This is a simple GIMP script, written in python, which creates spirograph type curves. To try this out, all you need to do is download the script, and store it in the gimp plugins folder, in your home directory. Remember to set the executable flag on the file.
The script can be downloaded from HERE.
An example shows how to use it. First, open an image with gimp.
Now, run the plugin, which is found under /Filters/Artistic/Farris Curves...
By entering different numbers, you can create a vast range of different curves. Be warned that not all of them are pretty! Make your selection, and click OK.
Several different examples can be seen by selecting Show Examples
The curve is placed on a new layer, and the layer name contains the numbers used to create it.
The script respects the current brush and colours, which can lead to some pretty results.
If you would like to leave feedback, you can do so HERE.