Fractalised lines

[CJRM]

I would like to be able to select a (vector) line or shape and apply a 'fractalise' effect to it that would make the each line segment appear jagged between its two end points. This should be adjustable to increase or decrease the jaggedness of the line, which would also affect how far the jaggies deviated from the original path. This would allow the easy creation of, say, lightning, or the line of a river, without having to manually draw the whole thing.

The attached screen capture shows an example from a program I used to use that does this. The base shape is just a square with four vertices at the indicated points. 'Fractalising' the square turned it into the shape shown in the image. If the fractalisation setting were turned down the shape would become less and less exaggerated. With the fractalisation turned to zero it would display as a simple square.