Dan said (apparently, though not to math-fun?)
BUT there is a lot of choice in how 6 copies of each rosette are placed around itself, so this method can give a plethora of different curves in the limit. (Probably continuum many, given a countable number of discrete choices.)
As it stands, I don't think this is quite correct. Modulo Euclidean isometry, there appear to be only the two generation rules illustrated by Bill at <http://gosper.org/flopnoflop.png> . Notice that both series of curves are rotated making curve start and finish on a horizontal line; but the (nascent) island coastlines are mirror images and at distinct angles. Therefore they can't be combined in the course of a single generation: if the smaller coastlines fit together, their curve endpoints do not meet. I think it may be possible to vary the rule as a function of generation n, yielding 2^(n-1) visually distinct curves; however I have yet to concoct an actual algorithm. By the way, notice also that although the limit coastline has 6-fold rotational symmetry, the discrete approximants (ignoring curve endpoints) have only 3-fold. This is easy to see from the filled plot I attempted to post earlier, which has apparently been ambushed at the pass ... Fred Lunnon