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Although converting to a vector (using r.line or r.poly) and using v.area will
allow me to interactively find the perimeter, as suggested by Darrell McCauley,
it is necessary to go beyond this.  What I eventually wish to do is to be able
to calculate the areas (this is possible) and the perimeters (???) for each of
the contiguous areas generated by r.clump and then produce a map layer of the
ratio between area and perimeter.  This would act as a complexity index of each
of the areas.

I will, however, play around with r.grow as suggested by Scott Tweddale.

Many thanks.