There are IFSs with c6-symmetry, in which the elements are laid out in the form of a modified hexagon. The overall attractor approaches a hexagon as the number of elements approaches infinity.
There are several means of constructing the lower order starflakes (e.g. by adding or removing elements from flowsnakes). However the construction which works for all orders is to take a rectangular section, of 3n+1 × 2n+1 units, and therefore consisting of alternating rows of 3n+1 and 3n elements, of a hexagonal grid, and to add additional rows above and below this rectangle, each row being 3 elements shorter than the preceding.
For each n there are cis- and trans- variants. The nth order starflake has 9n2 + 3n + 1elements, each of which is rotated by arctan(sin(60)/(0.5+3n))
Source: Independently discovered. No other source known.