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The Splitter plug-in can be used to split a picture according to a mathematical formula into two layers, translate and/or rotate the layers and optionally merge them back into one picture. Latest version is 0.3 and you can download it here (20k).
Building the plug-in is straightforward. First unpack the gzipped
tarfile:
After installation the plug-in can be found as "Filters/Generic/Splitter" by clicking with the right mouse button in a picture. After doing so the next dialog will appear: 
The first field is the entry labeled 'f(x,y)'. Here you can fill in any valid mathematical expression in x and y. The standard operators (+, -, *, /, ^, %) can be used as well as a lot of the standard C math functions (abs, ceil, cos, exp, floor, log, log10, min, max, mod, pow, rand, rint, sin, sqrt, tan, acos, asin, atan, atan2, sinh, cosh, tanh, ldexp). Four special symbols are provided:
The formula f(x, y) is evaluated for each point in your picture. If the resulting value is less than zero the point is asigned to the first layer, otherwise to the second layer. The other fields are more obvious: 'Translate x:' and 'Translate y:' perform a translation on the layer. 'Rotate:' does a rotation around the center of the layer. The checkbutton 'Merge visible layers' determines whether the seperate layers should be merged after splitting the picture.
First example: 
On the left side the original picture. The right picture was created with:
f(x, y): h/2 - h/8 * cos(x * 8 * pi / w) - y Second example:
On the left side the original picture. The right picture was created with:
f(x, y): (x - rint(x/15)*15)^2 + (y-rint(y/15)*15)^2 - 25
Next I selected the second layer (in the Layers & Channels dialog) and put a black background behind it.
There are a few things still left on my todo list. In no particular order:
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