script used to generate the photo plots:
   https://www.dropbox.com/s/6fvj2abrmj4mfep/pixelverter.pl
   This is the Arduino (Teensy) sketch that controls the electronics:
   https://www.dropbox.com/s/4qqyd2zk95t5r01/EtchASketch.ino